Diverse Styles of Lithospheric Dripping: Synthesizing Gravitational Instability Models, Continental Tectonics, and Geologic Observations

Density instabilities in the lithosphere can founder gravitationally via viscous dripping and decoupling from overlying crust. The lithospheric dripping concept has been invoked across the globe, but the diversity of crustal effects, observable evidence, and tectonic settings involved in dripping remain underexplored. Here, we synthesize numerical and analogue modeling studies and geologic data from the literature, including all proposed lithospheric dripping events to‐date. We argue that two distinct styles of dripping can occur depending on crustal strength (relative to that of the mantle lithosphere). Near‐surface contraction and subsidence of strong crusts contrasts with near‐surface extension and uplift of weak crusts. We discuss these events in terms of tectonic setting, timing, size, and the main types of data associated with each event. We also find that lithospheric dripping is associated with a distinct suite of geological observations including sedimentological, structural, volcanic, and geophysical data, which can be used to distinguish strong crusts from weak crusts. We find 27 events for which lithospheric dripping is a key hypothesis, including 9 with clear evidence for strong‐crust dripping and 3 with clear evidence of weak‐crust dripping. We review emerging research methods have the potential to detect the signals of dripping in the geologic and geophysical record, and we suggest additional techniques in light of our strong‐crust versus weak‐crust framework. The diverse tectonic settings and inferred consequences of these lithospheric drips, if confirmed, would demand a shift in our understanding of continental geology to emphasize the role of vertical removal of continental lithosphere.

Dripping of viscous lithosphere can be analyzed in terms of the Rayleigh-Taylor (R-T) instability (e.g., Jull & Kelemen, 2001). The R-T instability occurs when perturbations to an interface between two layers induces a pressure gradient that drives further growth of those perturbations (Chandrasekhar, 1961), leading to predictable relationships between drip wavelength, growth rate, and the size of regions affected by dripping. Numerical and analogue modeling experiments thus provide a powerful method for understanding lithospheric dripping, especially when combined with geologic data. Numerical studies show that lithospheric drips have widely varying, but predictable, effects on upper-crustal strain, surface topography, and volcanism (e.g., Neil & Houseman, 1999;, but this result remains underutilized by the broader research community. Efficient removal of negatively buoyant and/or ultramafic lithosphere would profoundly influence the evolution of Earth's continents (e.g., DeCelles et al., 2009;Jull & Kelemen, 2001) and may help explain the felsic bulk composition of the crust as well as the sharp Moho often observed in seismic data (Jull & Kelemen, 2001). Dripping in continental arcs may explain magmatic flareups and the growth of Cordilleran orogens Lee & Anderson, 2015;Paterson & Ducea, 2015). Dripping has also been invoked to explain sedimentary basins in orogenic hinterlands in the Andes (DeCelles, , Tibet (Kapp & DeCelles, 2019), and the western U.S. (Smith et al., 2017). Continental flood basalts have also been related to dripping in a wide range of tectonic settings (Furman et al., 2016;Hales et al., 2005;Mori et al., 2009). More broadly, lithospheric dripping may have played a role in the formation of early Archean cratons (e.g., Gorczyk et al., 2013;Rapp & Watson, 1995;Wiemer et al., 2018) and even circular tectonic provinces on Venus known as coronae (Elkins-Tanton, 2007;Hoogenboom & Houseman, 2006;Piskorz et al., 2014). If confirmed, the dripping events reported to date ( Figure 1, Table 1) would demand a shift in our understanding of continental geology.
In this paper, we explore the concept of lithospheric dripping of Earth's continental lithosphere. We first review numerical analyses of lithospheric dripping, including its expected temporal scale (Section 2.1) and characteristic spatial scale (Section 2.2). We then synthesize models of lithospheric dripping to suggest that two distinct types of lithospheric dripping may occur and develop a framework in which relative crustal strength controls dripping style (Section 2.3). We then collect the evidence for each lithospheric dripping event, including size, depth, age, and supporting geologic observations, such as near-surface deformation, sedimentation, and volcanism, and we categorize these events according to our framework (Section 3). Finally, we discuss the implications of this synthesis for future studies, including methods with potential for identifying drips in the geologic and geophysical record (Section 4).

Stages of Drip Growth and Detachment
The R-T instability is usually described in terms of four temporal stages ( Figure 2, Stages 1-4 Sharp, 1984), followed by a 5th relaxation and recovery stage (Figure 2, Stage 5). The first stage involves small perturbations to the interface, with magnitudes on the order of 10% of their wavelength, or 0.1λ (Figure 2, Stage 1). The system during Stage 1 is amenable to linear stability analysis, which predicts that a single, least-stable wavelength will dominate and grow exponentially, giving the system a characteristic wavelength, λ c . The second stage occurs as perturbations grow larger (∼1λ) and linear analysis breaks down; the interface is characterized by "spikes" of heavy fluid that accelerate downward separated by "bubbles" of light fluid that rise at approximately constant velocity ( Figure 2, Stage 2 Sharp, 1984;He et al., 1999). In three dimensions, the spikes may be organized into curtains, or may be largely separated (Figure 4). The third stage is characterized by the development of secondary turbulent structures and interaction between bubbles (Figure 2, Stage 3 Sharp, 1984). The fourth and final stage of the R-T instability involves the breakup of the spikes and mixing between the two fluids ( Figure 2, Stage 4 Sharp, 1984).
In it simplest form, the R-T instability involves two layers of equal viscosity but different densities. The lithosphere presents more complex scenarios that require modifying this traditional analysis. Most notably, the growth rate of lithospheric drips is inversely proportional to viscosity (Neil & Houseman, 1999). Cold, stiff lithosphere can prevent the initiation of the instability, suggesting that dripping may only occur in tectonic settings with Stage 1 (Figure 2) is difficult to observe in the geologic record because the slow growth of small perturbations (Houseman & Molnar, 1997) may not impart significant stresses in the upper crust (Neil & Houseman, 1999). Exponential growth (Figure 2, Stage 2) and detachment (Figure 2, Stage 4) are easier to distinguish. If basin sedimentation is associated with the drip, the depositional ages of the earliest sediments can be used to estimate the beginning of exponential growth (e.g., DeCelles, Carrapa, et al., 2015;Saleeby & Foster, 2004;Smith et al., 2017). Xenoliths have been used to infer the presence of a dense root and can sometimes place constraints on its removal (Ducea & Saleeby, 1998). Records of surface uplift and tilting (e.g., Unruh, 1991) may be used to infer the timing of exponential growth and detachment (Molnar & Jones, 2004).  Total  11  15  19  8  4  7  8  7  12 Note. TMVB = Trans-Mexican Volcanic Belt. EAR = East African Rift. Italic values denote sums.

of 40
Although drip detachment can be well-defined mathematically (e.g., Molnar et al., 1998;Neil & Houseman, 1999), such definitions are difficult to use in practice because they are functions of quantities such as lithosphere viscosity and the size of the initial perturbation (Molnar et al., 1998;Neil & Houseman, 1999), which are poorly constrained (e.g., Molnar & Jones, 2004). In this paper, we consider drip detachment as the moment when the drip mechanically decouples from overlying lithosphere (H. Wang & Currie, 2017), corresponding to Stage 4 of the R-T instability (Figure 2; Sharp, 1984). This decoupling is often accompanied by a marked increase in the downward velocity of the drip in geodynamic models (Beall et al., 2017;H. Wang & Currie, 2017) and an inflection point in surface uplift or subsidence rates (DeCelles, Carrapa, et al., 2015;Molnar, 2015;H. Wang & Currie, 2017;. Drip detachment also coincides with major crustal heating associated with asthenospheric upwelling (Göğüş & Pysklywec, 2008), though the lag between drip detachment, which occurs over <1 Myr timescales, crustal heating, and volcanism may be difficult to predict. Thus, the primary observables of drip detachment are a change in surface uplift/subsidence rates, basin inversion or extensional collapse, and an increase in heat flow and volcanism. Numerical models commonly depict detachment after 5-25 Myr (H. Wang & Currie, 2017;. For a wider range of densities and viscosities, drip detachment could occur after as little as 10 5 years or as long as 10 8 years or more (Jull & Kelemen, 2001;Molnar et al., 1998).

Spatial Scale and the Characteristic Wavelength
Numerical analyses of the R-T instability of a lithospheric layer define relationships between lithosphere thickness h and characteristic wavelength λ c (Table S1 in Supporting Information S1). These analyses suggest that lithospheric dripping will often occur with wavelengths of 2-3h, or 100-500 km depending on viscosity, density structure, and lithospheric thickness (Conrad & Molnar, 1997;Turcotte & Schubert, 2002). The characteristic wavelength also depends on relative crustal thickness (see Figure 3 for illustration; Neil & Houseman, 1999). Very thin crusts (on the order of 10% of the total lithospheric thickness) favor larger wavelengths, but such crusts are more representative of oceanic lithosphere. Crusts comprising 1/2 to 1/3 of the lithosphere result in wavelengths of 2-2.5h (Table S1 in Supporting Information S1). Prescribing a stress-free boundary at the top of the mantle lithosphere, representing decoupling from overlying crust, can increase the wavelength to 12h or greater, depending on the viscosity decay length L and viscosity exponent n, but for realistic ranges of these values, λ c is approximately 2.5h (Harig et al., 2008, Table S1 in Supporting Information S1). Thus, we expect dripping to occur with a wavelength ∼2.5h except for regions with anomalously thin crusts or steep temperature gradients.
For a periodic instability, the wavelength λ is the average horizontal distance between neighboring drips, that is, the distance between maxima or minima in lithospheric thickness ( Figure 5). Periodic drips can occur if the density anomaly is elongated (Harig et al., 2008) or sometimes during tectonic compression or extension (Text S2 in Supporting Information S1). For a single instability, the wavelength corresponds to the width of thinned lithosphere, and therefore directly influences the size of the region experiencing volcanism, uplift/subsidence, or crustal deformation (Figure 6). For a drip that pulls down the topographic surface, lithospheric thinning around Figure 2. Cartoon depicting stages of Rayleigh-Taylor instability as applied to the mantle lithosphere (ML). Panels 1 through 4 correspond to the traditional stages 1 through 4 Sharp (1984), while panel 5 represents post-detachment relaxation and recovery. "Bubbles" and "spikes" are the traditional names for the ascending and descending fluid interfaces, respectively (Sharp, 1984); spikes correspond to lithosphere drips. Stage 3 depicts the development of Kelvin-Helmholtz (K-H) instabilities, which are not expected for dripping of lithosphere because of its high viscosity.
the flanks of the drip produces an annulus of surface uplift (Neil & Houseman, 1999) or a "peripheral bulge" (Kapp & DeCelles, 2019), apparent in numerical models of both periodic and single drips ( Figure 5). The width of this peripheral bulge corresponds to the instability wavelength (Figures 7 and 6). If sediment accumulates in the topographic depression, the width of sedimentary basin fill can serve as an estimate of the characteristic wavelength that is more likely to be preserved through geologic time ( Figure 6). Similarly, drip-induced topographic uplift or post-drip rebound can also approximate the characteristic wavelength. Thickened crustal welts associated with dripping may be distinguished by an increase in Moho depth within a region corresponding to the wavelength ( Figure 8). As a direct result of lithospheric thinning, crustal heating and partial melting of the crust (H.  can also serve as indicators of wavelength ( Figure 6).
While a drip's wavelength is fundamental to the R-T instability, its width, d, also depends on other factors. During the early stage of instability, d is approximately λ/2, because the downgoing lithospheric material is compensated by lithospheric thinning (Figure 5). At later stages, the morphology of the sinking drip depends on the density ratio between it and the surrounding asthenosphere given by the Atwood number A (Figure 3; He et al., 1999) and on the viscosity contrast between the lithosphere and asthenosphere (Figure 4; Jellinek et al., 1999;Prakash et al., 2017). Lithosphere and asthenosphere typically have A < 0.01, but because the viscosity of mantle asthenosphere is much less than the viscosity of the dripping lithosphere, the drip undergoes vertical stretching (Lorinczi & Houseman, 2009;Molnar & Bendick, 2019) and takes on an elongated morphology (Jellinek et al., 1999;Prakash et al., 2017). Most numerical models of lithospheric dripping produce drips that are less than λ/2 in width (e.g., Beall et al., 2017;; in fact, drip widths are often smaller than λ/4 in such models ( Figure 5). More equant lithospheric drips would only be expected in cases where the sinking material is lower in viscosity than surrounding material (Figure 4). Given a drip's width d, its wavelength λ ranges Figure 3. (a) Illustration of a common lithospheric drip model with uniform layer density and viscosity (ρ and η, respectively) in a periodic domain of one-half wavelength (λ/2). Small initial perturbations to the interfaces (dashed lines) trigger the instability (modified from Neil & Houseman, 1999). (b) Parameters derived from Rayleigh-Taylor instability analysis relevant to lithospheric dripping. The final column denotes ranges of values expected for Earth (Gorczyk et al., 2013;Jellinek et al., 1999;Molnar, 2015;Molnar & Houseman, 2013;Neil & Houseman, 1999;Prakash et al., 2017). 7 of 40 from 2d to 4d or larger ( Figure 6). In practice, this means that evens relatively small drips (e.g., when imaged as a seismic anomaly) could affect much larger areas with lithospheric thinning and volcanism ( Figure 6).

Upper Crust and Topographic Response: Two Types of Dripping
Variations in the viscosity structure of the crust and mantle lithosphere during dripping produce two distinct responses in the upper crust and topographic surface: uplift and extension versus subsidence and compression (Figure 1, inset). We denote these two tendencies as weak-crust and strong-crust drips, respectively, and also identify variations within these tendencies, such as permanent topographic depressions versus transient basins, and uplift-dominated versus extension-dominated crusts (Table 2). Given realistic ranges of parameters, these models suggest that the average viscosity of the crust relative to that of the mantle lithosphere, η′ = η c /η m , where η c and η m are the effective viscosities of the crust and mantle lithosphere, respectively, largely determines the behavior of the crust and topographic surface during dripping (e.g., Molnar, 2015;Neil & Houseman, 1999). It has long been recognized that the near-surface expression of lithospheric dripping largely depends on crustal strength (DeCelles, Molnar & Houseman, 2004;Neil & Houseman, 1999).
Previous studies have also attempted to categorize or describe contrasting styles of lithospheric dripping. H.  presented a classification of lithospheric drips that recognized two styles of crustal and topographic deformation: (a) surface subsidence on the order of >500 m followed by rebound, and (b) uplift of a few hundred meters followed by topographic collapse. West et al. (2009) note that under some circumstances, the effects of dripping can be decoupled from surface deformation. These classifications are special cases of the strong-crust versus weak-crust framework. As we show below, topographic uplift or subsidence is largely dependent on overall crustal strength and is also correlated with shortening or extension, respectively. Decoupling of the upper crust In the left column, large values of U (unstable material less viscous than background material) produce spherical instabilities applicable to hot mantle plumes. In the right column, small values of U (unstable material more viscous than background) produce sheets and finger-like instabilities applicable to lithospheric dripping. Images in right column rotated 180° (denoted by arrow indicating gravity, g) to emphasize applicability to dripping. Top row from Jellinek et al. (1999, ∼30 cm wide); bottom row from Prakash et al. (2017, 15.5 cm wide).
from the descending drip can occur either when the crust is very weak, that is, by strain in the lowermost crust, or when it is very strong, that is, by strain in the uppermost mantle lithosphere.

Strong-Crust Drips
Models suggest that values of η′ greater than 10-13 (i.e., when the average crustal viscosity is at least an order of magnitude greater than that of the mantle lithosphere) give rise to a type of dripping we denote as "strong-crust" (Neil & Houseman, 1999).
Strong crusts behave like an elastic plate that flexes down during drip growth and rebounds after detachment (DeCelles, Carrapa, et al., 2015;Göğüş & Pysklywec, 2008;Göğüş et al., 2017;. During drip growth, the topographic surface pulled down above the center of the drip and flexural uplift occurs on peripheral bulges located approximately 1/2λ from the center (Figure 7). The amount of syn-drip surface subsidence increases with η′, at least up to ∼100, beyond which the crust deforms very little (Neil & Houseman, 1999). The amount of subsidence also depends on relative layer thicknesses and densities ( Figure 3). Numerical models with reasonable choices for these parameters predict magnitudes of surface subsidence ranging from 0.5 to 1.5 km (Göğüş & Pysklywec, 2008;Göğüş et al., 2017;. Post-detachment rebound is negligible (<50 m) for the strongest crusts (η′ ≥ 100 Elkins-Tanton, 2007) but is significant for crusts with more moderate strengths (η′ ∼ 10, H. . Rebound is also increased by weakening the middle-lower crust, which allows for some lower-crustal thickening during drip growth (e.g., Göğüş & Pysklywec, 2008;Göğüş et al., 2017;Kaus & Becker, 2007;H. Wang & Currie, 2017;. The thickened low-density crust increases isostatic rebound, in some cases completely inverting the topographic depression and permanently elevating the topography (Figure 7 and Figure S1 in Supporting Information S1; Elkins-Tanton, 2007; Göğüş et al., 2017;. For the models in Göğüş and Pysklywec (2008), post-detachment rebound results in ∼1 km of increased elevation above the center of the drip. The typical strong-crust response to dripping can therefore be characterized as a transient basin. Sedimentological observations and numerical models predict that such basins experience subsidence for ∼5-20 Myr Figure 5. Illustration of characteristic wavelength (λ) and how it relates to the width of isolated drips (d i ). The first panel illustrates an idealized scenario, and the others are numerical modeling results. Drip widths are consistently less than one-half drip wavelength. For single drips, the wavelength corresponds to the width of the topographic depression. For multiple drips, even though the wavelength or drip spacing is relatively consistent, drip widths vary between λ/2 and λ/4, depending in part on where the measurement is taken. Together, these results illustrate the variable nature of drip morphology, even for a consistent drip wavelength.
The distribution of crustal strain during a strong-crust drip is largely controlled by flexural bending stresses. The upper crust first experiences horizontal contraction caused by compressive bending stresses. Sediments deposited in the transient basin may therefore record evidence of syn-contractional deposition, such as growth strata or folding that decreases in amplitude up-section (DeCelles, Carrapa, et al., 2015;DeCelles, Zandt, et al., 2015;Kapp & DeCelles, 2019). Meanwhile, the uplifted peripheral bulges circumscribing the drip experience extensional bending stresses and may remain relatively undeformed (DeCelles, Carrapa, et al., 2015;DeCelles, Zandt, et al., 2015;Kaus & Becker, 2007). After drip detachment, the pattern of upper-crustal stresses is inverted. The central region experiences horizontal extension due to unbending, updoming by upwelling asthenosphere, and gravitational potential energy contrasts generated by the elevated topography (Göğüş et al., 2017).

Weak-Crust Drips
Models with η′ < 10 predict that stresses imposed by the growing lithospheric drip are compensated by flow within the crust (Figure 9a; Molnar, 2015). We denote this style of dripping "weak-crust" (Figure 8). The upper-crustal expression of weak-crust dripping is distinct from that of strong-crust dripping, and syn-drip surface uplift and extension occur rather than subsidence and contraction ( Figure 8 and Figure S1 in Supporting Information S1; Neil & Houseman, 1999).
Upper-crustal extension occurs when thickening is significant enough to cause the middle crust to flow upward, generating surface uplift. Surface uplift is resisted by gravity, causing vertical compression and horizontal extension of the upper crust (Molnar, 2015). Weak-crust drips therefore yield upper-crustal extension and thinning at the same time as the middle to lower crust is being shortened and thickened by the growing drip ( Figure 9a).
Models of weak-crust dripping are summarized in Figure 9. Their behavior is sensitive to the viscosity structure of the crust and mantle lithosphere (Figures 9a-9c and 9e), the instability wavelength (Figure 9b), and crustal thickness and density (Figures 9c and 9d). Thickening and uplift are greatest when the viscosity contrast between the crust and the negatively buoyant lithosphere is negligible, that is, when η′ = 1 (Figure 9d; Neil & Houseman, 1999), and in such models the crust can thicken by a factor of up to 1.4 (Neil & Houseman, 1999). As η′ decreases below 1, surface uplift diminishes and horizontal extension rates increase until the magnitude of surface uplift is negligible (Figure 9d; Molnar & Houseman, 2013). Decreasing the viscosity of the lower crust (represented by a large viscosity decay factor) tends to decouple surface deformation from mantle flow and thus suppress the near-surface expression of dripping. For moderate values of the decay factor (e.g., decay by a factor of 10 throughout the crust), crustal thickening and near-surface extension are reduced by approximately 50%, becoming negligible at larger values of the decay factor (e.g., 1,000; Figure 9e; Molnar, 2015). For realistic decay factors expected for a temperature-dependent viscosity (e.g., 10-100), syn-drip extension of the upper crust is reduced but still significant (Figure 9e; Molnar, 2015). Numerical models with a weak mid-or lower-crustal channel show that surface uplift can result from lower crustal thickening caused by Poiseuille flow within the channel (H. Wang & Currie, 2017).
The instability wavelength (relative to lithosphere thickness) exerts a strong control on the upper crust during dripping (Molnar, 2015). In general, longer wavelengths induce a stronger surface uplift response than smaller instabilities (Figure 9b), but the critical η′ value that separates strong-crust and weak-crust dripping increases for large instabilities (Figure 9b; Neil & Houseman, 1999). Wavelengths on the order of 1,000 km can overwhelm crustal strength and lead to thickening and surface uplift of even very strong crusts ( Houseman, 1999;Pysklywec & Shahnas, 2003). For wavelengths of lithospheric instabilities realistic for continental regions on Earth (100-500 km), the surface switches from uplift to subsidence between η′ = 10 and η′ = 100, often around η′ = 13 (Figures 9a, 9b, and 9d).
Increasing the crustal thickness relative to the lithosphere damps the surface uplift response, both because the thinner mantle lithosphere results in smaller drips that impart smaller stresses to the base of the crust, and because the increased crustal buoyancy works against the downward deflection of the Moho that drives crustal thickening and internal flow (Figures 9c and 9d; Neil & Houseman, 1999). Decreasing the density of the crust increases the contribution of crustal thickening to surface uplift but reduces the magnitude of crustal thickening, so that the magnitude of surface uplift tends to peak at moderate crustal density contrast ratios, ρ′, around −20, where ρ′ = (ρ c − ρ a )/(ρ m −ρ a ), and c, a, and m denote the crust, asthenosphere, and mantle lithosphere, respectively (Neil & Houseman, 1999). Because crust with an average density of 2,800 kg m −3 would yield a density contrast ratio of −16.7 for ρ m = 3,330 kg m −3 , ρ a = 3,300 kg m −3 (Neil & Houseman, 1999), realistic variations in crustal or lithospheric densities would have notable effects on surface uplift ( Figure 9).
Numerical models that include temperature-and strain rate-dependent rheologies suggest that syn-drip surface uplift may be limited to a few hundred meters at most (H. . This result agrees with studies of gravity anomalies suggesting that the large crustal welts typical of orogenic plateaus have not been generated by lithospheric dripping (Molnar & Houseman, 2013).
An analogue model experiment that investigated different crustal strengths lends support to the strong-crust versus weak-crust framework (Pysklywec & Cruden, 2004). In this experiment, the stronger crust (η′ = 2.1) behaved as a classic strong-crust drip, resulting in a topographic depression that rebounded after detachment ( Figure 10). The weaker crust (η′ = 0.88) initially developed a topographic depression created by isostatic subsidence, but it transitioned to crustal thickening and uplift; after the drip detached, the crustal welt slowly relaxed and the topography decreased (Pysklywec & Cruden, 2004). In experiments with a brittle layer approximating the upper crust, a network of radial contractional structures developed over the center of the drip, while the distal regions developed extensional structures ( Figure 10). These upper crustal features demonstrate how dripping in three dimensions is likely to be significantly more complex than 2-D and 2.5-D numerical models predict but still amenable to the strong-crust versus weak-crust framework.

Synthesis of Potential Dripping Events
In the following sections, we synthesize the evidence for lithospheric dripping events reported in the literature. We recognize that each observation is likely to have multiple competing interpretations, and in most cases, lithospheric dripping is only one hypothesis among many under active investigation. Some locations currently have little evidence in support of a lithospheric dripping event, while others have more; this could indicate a difference in the volume of work done in a given area, the volume of evidence that exists, or a combination of both. It is beyond the scope of our work to attempt to confirm or refute the dripping hypothesis for any particular location. Our goal is to synthesize, to the best of our ability, the evidence for all events around the globe for which any researchers have proposed a drip origin, regardless of the amount of evidence or the existence of competing hypotheses.
We first focus on the main lines of evidence that have been reported in the literature. We then summarize the reported evidence for each dripping event, and estimate size (characteristic wavelength), timing of detachment, Figure 7. Illustration of strong-crust dripping, which occurs when relative crustal viscosity η′ > 10. The strong crust deforms flexurally, producing a central depression and peripheral bulges. The drip pulls down the topographic surface as it grows (t 1 ) leading to the formation of a transient basin (t 2 ). Basin deposits experience syn-to post-depositional compression, while the peripheral bulge experiences flexural extension. Basin deposits are uplifted and inverted after detachment (t 3 ). Upwelling of hot asthenosphere induced by the drip can lead to partial melting of remaining crust, mantle lithosphere, or decompression melting of the asthenosphere. and type of drip (weak-crust vs. strong-crust) where possible. A detailed description of how we gleaned this data from the literature for each drip is given in Text S1 in Supporting Information S1.

Types of Evidence
Five main categories of evidence for lithospheric dripping have been reported: topographic subsidence and uplift, upper-crustal deformation, volcanism and magmatism, xenoliths, and geophysical observations. The spatiotemporal pattern of such evidence can be plotted for each drip, and related to stages of drip growth, detachment, and relaxation as illustrated by Figure 11. Weak-crust drips should yield syn-drip surface uplift and extension followed by gravitational collapse and potentially topographic subsidence after detachment. Strong-crust drips should yield syn-drip surface subsidence and horizontal shortening followed by uplift and potentially extension after detachment. While certain aspects of xenolith and igneous data may differ between the two types of drip, we assume their spatiotemporal patterns relative to drip detachment are not dependent on drip type.

Topographic Uplift and Subsidence
Drips are often associated with surface subsidence and sedimentation, sometimes creating subdued topography above the purported dripping center (Figures 12a and 12b). In some cases, more recent sediments may onlap basement rocks, indicating localized surface subsidence (Figure 12a, Saleeby & Foster, 2004). In regions with limited post-drip landscape development, syn-drip subsidence and sedimentation can produce circular regions of smoothed topography approximately one wavelength in diameter ( Figure 12b). In some locations, a pulse of uplift has been attributed drip detachment. The main examples come from the Altiplano and Eastern Cordillera of the Central Andes, where rapid surface uplift of at least three distinct regions has been inferred from paleoaltimetry studies (Garzione et al., 2006Sundell et al., 2019). Such syn-drip subsidence and post-drip rebound is one of the strongest lines of evidence for strong-crust dripping as described in Section 2.3.1.
A few drips are associated with syn-drip surface uplift and crustal thickening indicative of a weak-crust drip. Such regions tend to display more complex topography (Figures 12b-12d). In some cases, tectonic convergence in a collisional orogen may have originally thickened the crust, leading to a lithospheric drip superimposed on an active collisional belt (Figures 12d and 12e). Such cases should produce extension-related topography such normal fault scarps, horst-and-graben topography, hanging-wall basins, and footwall ranges within a compressional orogen (e.g., McMillan et al., 2022;Tye et al., 2022). Figure 8. Illustration of weak-crust dripping, which occurs when relative crustal viscosity η′ < 10. The weak crust flows in response to drip-imposed stresses, producing a thickened crustal welt. The crust thickens as the drip grows (t 1 ), leading to syn-drip uplift and horizontal extension in the upper crust (t 2 ). The thickened crust is prone to partial melting and may collapse gravitationally after detachment (t 3 ). Upwelling of hot asthenosphere induced by the drip can also lead to partial melting of remaining crust, mantle lithosphere, or decompression melting of the asthenosphere.

Type
Syn Note. η′ = η c /η m denotes the viscosity of the crust η c scaled to that of the mantle lithosphere η m .

Table 2
Summary of Dripping Scenarios Predicted by Numerical Models Figure 9. Drip model results (Molnar, 2015;Molnar & Houseman, 2013;Neil & Houseman, 1999), illustrating the conditions that favor strong-crust versus weak-crust dripping. (a) Three models illustrate the weak-crust and strong-crust scenarios in terms of crustal flow. Four specific cases are tracked through the following panels (see Figure 3

Crustal Deformation and Sedimentation
Lithospheric dripping has been used as an explanation for crustal deformation where more traditional mechanisms are difficult to reconcile with observations (e.g., DeCelles, Carrapa, et al., 2015). The most common observation of deformation associated with dripping is the occurrence of horizontal shortening coeval with sedimentary basin development (DeCelles, Carrapa, et al., 2015;Kapp & DeCelles, 2019;Smith et al., 2017), indicative of strong-crust dripping. A rapid switch from shortening to extension in a convergent setting has also been attributed to the removal of lithosphere in a drip (England & Houseman, 1989;Göğüş et al., 2017;Molnar & Houseman, 2004). Lithospheric dripping may also explain localized deformation in orogens, where regions of shortening (Kapp & DeCelles, 2019) or extension  are flanked by relatively undeformed regions. In these cases, crustal deformation potentially driven by lithospheric dripping should be carefully distinguished from that which can be attributed to orogenic shortening . It is likely that drip-related stresses will reactivate pre-existing structures both during drip growth and after detachment (e.g., McMillan et al., 2022;Tye et al., 2022). The spatiotemporal pattern of shortening and extension can shed light on the type, wavelength, and timescale of a drip. Strong-crust drips displaying syn-drip upper-crustal shortening in a region approximating the wavelength, which switches to extension during detachment. Weak-crust drips display syn-drip extension in a region approximating the wavelength, and extension may accelerate or diminish after drip detachment depending on the magnitude of crustal thickening.

Magmatism and Volcanism
Locations where the lithosphere thins are also prone to magmatism and high temperature metamorphism after drip detachment (Molnar & Houseman, 2004), and middle to lower crust thickened by the growing drip is prone to partial melting and silicic magmatism (R. W. Kay & Kay, 1993). Heating and partial melting of the crust and upper mantle follow as a consequence of lithospheric thinning and upwelling of the asthenosphere after drip detachment (H. . Melts can also be generated by partial melting of the drip itself as it descends through the upper mantle (Ducea et al., 2013;Elkins-Tanton, 2007 that is, within a radius of λ/2 from the dripping center ( Figure 6), but its ultimate occurrence at the surface as volcanic products may be more complex.
A wide range of mafic, intermediate, and felsic volcanic products have been associated with lithospheric dripping (Figure 13). Potassic/adakitic magmas, traditionally associated with slab melts, are sometimes hypothesized to reflect melting of continental lithosphere during delamination or dripping, especially in the Central Andes and Tibet (Chapman et al., 2018; R. W. Kay & Kay, 1993). Major and trace element geochemistry can also be used to infer the lithology of the source region. Experimental work suggests that the fractionation of first-row transition elements during partial melting is largely controlled by mineralogy, specifically the content of pyroxene and garnet (Davis et al., 2013;Le Roux et al., 2010. Zn/Fe ratios >13 × 10 4 may therefore reflect pyroxenite versus peridotite melting, and in the context of lithospheric dripping are often interpreted as drip melts (Ducea et al., 2013).
The geochemistry of volcanic rocks and mineralogy xenoliths also shed light on the source region (Furman et al., 2016). Densification of the lithosphere often involves both silicate melt metasomatism and hydrous metasomatism. The former produces dense, iron-rich peridotites or pyroxenites, and the latter produces hydrous phases that melt more readily than anhydrous phases (Furman et al., 2016). The presence of high pressure phases (e.g., garnet), water, and metasomatic minerals (e.g., amphibole and phlogopite) in the source region helps distinguish drip melting from other sources of magmatism (Elkins-Tanton, 2007).
Melting of descending drips involves progressively higher temperatures and pressures (Elkins-Tanton, 2007), but adiabatic decompression melting is characterized by progressive shallowing of the top of the melting column over time (Furman et al., 2016;Holbig & Grove, 2008). Plotting the olivine component from Sack et al. (1981), a proxy for pressure, against chromium concentration, a proxy for melt extent (and therefore temperature), is one way to interrogate this relationship (Furman et al., 2016;Holbig & Grove, 2008).
Removal of the lithosphere ultimately results in a region of elevated crustal heating and surface heat flow (Göğüş & Pysklywec, 2008). Silicic magmatism can result from lower crustal melting, especially in regions of thickened crust (H. . In the Central Andes, silicic volcanic centers are consistently offset to the east of hinterland sedimentary basins, the pattern that would be expected if lithospheric dripping occurred in the mantle wedge of the Andean subduction zone (H. Wang et al., 2021).

Xenoliths
Xenoliths provide data on processes that occur deep within the crust or mantle, and may even offer samples of the foundering material itself. Shifts in xenolith provenance, or "temporal changes in xenolith demographics" (Lee & Anderson, 2015), within a region may imply a change in lithosphere composition. The shift from garnet-pyroxenite cumulates to mantle peridotite in the Southern Sierra Nevada is a classic example that has been used to argue for foundering (e.g., Ducea & Saleeby, 1998;Jones et al., 1994;Molnar & Jones, 2004). Such arguments for foundering are strengthened if the two xenolith populations are derived from similar depths (Byerly & Lassiter, 2012;Ducea & Saleeby, 1998). In ideal cases, the replacement of "pre-drip" xenoliths (e.g., garnet-pyroxenite cumulates or other lower crustal lithologies) with "post-drip" xenoliths (e.g., mantle  peridotite) can be dated with enough precision to constrain the timescale of drip growth and detachment (Molnar & Jones, 2004).
Detailed pressure-temperature analyses and radiometric dating of xenoliths can sometimes indicate a period of rapid sinking prior to eruption, consistent with a lithospheric drip (Shaffer et al., 2017). Xenoliths that record high strain rates may indicate rapid stretching in the neck of a lithospheric drip in central Nevada, U.S. (Dygert et al., 2019).

Seismic Tomography and Seismicity
Geophysical data are often cited as evidence for lithospheric dripping (Figure 14). The most common expressions of lithospheric drips are vertically-elongated fast P-wave anomalies (Figures 14a-14c, 14e, and 14f). Other geophysical data associated with dripping include S-wave anomalies (Figure 14d), receiver function interfaces (Levander et al., 2011), mantle shear-wave splitting patterns (West et al., 2009), and lower crustal anisotropic fabrics (Zandt, 2003). The interpretation of these anomalies as lithospheric drips is often largely dependent on their morphology (e.g., the "isometric drop" of Koulakov, 2011), which can be problematic (Foulger et al., 2013), but such interpretations are strengthened in regions with independent lines of evidence such as sedimentation, volcanism, and uplift.
Assuming that a given seismic anomaly corresponds to a dense piece of foundering lithosphere, estimating the size of the drip from the anomaly is not straightforward. It is not clear a priori what threshold relative wavespeed should be used to delineate the drip (e.g., Calixto et al., 2013;Jones et al., 2014). Crudely estimating the width of the strongest part of the anomaly allows some information to be gleaned from the tomographic image, but it is affected by the resolution and sensitivity of the tomographic model; some models will show a large, strong anomaly where others show a small, weak one. For example, in the P-wave tomography model of Roth et al. (2008), the "Nevada cylinder" anomaly has a fast relative wavespeed that is similar to the wavespeed of the Juan de Fuca plate and has an inferred width of ∼150 km. In the model of Schmandt and Humphreys (2010), however, the Nevada cylinder appears as a broader (∼225 km wide), more muted anomaly. As noted by Jones et al. (2014), a compact high-velocity body in the upper mantle can be smeared to a larger, lower amplitude anomaly in a tomographic model. Seismic anomalies can therefore only provide a rough estimate of the width of dripping lithosphere and are most useful for ruling out hypotheses that call for drastically larger or smaller drip sizes. Some relatively small anomalies near the resolution of tomographic data (50-100 km in diameter) have been argued to reflect small drips (Bianchi et al., 2013;Calixto et al., 2013).
Two upper-mantle seismic zones may be related to lithospheric dripping (Figures 14e and 14f). Mantle seismicity beneath the SE Carpathians (#16) and Hindu Kush (#19) cluster in a narrow zone situated above a large P-wave anomaly, and their focal mechanisms indicate rapid vertical stretching consistent with drip necking (Lorinczi & Houseman, 2009;Molnar & Bendick, 2019). The interpretation of these zones as either dripping lithosphere, delaminating lithosphere, or remnant oceanic slabs is a topic of ongoing research (Göğüş et al., 2016;McKenzie et al., 2019;Şengör & Dewey, 2020).

Purported Dripping Events
In this section we summarize each purported dripping event in terms of the evidence discussed previously (Table 1). Detailed descriptions of each event, including how we analyze and interpret the evidence reported in the literature, are included in Text S2 in Supporting Information S1.
syn-drip subsidence of the Tulare Lake basin and post-drip uplift of the Sierra Nevada are consistent with the strong-crust style of dripping (Section 2.3.1).

Northern Sierra Nevada (#2)
Relatively few studies have hypothesized lithospheric dripping for the Northern Sierra Nevada. A high wavespeed anomaly ("Redding Anomaly") beneath the northern Sierra Nevada (Benz & Zandt, 1993) has been interpreted as a lithospheric drip (Harig et al., 2008;Molnar & Jones, 2004). Jones et al. (2014) connected the Redding anomaly to the Isabella anomaly (#1) to suggest the two events are related. We omit the northern Sierra Nevada event from our analysis as it lacks sufficient evidence (Figure 15). Figure 15. Potential dripping events in North America. Lines of varying colors plot the temporal range of various geological observations. Gray shapes represent our inferred periods of drip growth (parabolic heads), detachment (vertical bars), and lithospheric rebound/relaxation (tapering tails). Drips are labeled and numbered according to Figure 1. Dripping events are scaled according to their inferred wavelengths (see text for discussion). The axis on the right side plots the approximate widths and depths of seismic anomalies associated with each drip (blue for P-wave, purple for S-wave models). MCCs: metamorphic core complexes.

Wallowa Mountains (#3)
Lithospheric dripping of the Wallowa pluton (NE Oregon, U.S.) has been related to the eruption of the Columbia River flood basalts ca. 16 Ma (Hales et al., 2005). Gravitational instability may have been triggered by the Yellowstone plume, which could have both decreased the density of the sublithospheric mantle and thermally weakened the lithosphere (Camp & Hanan, 2008). Camp and Hanan (2008) propose melting of foundering lower crust composed of pyroxenite or eclogite for the rapid eruption of high volume, evolved lavas of the Grande Ronde Basalt. Topography and crustal thickness above the purported dripping event is currently elevated (Figure 12c). Uplift of ∼2 km coincident with volcanism (Hales et al., 2005), significant crustal thickening (Darold & Humphreys, 2013), and high surface heat flux >100 mW m −2 (Wisian et al., 1999) are all consistent with weak-crust dripping (Section 2.3.2). Based on the timing and size of the volcanic province, we estimate an age of 15 Ma for drip detachment and a characteristic wavelength of ∼200 km (Figure 15).

Central Nevada (#4)
Lithospheric dripping is a potential explanation for the Nevada Cylinder seismic anomaly (see Roth et al., 2008) and shear-wave splitting patterns beneath the Great Basin region (West et al., 2009). Dripping may have triggered the eruption of Lunar Crater Volcanic Field (LCVF) basalts (6 Ma to 35 ka), which erupted from progressively deeper sources (Yogodzinski et al., 1996) and contain dunite xenoliths that were deformed in a low-viscosity, rapidly straining region of the mantle (Dygert et al., 2019). Dripping may also be associated with a ∼300 km wide region of topography that is ∼100 m higher on average (Dygert et al., 2019). Drip growth is constrained to later than 6 Ma (LCVF basalts) and likely occurred as a weak-crust drip (Section 2.3.2) in an extensional tectonic setting with elevated crustal temperatures (Wisian et al., 1999). The region of elevated topography suggests a ∼300 km wavelength (Figure 15).

Elko, Nevada (#5)
Smith et al. (2017) proposed lithospheric dripping as an explanation for Eocene basin development and volcanism within the orogenic hinterland of the North American Cordillera. Eocene sediments are capped by a ∼20 Myr unconformity and Oligocene volcanic deposits, indicating uplift and volcanism largely after lacustrine sedimentation (Smith et al., 2017). The distribution of sedimentary and volcanic deposits suggests a ∼200 km wavelength. Drip detachment may have contributed to crustal extension in the Ruby Mountains core complex during the Oligocene (Smith et al., 2017). Syn-drip basin development followed by uplift and extension is consistent with strong-crust dripping (Figure 15). Levander et al. (2011) proposed lithospheric foundering to explain shear-wave anomalies (Obrebski et al., 2011;Schmandt & Humphreys, 2010) and receiver functions (Levander et al., 2011) beneath the western Colorado Plateau. Incision of the Colorado River in the Grand Canyon suggests that foundering began ∼6 Ma (Levander et al., 2011). Asymmetric thinning of the lithosphere and surface uplift migrated horizontally (Levander et al., 2011), suggesting an intermediate style of foundering that has been characterized as a stalled delamination event (Beall et al., 2017). If lithospheric dripping is involved, post-drip surface uplift suggests detachment of a strong-crust drip with a wavelength of ∼280 km (Figure 15).

S Colorado Plateau (#7)
Shear wave anomalies, Cenozoic volcanism, and elevated topography along the edges of the Colorado Plateau may be explained by multiple lithospheric dripping events (J. W. van Wijk et al., 2010). Numerical models suggest that instability of a lithospheric step would yield drips spaced ∼275 km apart. Volcanism ca. 2.1-1.4 Ma concentrated around the edges of shear-wave anomalies indicates that foundering may have begun ∼3 Ma (J. W. van Wijk et al., 2010). Numerical models also suggest that instability of a lithospheric step migrates horizontally in a manner intermediate to delamination and dripping (Beall et al., 2017). Given the asymmetric nature of convective instabilities on the edges of the Colorado Plateau (Karlstrom et al., 2022), more suggestive of delamination than dripping, we exclude the S Colorado Plateau events from our analysis.

Rio Grande Rift (#8)
A steeply dipping tomographic anomaly beneath the eastern flank of the Southern Rio Grande Rift (Schmandt & Humphreys, 2010;Song & Helmberger, 2007) has been interpreted as foundering cratonic lithosphere (Agrawal et al., 2019). Foundering is supported by the presence of seismic gaps in the Moho and LAB and elevated surface topography above the anomaly (Agrawal et al., 2019). While Agrawal et al. (2019) argued for delamination of the craton edge, J. van  proposed that the edge is foundering in multiple lithospheric drips approximately 100 km in width. Xenoliths derived from asthenosphere and cratonic lithosphere equilibrated at 45 km depth, suggesting wholesale removal of the mantle lithosphere did not occur (Byerly & Lassiter, 2012). Partial removal of the lower lithosphere is more consistent with dripping than with delamination. Other workers interpret the seismic anomaly as a fragment of the Farallon slab (Ricketts et al., 2016;Schmandt & Humphreys, 2010). Because the most likely scenario for lithospheric foundering involves instability of the craton edge, we consider this event to be intermediate in style between dripping and delamination (Beall et al., 2017) and omit it from our analysis.

Mori et al. (2009) proposed lithospheric dripping as an explanation for volcanic patterns in the western Trans-Mexican Volcanic Belt (TMVB),
where large-scale silicic volcanism (Sierra Madre Occidental, Ferrari et al., 2002) was followed by a volcanic gap and late Miocene flood basalt volcanism, potentially reflecting the building and foundering of an ultramafic root (Mori et al., 2009). The diameter of the volcanic province suggests a ∼200 km wavelength, and the onset of volcanism suggests detachment ca. 12 Ma. The lack of a clear topographic signal (Ferrari et al., 2012) or crustal welt (Urrutia-Fucugauchi & Flores-Ruiz, 1996) is consistent with very weak-crust dripping ( Figure 9) and elevated crustal temperatures, which may be reflected by the continental arc setting and high surface heat flux >200 mW m −2 (Prol-Ledesma & Morán-Zenteno, 2019) ( Figure 15).

Bloch et al. (2017) identify lower-crustal and upper-mantle xenoliths in the
Northern Volcanic Zone of the Andes (1°S to 5°N) as pieces of a negatively buoyant crustal root potentially in the early stages of foundering. Given the relative lack of data for event and the early stage of instability, we are unable to infer the timing, size, or style.

Northern Altiplano (#11 and #12)
Evidence for two lithospheric dripping events in the Northern Altiplano (Central Andes, 14°S to 16°S) is largely based on hydrated volcanic glass paleoelevation proxy data (Sundell et al., 2019). Sundell et al. (2019) hypothesized that surface uplift on the order of ∼3 km decoupled from crustal shortening may be related to drip detachment or lower crustal flow. The spatiotemporal pattern of surface uplift (Sundell et al., 2019) constrains the detachment of the two drips to approximately 21 and 15 Ma, respectively, and allows us to estimate the instability wavelength of ∼200 km. Alternatively, Göğüş et al. (2022) hypothesize that the two regions of rapid surface uplift correspond to the peripheral bulges of a larger, single drip approximately 300 km in wavelength. Lack of crustal shortening and thickening during dripping and surface uplift that postdates drip detachment are consistent with strong-crust dripping (Figure 16).

Southern Altiplano (#13)
Lithospheric foundering has long been hypothesized beneath the Southern Altiplano (Central Andes, 20°S) based on tomographic anomalies (Beck & Zandt, 2002;Myers et al., 1998). Garzione et al. (2006) linked a phase of rapid uplift from 10.3 to 6.8 Ma inferred from paleoelevation data to lithospheric dripping. This late Miocene time frame also corresponds to incision of low-relief paleosurfaces, accelerated exhumation of the Eastern Cordillera, eruption of mafic lavas that began ∼7.5 Ma (Garzione et al., 2006, and references therein) and the eastward propagation of the Andean strain front ca. 11-8 Ma (Anderson et al., 2018). The ∼3 km of inferred surface uplift is consistent with removal of a thick portion of mantle lithosphere after the crust had been mechanically thickened to ∼70 km (Molnar & Garzione, 2007). Crustal mass balance calculations suggest that ∼10 km of crust may have been removed along with the mantle lithosphere (McQuarrie, 2002). The region of uplift inferred by Garzione et al. (2008) suggests a ∼400 km wavelength. Surface uplift following drip detachment and the lack of syn-drip crustal thickening are consistent with strong-crust dripping ∼10 Ma (Section 2.3.1). Molnar and Garzione (2007) inferred from the rapid timescale of drip growth and detachment that the mantle lithosphere was relatively weak, also consistent with strong-crust dripping (Figure 16).

Arizaro Basin (#14)
Lithospheric dripping has been hypothesized for the Miocene Arizaro Basin in the Puna Plateau (Central Andes) as an explanation for hinterland basin development, silicic volcanism, and upper-crustal extension (DeCelles, Carrapa, et al., 2015;Schoenbohm & Carrapa, 2015).  used low-temperature thermochronology to document upper-crustal burial and heating followed by exhumation and cooling related to basin development and inversion, respectively. A 50-75 km tomographic anomaly in the upper mantle beneath the Eastern Cordillera may reflect pieces of detached lithosphere (Bianchi et al., 2013;Calixto et al., 2013;Schurr et al., 2006). Combined with modeling studies, the <150 km diameter of the sedimentary basin and ∼75 km seismic anomaly suggest a wavelength of ∼200 km (H. . Syn-drip flexural subsidence and sedimentation followed by post-drip rebound is consistent with strong-crust dripping (Section 2.3.1). Sediment accumulation suggests the drip began growing by ∼20 Ma, with upper-crustal shortening documented at ∼10 Ma (DeCelles, Carrapa, et al., 2015). Based on this evidence, detachment likely occurred ca. 7 Ma (DeCelles, Carrapa, et al., 2015;, though other workers point to the eruption of Aguas Calientes ignimbrites (17.2 and 10.5 Ma, Petrinovic et al., 2010) to suggest detachment as early as 17 Ma (Figure 16).

SE Carpathians (#16)
The primary evidence for lithospheric foundering in the SE Carpathians (Romania) consists of an active seismic zone in the upper mantle extending to depths of 200 km (Figure 14e; Roman, 1970). Early work tied mantle earthquakes to volcanism and gravity anomalies to hypothesize foundering lithosphere beneath the SE Carpathians (Roman, 1970) which became the dominant interpretation of the region (Horváth, 1993;Wortel & Spakman, 2000). A large seismic anomaly imaged beneath the mantle seismogenic zone has been interpreted as foundering continental or oceanic lithosphere (Fillerup et al., 2010;Martin & Wenzel, 2006;Ren et al., 2012). Lorinczi and Houseman (2009) developed the hypothesis of lithospheric dripping as an explanation for mantle seismicity and the topographic development of the SE Carpathians. Alkali basalts of the Perşani volcanic field derive from decompression melts of the asthenosphere at 60-90 km depth and may support the dripping hypothesis (Harangi et al., 2013). The geometry of the seismic anomalies and regional topography suggest a wavelength of ∼350 km. Geodynamic models that reproduce the regional topography by inducing a drip of this size suggest that significant crustal thickening occurs during dripping (Lorinczi & Houseman, 2009), consistent with weak-crust dripping (Figure 17).

10.1029/2022GC010488
23 of 40 Göğüş et al. (2017) proposed lithospheric dripping beneath the Central Anatolian Plateau to explain enigmatic surface uplift, syn-convergent extension, upper mantle seismic anomalies, and volcanism in the Cappadocia and Galatia volcanic provinces. Paleoelevation proxies suggest surface uplift of the interior plateau followed by rapid uplift and shortening of the southern margin, which can be explained by growth and detachment of a lithospheric drip during the Late Miocene (Meijers et al., 2018). The >1 km of surface uplift ∼8 Ma in southern Anatolia (Schildgen et al., 2012) has been used to suggest drip detachment at 8-6 Ma (Göğüş et al., 2017). Geodynamic models of foundering of the late Cretaceous Kırşehir arc root predict moderate crustal thickening and syn-drip subsidence, yielding a wavelength of ∼450 km (Göğüş et al., 2017). Syn-drip subsidence and upper-crustal shortening followed by uplift and upper-crustal extension is consistent with strong-crust dripping (Figure 17).  Gall et al. (2021) report evidence of drip melting in Quaternary alkaline mafic lavas and hypothesize that two or more small-scale drips (∼20 km wavelength) occurred during the Quaternary. Mafic volcanic isotopic trends across Anatolia indicate a geodynamic shift ∼5 Ma, which reconfigured the mantle sources of volcanism after rollback of the Neotethyan slab . Furman et al. (2021) argue for mantle upwelling through slab tears, incorporating melts derived from slab sediments, and potentially triggering small-scale instabilities at the base of the lithosphere.

Western Iran (#18)
Dripping beneath the Iranian Plateau may explain its relatively high elevation and post-collisional volcanism (François et al., 2014;Hatzfeld & Molnar, 2010;Salehi et al., 2020). Quaternary alkaline mafic lavas show evidence of pyroxenite melting consistent with dripping (Salehi et al., 2020). These lavas encompass a region approximately 140 km in diameter and the lithosphere is approximately 60 km thinner than surrounding regions (Salehi et al., 2020), and both lengths are consistent with an instability wavelength of ∼150 km. The timing of dripping is not well constrained, but research points to the accelerated deformation of the Iranian Plateau and Zagros fold-and-thrust-belt ∼12 Ma (Hatzfeld & Molnar, 2010). Fedele et al. (2022) related the eruption of alkaline lavas to an inferred pulse of Quaternary extension. Assuming volcanism corresponds with or postdates drip detachment, we estimate detachment during the Pliocene to early Quaternary (5-0.5 Ma). Lava flows overlie Miocene-Pliocene limestones (Salehi et al., 2020), but it is not clear if the latter were deposited in a basin potentially related to dripping. Based on the assumption that pyroxenite-derived volcanism and upper-crustal extension (Fedele et al., 2022;Salehi et al., 2020) coincided with drip detachment, we infer a strong-crust dripping style.

Hindu Kush (#19)
Lithospheric dripping beneath the Hindu Kush has been proposed as an explanation for a high-wavespeed tomographic anomaly ("isometric drop", Koulakov, 2011) and upper mantle seismicity (Molnar & Bendick, 2019). Similar to the SE Carpathians, the narrow seismogenic zone beneath the Hindu Kush stretches to depths of 250 km (Figure 14f; Sippl et al., 2013) with earthquake focal mechanisms indicating vertical stretching consistent with necking of an actively sinking drip (Molnar & Bendick, 2019). The deeper tomographic anomaly is interpreted as the body of the drip (Figure 14f). Molnar and Bendick (2019) distinguish the Hindu Kush seismic zone from similar zones beneath the Pamir, which they consider oceanic slab remnants. The Hindu Kush is a thick crustal welt characterized by upper-crustal extension in its interior and contraction around its edges (Molnar, 2015), a pattern that is consistent with a large, weak-crust drip. We estimate a wavelength of 500 km based on the width of the crustal welt and high topography, which is also consistent with the ∼250 km wide tomographic anomaly ( Figure 18). Chapman et al. (2018) propose melting of a lithospheric drip for the emplacement of the Vanj magmatic complex within an ellipsoidal region ∼250 × 150 km during the Eocene. The average diameter of the magmatic region indicates a wavelength of ∼200 km. We assume that the age of magmatism reflects the late stages of drip growth and the early stages of detachment and sinking of the drip, and therefore estimate an age of 39 Ma. We lack the data to infer the type of drip, but foundering may have been triggered as a result of India-Asia convergence and thickening Chapman et al. (2018), potentially favoring a weak-crust drip (Figure 18).

Pamir, Dunkeldik (#21)
The Dunkeldik and Taxkorgan igneous rocks in the SE Pamir (Tajikistan) have been related to a lithospheric drip (Chapman et al., 2018;Shaffer et al., 2017). Lower crustal xenoliths descended to ∼100 km depth 14-11 Ma before being erupted at 11 Ma (Ducea et al., 2003;Shaffer et al., 2017), indicating significant drip growth by 14 Ma and detachment at 11 Ma (Shaffer et al., 2017). Given an estimate of 40 km thick crust lost to foundering (Shaffer et al., 2017), indicates a minimum wavelength of 120 km. Like the Vanj drip, we lack the data necessary to estimate drip type, but infer that a weak-crust drip, associated with tectonic convergence and thickening, to be most likely (Figure 18).

Tibet, Nading Field (#22)
Kapp and DeCelles (2019) hypothesized lithospheric dripping for two episodes of hinterland basin sedimentation and volcanism in Tibet during the Paleogene. The Nading volcanics (∼36-28 Ma) have been interpreted as lithospheric melts generated by asthenosphere upwelling (Qi et al., 2021). Nading volcanics were erupted on the periphery a syn-contractional sedimentary basin consisting of folded, ∼35 Ma, lacustrine strata (Kapp & DeCelles, 2019). Paleoaltimetry studies indicate ∼1.5-3 km of surface uplift during the Oligocene to Early Miocene (Lu et al., 2018), which would post-date drip detachment. This scenario is consistent with strong-crust dripping (Section 2.3.1). Metasomatism and weakening of the Asian mantle lithosphere (Kapp & DeCelles, 2019;Zeng et al., 2020) may explain the high relative strength of the crust. Sedimentary basins ∼100 km in diameter flanked by 100-150 km-wide volcanic regions together suggest a wavelength of 200-250 km, evidently smaller than the distance between the potential Nading and Dogai dripping events (∼400 km) but consistent with the ∼80 km thickness of lithosphere removed from Tibet (Lu et al., 2018) (Figure 18).

Tibet, Dogai (#23)
Kapp and DeCelles (2019) inferred a second Paleogene lithospheric dripping event in Tibet associated with hinterland basin deposits and volcanics of the 46-38 Ma Dogai complex. Dogai volcanic geochemistry is consistent with melting of lower crustal eclogite (Zeng et al., 2020). Like the purported Nading dripping event, we estimate a wavelength of 200-250 km and a strong-crust dripping style (Section 2.3.1). More precise dating of the Dogai event is needed, but we estimate ∼42 Ma detachment based on the age of volcanism (Figure 18).

North China Craton (#24)
Lithospheric dripping has been invoked as an explanation for the destruction of cratonic lithosphere beneath the eastern part of the North China Craton (Gao et al., 2004;K. J. Zhang, 2012). Crustal thinning (Sun et al., 2017), lower crustal melting and magmatism (J. B. Zhang et al., 2014), sedimentation and horizontal extension and metamorphic core complex development (J. Liu et al., 2005) have all been related to R-T instability driven by cratonic collision (K. J. Zhang, 2012). The distance between neighboring Mesozoic basins suggests a wavelength of ∼550 km, consistent with R-T instability of a 180-200 km thick layer. Syn-drip extension centered on the inferred dripping centers, possibly involving lower crustal thickening (K. J. Zhang, 2012), suggests a weak-crust style of dripping ( Figure 18). Furman et al. (2016) hypothesized lithospheric dripping beneath the East African Rift as an explanation for the geochemistry of Oligocene flood basalts (∼30 Ma). In the Afar region of Ethiopia, a suite of enigmatic, high-Ti flood basalts show geochemical ratios indicative of melting driven by devolatilization of descending lithosphere (HT2, Furman et al., 2016). These are encircled by a broader region of basalts derived mainly from the asthenosphere, without lithospheric signatures (HT1 and LT, Furman et al., 2016). The inferred positive correlation between melting extent and depth matches models of drip magmatism (Elkins-Tanton, 2005, 2007. Furman et al. (2016) infer a drip diameter of 50-100 km and therefore a wavelength of approximately 300 km. A wavelength of ∼250-300 km is also supported by the inferred ∼100 km of lithospheric thinning (Furman et al., 2016). Oligocene volcanism was preceded by 1-2 km of uplift, but it is not currently possible to distinguish uplift resulting from continental rifting, plume impingement, and lithospheric dripping. Based on evidence for a strong, thick crust in the Afar region (Ebinger et al., 1989), combined with a metasomatized mantle lithosphere (Furman et al., 2016), we infer a strong-crust style of dripping for the Afar event ( Figure 17). Furman et al. (2016) also proposed a lithospheric dripping event for the endorheic Turkana depression based on Early Miocene mafic lavas (23-16 Ma), which display evidence of pyroxenite melting and melting of descending lithosphere (Furman et al., 2016). Furman et al. (2016) suggest that this event may be related to uplift of the southern portion of the Ethiopian dome 19-12 Ma. Given the overlapping timing of volcanism and surface uplift, we tentatively infer drip detachment ∼19 Ma as a strong-crust drip. It is difficult to estimate a characteristic wavelength based on existing data. If the Afar and Turkana events are two related, but distinct, lithospheric drips, their spatial separation would imply a wavelength of ∼400 km, but their differing ages are not consistent with such a relationship. We tentatively estimate a ∼300 km wavelength by analogy to the Afar drip (#25), which approximately matches the size of the volcanic region in Turkana (Figure 17), but both events are not very well constrained because of the overriding influence of mantle plumes.

New Zealand (#27)
Lithospheric foundering has long been hypothesized beneath the North Island of New Zealand (Dimech et al., 2017;Stern et al., 2010Stern et al., , 2013. Current studies suggest that foundering lithosphere migrated during the Middle to Late Miocene (Stern et al., 2013) in a manner similar to styles of foundering intermediate to dripping and delamination (Beall et al., 2017); we omit this event from our analysis. Numerical models that reproduce the spatial pattern of sedimentation associated with the migrating hinge imply a rheologically weak crust (η′ = 5 for the upper crust, η′ = 0.1 for the lower crust, Stern et al., 2013), and surface uplift occurs above the hinge, similar to weak-crust dripping.

Summary of Potential Dripping Events
All but one of the 27 proposed drips are located in tectonically active continental regions (Figure 1). The one potential exception, the North China Craton (#24), is located in a formerly cratonic region that experienced Mesozoic tectonism prior to decratonization and the purported dripping event. It therefore seems that tectonic deformation plays an important role in seeding, triggering, or otherwise allowing lithospheric dripping. Relevant tectonic processes include the accumulation of dense magmatic residues in continental arcs (e.g., Southern Sierra ). As suggested by the purported drips in back-arc regions (e.g., western margins of North and South America), fluids released by oceanic slabs may participate to lithosphere removal, whether by inducing metamorphism (Austrheim, 1987), metasomatism (Furman et al., 2016), or rheological weakening (Kusky et al., 2014). As suggested by the dripping events in the East African Rift (Turkana [#26], and Afar [#25]) and the Wallowa Mountains (#3), mantle plumes may also destabilize continental lithosphere and lead to dripping. Mantle plumes may provide metasomatic fluids that densify the lower lithosphere, and hot plume material would further enhance the density contrast (Furman et al., 2016).  Figure 19). Subsurface evidence for dripping events tends to be erased over time as the detached lithosphere warms and sinks deeper into the mantle and becomes more difficult to detect. Near-surface evidence such as volcanics, uplift, subsidence, and sedimentation can be overprinted, buried, or erased by later events. While we cannot directly rule out an increase in lithospheric dripping during the Cenozoic, the simpler explanation of the cluster of dripping events in the Late Cenozoic is a lack of data for earlier events.
Of the 23 events for which we were able to estimate the characteristic wavelength, 11 have a wavelength between 170 and 270 km (Figure 19), indicative of an unstable lithospheric column ∼60-100 km thick (Table S1 in Supporting Information S1). Another peak around ∼400 km may reflect the influence of tectonic convergence and lithospheric shortening. Shortening leads to a downward deflection of the Moho and lithosphere-asthenosphere boundary, potentially setting up a convective instability larger than would grow from initially small perturbations (Molnar & Houseman, 2013). The largest wavelength we infer is the ∼550 km drip beneath the North China Craton (#24). This wavelength may reflect the large initial thickness of cratonic lithosphere, potentially combined with long-wavelength lithospheric folding that provided the initial perturbation to the lithosphere-asthenosphere boundary (K. J. Zhang, 2012). The wavelengths of these larger events are less well constrained, however, and future work may uncover evidence for multiple smaller dripping events in these locations (as discussed for the North China Craton in Text S2 in Supporting Information S1).
At the other extreme, regions subjected to back-arc volcanism, elevated mantle heat flux, and hydration from subducting slabs, such as the modern Central Andes and Mesozoic North America, display smaller wavelengths (<200 km). Small drips associated with active Cordilleran orogens is consistent with modeling studies that infer smaller drips for sections of lithosphere with steeper temperature and viscosity gradients, or for lithosphere that has been previously thinned by metasomatism or thermal erosion in continental arc settings.
Weak and strong-crust drips do not seem to correspond to tectonic setting in our data set. In at least one case, we find neighboring drips with strongly contrasting styles. The Southern Puna (#15) is one of the most typical weak-crust drips that we identify here, but less than 200 km along strike from the strong-crust Arizaro Basin drip Figure 19. Histograms of detachment age (5-Myr bins) and wavelength (50-km bins) for reported dripping events. The North China Craton drip (NCC) is labeled. Dripping events cluster in the Middle and Late Cenozoic, which likely reflects a measurement bias. Drip wavelengths cluster around ∼200 and ∼400 km wavelengths, which may reflect original lithospheric thickness, the influence of background tectonic deformation, or both.
(#14). Similarly, cratonic regions have evidently undergone both weak and strong-crust dripping, but more work is necessary to tease apart the effects of the purported drips from those of background collision (North China Craton [#24]) or extension (East African Rift [#25 and #26]).
By reference to the plots synthesizing each dripping event (Figures 15-18), the evidence for each dripping event varies in quantity and quality (Figure 11). Only a few of the inferred dripping events match the idealized scenarios described in Figure 11 to some degree. The Southern Altiplano drip (#13; Figure 16) matches the strong-crust scenario well because surface subsidence and upper-crustal shortening were followed by rapid uplift and volcanism. On a smaller scale, the Arizaro Basin drip (#14; Figure 16) matches the strong-crust dripping hypothesis, but its detachment is not associated with a pulse of large-scale surface uplift and its timing remains somewhat unclear. In North America, the Elko, Nevada drip (#5) best matches the strong-crust scenario, though it also occurred in the context of flat-slab subduction and widely distributed continental extension. The Dogai and Nading Field drips in Tibet (#23 and #22; Figure 18) display key evidence of strong-crust dripping, such as syn-drip surface subsidence and crustal shortening. Weak-crust drips are best represented by the Southern Puna drip (#15; Figure 16) which only lacks xenolith evidence. Geologic observations throughout the Southern Puna (Section 3.2.14 and Text S2 in Supporting Information S1) constrain the location and timing of upper-crustal strain, sedimentation, and volcanism not only above the center of the purported drip, but around its edges as well. Unlike for the Southern Puna drip, the protracted pulse of surface uplift after the inferred detachment of the Wallowa drip (#3) most likely indicates significant isostatic rebound, and syn-drip upper-crustal extension, a critical piece of evidence for weak-crust dripping, has currently not been documented for the Wallowa Mountains drip.

Discussion
To evaluate the applicability of the strong-crust versus weak-crust lithospheric dripping framework, we synthesized studies that propose lithospheric dripping based on geophysical and geological data, and we estimated the size, timing, and type of drip. The data for some proposed lithospheric dripping events is sparse, and alternative explanations are also viable. Nonetheless, of the 27 reviewed dripping events, we found that 13 displayed some evidence for the strong-crust style, while 9 displayed some evidence for the weak-crust style ( Table 1) While we are unable to confirm lithospheric dripping hypothesis for any particular location, the quantity of proposed drips suggests that lithospheric dripping is an important explanatory concept. Evidence indicating both strong-crust and weak-crust drips (Sections 2.3.1 and 2.3.2) further suggests that the predictable patterns of crustal deformation displayed by numerical studies (Section 2) are borne out in the geologic record. In the following sections, we discuss the implications of these findings and directions for future research, which are largely focused on methods for testing the dripping hypothesis.

Implications of Strong-Crust and Weak-Crust Drips
The strength profile of the lithosphere is a longstanding topic of research in geodynamics (cf. Burov, 2011). Because lithosphere rheology is generally poorly known, inverse approaches that combine geodynamic modeling with observations are useful (Jain & Korenaga, 2020). For example, a suite of geodynamic models allowing large rheological variations can attempt to reproduce geophysical observations, and the narrower set of models that satisfy observational constraints can be used to further constrain the rheology of the lithosphere (Jain & Korenaga, 2020). Lithospheric dripping provides a target for such modeling in locations where the timing of drip initiation and detachment are well-constrained (e.g., Molnar & Garzione, 2007;Molnar & Jones, 2004). The time period involved (∼1-30 Myr) and spatial extent of a dripping event (150-500 km) probe large spatiotemporal scales not involved in other geodynamic processes such as post-seismic deformation (1-10 yr; e.g., Hines & Hetland, 2016) and glacial isostatic rebound (10-20 kyr; e.g., Lambeck et al., 1998), but are similar to the growth of orogenic or volcanic loads (Watts et al., 2013). The occurrence of strong-crust or weak-crust dripping contains critical information on the relative strength of the crust. Lithospheric dripping can also be used to estimate lithospheric strength in the geologic past, perhaps in periods where the thermomechanical configuration of the lithosphere was different from the present, for example, the orogenic setting during the Oligocene in western North America prior to widespread Basin and Range extension (Smith et al., 2017).
The prevalence of strong-crust drips in our data set may reflect typical lithospheric conditions. Felsic crustal rocks such as granite and quartzite are weaker than mantle olivine at equivalent temperatures, but they are significantly stronger at the cooler temperatures representative of upper continental crust (e.g., Brace & Kohlstedt, 1980;Beaumont et al., 2006;Bürgmann & Dresen, 2008, and see Figure S1 in Supporting Information S1). The overall strength of the crust therefore depends to first order on the geothermal gradient (Burov, 2011), and strong-crust drips would be expected in regions with low crustal heat production and compositionally strong crustal lithologies (e.g., diorite, dry feldspar, or diabase; Burov, 2011;Bürgmann & Dresen, 2008). If the upper crust is sufficiently weakened by frictional-plastic yielding, brittle faulting, radiogenic heating, or composition, a strong lower crustal layer and/or a weakened mantle lithosphere may be required to sustain strong-crust drips (e.g., H. H. Wang & Currie, 2017). Conversely, weak-crust drips are expected in regions of high heat flow (H. Wang & Currie, 2017), regions weakened by faulting (H. , or regions of high regional strain rates (Molnar, 2015). Collisional tectonics may be capable of weakening the crust sufficiently for weak-crust dripping (e.g., the SE Carpathians [#16], Pamir [#20 and #21], Hindu Kush [#19]). Evidence for a weak-crust drip is more difficult to collect because it is necessary to more precisely constrain the timing of drip detachment, surface uplift, and the kinematics of upper-crustal deformation, and the effects of weak-crust dripping may be subtle. Models predict moderate amounts of crustal thickening (∼5-10 km) and surface uplift on the order of a few hundred meters, combined with moderate amounts of syn-drip extensional strain (H. Wang & Currie, 2017;, which may be difficult to detect in tectonically active settings.

Competing Hypotheses
Although a number of drips have been inferred using only a few lines of evidence (often geochemistry) and lack other types of supporting data (Table 1), the most significant controversies surrounding the identification of lithospheric dripping seem to occur in regions that have been studied most intensely using seismic tomography. In the Western U.S., for example, existing studies closely agree on the locations, but not the precise sizes and relative magnitudes, of major tomographic anomalies in the upper mantle (e.g., Becker, 2012). The ongoing debates over the Isabella Anomaly (e.g., Cox et al., 2016;Pikser et al., 2012;Y. Wang et al., 2013;Yu et al., 2020), Wallowa Anomaly (Darold & Humphreys, 2013), and Nevada Cylinder (Pavlis et al., 2012;van der Meer et al., 2018;Zandt & Humphreys, 2008) suggest that even as tomographic models improve, distinguishing drips from other scenarios such as slab fragments (e.g., Porritt, 2013;Y. Wang et al., 2013) will remain contentious. Tomographic anomalies below active seismic zones in the mantle beneath the SE Carpathians and the Hindu Kush have also been interpreted as both lithospheric drips (Molnar & Bendick, 2019)  In the Central Andes, however, small tomographic anomalies do not correspond to the subducting Nazca slab, nor have they been interpreted as remnants of previously subducted slabs (e.g., Beck & Zandt, 2002;Beck et al., 2015;Bianchi et al., 2013). While the interpretation of tomographic anomalies is less equivocal in the Central Andes than in the regions discussed above, the sedimentation and volcanism associated with lithospheric dripping has alternatively been interpreted in the context of flat-slab subduction (e.g., Ramos & Folguera, 2009). Though the existence of past flat slab events and their potential effects on upper-crustal strain and volcanism are still debated (e.g., DeCelles, , the hypothesis provides an alternative explanation involving more traditional plate tectonic processes. It is also likely that drip-and slab-related deformation and volcanism are not mutually exclusive, as slab rollback and breakoff can induce lithospheric melting Gall et al., 2021) and foundering (Smith et al., 2017). Dehydration of subducted crust, especially in flat slab settings, can also metasomatize and weaken the mantle lithosphere, allowing it to founder (Kusky et al., 2014).
Many proposed drips have also been interpreted as delamination events (Figure 1, inset), including the Southern Sierra Nevada (e.g., Liang et al., 2014). In our view, these debates represent opportunities for geodynamic models to provide detailed predictions for each scenario and identify specific observations that may be able to falsify one hypothesis or the other in a given location.

Directions for Future Research
The primary geologic evidence for lithospheric dripping includes surface uplift, surface subsidence, hydrous or potassic mafic volcanism, silicic volcanism, mantle xenoliths, and upper-crustal deformation (Figure 11). This full suite of evidence, however, is rarely reported in support of a purported dripping event (Table 1). Numerical and analogue models are critical to our understanding lithospheric dripping (Section 2.3), but the full range of outcomes expected from dripping remains unexplored. Tectonic deformation seems to be key for triggering lithospheric dripping (Section 3.3), but background tectonic stresses are rarely incorporated into models of lithospheric dripping. Superimposing regional compression or extension is applicable to most lithospheric drips discussed above, especially those in continental rifts (e.g., Central Nevada [#4]) or orogens (e.g., Southern Puna [#15]). In the context of mantle plumes, Burov and Gerya (2014) found that a small, background extensional stress dramatically altered the patterns of upper-crustal deformation associated with plume impingement (Burov & Gerya, 2014). We hypothesize a similarly complex interaction with background stresses for lithospheric dripping.
Modeling experiments can also compare and contrast the effects of dripping, delamination, and related processes (Beall et al., 2017;Göğüş & Pysklywec, 2008;Krystopowicz & Currie, 2013;. Similar studies in the future should include flat slab subduction, slab breakoff, or other processes that directly compete against the lithospheric dripping hypothesis in a specific location. Drip-related uplift and subsidence provides another topic for which coupled geodynamic and landscape evolution models (e.g., Beucher et al., 2019) may be useful. A key challenge of such models is the requirement that the topographic surface respond freely and accurately to geodynamic stresses, which becomes unwieldy in three dimensions (Crameri et al., 2012;Kaus et al., 2010). Improving the numerical performance of rheological formulations is a topic of current work (e.g., Duretz et al., 2020;Spiegelman et al., 2016), as is finding more efficient algorithms for solving nonlinear systems (e.g., Fraters et al., 2019). A semi-analytical propagator matrix approach, for example, allows a wide range of parameter space to be explored in a computationally efficient manner and is applicable three-dimensional domains (Mondal & Korenaga, 2017). Some geomorphological techniques are well suited to study these topographic effects. For example, the record of Colorado River incision in the Grand Canyon (western U.S.) inferred by Karlstrom et al. (2008) suggests northward propagating incision, in agreement with seismic anomalies interpreted as northward-foundering material (Section 3.2.6; Levander et al., 2011). In the Colorado River system more broadly, knickzones and rapid incision rates often correspond to seismic anomalies and other geologic data indicative of dynamic upper mantle processes (Karlstrom et al., 2012). At a regional scale, Roberts et al. (2012) lend support to the general idea of "gradual convective removal of the lithosphere" beneath the western U.S. by inverting the profiles of major drainage systems. River profile analysis (Krugh & Foreshee, 2018), uplifted marine deposits (Göğüş et al., 2017;Schildgen et al., 2012), and paleoelevation studies (Garzione et al., 2006(Garzione et al., , 2014Sundell et al., 2019) show how quantitative landscape analyses can be used to test or refine hypotheses related to lithospheric dripping.
The interactions among crustal thickening, upper crustal burial or exhumation, and heat flux from the mantle creates a complex thermal setting during a lithospheric dripping event. In some cases, low-temperature thermochronology may provide an independent test of the dripping hypothesis. Low-temperature thermochronology data have been used to constrain the timing and location of lithospheric dripping in the Arizaro Basin DeCelles, Carrapa, et al., 2015), Southern Sierra Nevada (M. R. Cecil et al., 2014;McPhillips & Brandon, 2010), and the Southern Puna . These studies suggest that both heating driven by burial and cooling driven by exhumation can be detected, even in the upper crust. Dripping would affect the temperature of the middle to lower crust even more strongly, whether through removal of the mantle lithosphere (e.g., R. W. Kay & Kay, 1993), or through the increased radiogenic heating of a locally thickened crust (e.g., Huerta et al., 1998). High-temperature thermochronometers can record thermal perturbations to the lower crust (Blackburn et al., 2011) and have been used to record heating by mantle plume impingement and lithosphere removal in the 1.1 Ga Midcontinent Rift System of North America (U-Pb in rutile and apatite; Edwards & Blackburn, 2018). Similar techniques may be able to investigate the occurrence of lithospheric dripping in the geologic past if crustal rocks are exposed by later volcanism or exhumation. Geodynamic models can also be used to generate time-temperature predictions that can be tested by reverse thermal modeling of thermochronological data (e.g., Ketcham, 2005).
Igneous rocks provide important evidence for lithospheric dripping (Table 1), but most geodynamic models do not incorporate melt generation and migration. This limits the ability of geodynamic models to investigate devolatilization and drip melting (Elkins-Tanton, 2007). Such models could also be useful for placing tighter constraints on the timing and spatial extent of volcanism relative to drip detachment. Multiphase (i.e., solid and liquid) flow models, in addition to melt migration, can shed light on interactions between geodynamics and the fluid-mediated metamorphic and metasomatic processes that produce negatively buoyant lithologies such as eclogite (Austrheim, 1990) or pyroxenite (Furman et al., 2016), potentially linking lithospheric foundering to slab dehydration and aqueous fluid migration (e.g., Wilson et al., 2014).
Geochemical fingerprinting of pyroxenite melting is a topic of ongoing geochemistry research (Ducea et al., 2021;Gall et al., 2021). The most commonly used proxy for garnet pyroxenite melting is the Zn/Fe ratio (Le Roux et al., 2010). Ratios of other transition elements, however, often do not unambiguously indicate pyroxenite melting, and these ratios may also be influenced by differentiation, slab fluids, and crustal contamination (Maro et al., 2017). Additional studies are needed to constrain the factors that influence the partitioning of Zn/Fe and other elements into partial melts in the context of lithospheric foundering. Nevertheless, transition metal partitioning does not shed light on the mechanism of melting. The positive correlation between melting depth and extent (proxied by normative olivine content and chromium concentration, respectively) (Holbig & Grove, 2008), which is expected for drip melts (Furman et al., 2016), is one way to distinguish between drip melting and scenarios such as adiabatic decompression melting, edge convection, and flux melting in a subduction wedge (Furman et al., 2016).
A promising technique is to analyze silicate melt inclusions trapped within individual volcanic crystals, such as olivine phenocrysts in porphyritic basalts (Salehi et al., 2020). The chemistry of melt inclusions is isolated from the surrounding magma by growth of the host crystal, and minerals that crystallize at different temperatures can in theory be used to investigate the evolution of magma chemistry over time. As one of the first minerals to crystallize in many mafic systems, olivine often hosts melt inclusions that preserve indicators of the magmatic source lithology (Salehi et al., 2020).
A relatively new technique for investigating lithospheric foundering is described by Dygert et al. (2019), who use laboratory relationships between differential stress and the grain size of recrystallized olivine in mantle xenoliths. When combined with geothermometry and olivine flow laws (Hirth & Kohlstedt, 2003), olivine grain size can yield estimates of the viscosity and strain rate of the lithosphere ( Van der Wal et al., 1993). Dygert et al. (2019) argued that low viscosity and rapidly deformed olivine xenoliths in the Lunar Crater Volcanic Field were indicative of deformation in the neck of a lithospheric drip (Central Nevada [#4]).

Conclusions
In this paper, we synthesize the literature related to lithospheric dripping to suggest that, in the upper crust and near-surface environment where most geologic observations are available, the process of lithospheric dripping displays two distinct tendencies, summarized as strong-crust and weak-crust drips. Whether a lithospheric dripping event results in syn-drip upper-crustal compression and subsidence (strong-crust) or syn-drip crustal thickening and surface uplift accompanied by upper-crustal extension (weak-crust) mainly depends on the strength of the crust relative to the mantle lithosphere. While additional research is necessary to fully understand the range of possible outcomes of lithospheric dripping, our synthesis suggests that continental lithosphere can produce both strong-crust and weak-crust drips, depending on the thermal, compositional, and mechanical structure of a particular region.
We compile evidence for all the proposed lithospheric dripping events on Earth identified to date, to the best of our knowledge, to infer wavelength, age of detachment, and associated geologic effects of each. Of the 27 proposed dripping events, we find that 13 display some evidence for the strong-crust style, while 9 display some evidence for the weak-crust style. Strong-crust drips may result in the formation of transient sedimentary basins in orogenic hinterlands, while weak-crust drips may result in surface uplift and extension. Other evidence such as volcanic and magmatic products, mantle xenoliths, and tomographic anomalies are associated with both types of drip. The identification of differing styles of lithospheric dripping in Earth's continental regions can provide insight into the long term (∼10 Myr) rheology of the continents, pinpointed to specific times and locations, and may thus be used to infer thermal or compositional states of the lithosphere. However, the evidence for many of the purported dripping events is sparse, especially concerning the timing of drip growth and detachment.
This work represents the first comprehensive synthesis of inferred lithospheric dripping events for Earth's continents. While the prevalence of lithospheric drips globally suggests that dripping is fundamental to continental geodynamics, lithospheric instability is closely linked to plate tectonics, at during the Cenozoic and Mesozoic, as all purported dripping events occurred in tectonically active regions. Interactions between plate tectonics and continental lithosphere, including metasomatism and eclogitization, crustal thickening in orogens, continental arc magmatism, continental collision, and potentially flat slab subduction, are likely required to trigger lithospheric dripping within a realistic timescale.

Data Availability Statement
No new data were generated in producing this review. Tabulated Rayleigh-Taylor instability analysis data are compiled from Turcotte and Schubert (2002); Conrad and Molnar (1997); Harig et al. (2008).