Correlation between the Fluctuations in Worldwide Seismicity and Atmospheric Carbon Pollution

The crucial stages in the geochemical evolution of the Earth’s crust, ocean, and atmosphere could be explained by the assumed low-energy nuclear reactions (LENR) that are triggered by seismic activity. LENR result in the fission of medium-weight elements accompanied by neutron emissions, involving Fe and Ni as starting elements, and C, N, O as resultants. Geochemical data and experimental evidences support the LENR hypothesis. A spectral analysis of the period 1955–2013 shows common cycles between interannual changes in atmospheric CO2 growth rate and global seismic-moment release, whereas the trending behavior of the atmospheric CO2 was in response to the anthropogenic emissions. Assuming a correlation between such seismic and atmospheric fluctuations, the latter could be explained by cycles of worldwide seismicity, which would trigger massively LENR in the Earth’s Crust. In this framework, LENR from active faults could be considered as a relevant cause of carbon formation and degassing of freshly-formed CO2 during seismic activity. However, further studies are necessary to validate the present hypothesis which, at the present time, mainly aims to stimulate debate on the models which regulates atmospheric CO2.


Introduction
Several geochemistry studies have demonstrated that the Earth's crust and atmosphere have undergone significant changes in their chemical composition over the last 4.5 billion years [1][2][3][4][5][6][7][8][9][10].Undoubtedly, one of the basic characteristics of the early stages of the Earth's formation was the presence of a highly toxic primordial atmosphere, very different the current one, of which the origin is still being investigated.Various hypotheses have been formulated regarding the variation in the atmospheric composition over the Earth's lifetime such as degassing from volcanism [11][12][13][14][15], heavy bombardment by asteroids [16,17], and production of free oxygen by cyanobacterial photosynthesis leading to the Great Oxidation Event [18][19][20], but none of them are fully convincing and conclusive.
On the other hand, the changes in element concentrations appear to be intimately correlated to the Earth's tectonic activity.Recent data on the composition time variations in the Earth's atmosphere have shown that CO 2 and H 2 O concentrations in the atmosphere increased dramatically during the Archean era, occurring 3.8 to 2.5 Gyr ago, between the tectonic plate formation and the most severe tectonic activity.This primordial carbon pollution is related to decreases in the concentrations of Fe and Ni as well as to increases in the concentrations of Si and Al that occurred in two step-wise transitions: 3.8 Gyr ago, at the beginning of tectonic activity, and then 2.5 Gyr ago, during the period of the most severe tectonic activity [21][22][23][24][25][26], as shown in Figure 1. , was produced by collecting information taken from [21][22][23][24][25][26]; more details are reported in [28]).
Successively, between 2.5 and 2.0 Gyr ago, N2 and O2 concentrations increased sharply (Great Oxidation Event) in concomitance with the most relevant formation of the Earth's continental crust [18][19][20].Thus, a significant coupling appears between the periods of intense tectonic activity and the sudden increments of CO2 (and H2O), occurred 3.5 Gyr ago, and later, 2.5 Gyr ago, of N2 and O2 levels, in the atmospheric composition over the Earth's lifetime [1,19,20] (see Figure 2).
The chemical balances underlying the geochemical evolution of the Earth's crust, ocean, and atmosphere can be considered as indirect evidences of recently hypothesized low-energy nuclear reactions (LENR) [27][28][29][30][31], occurring massively in the Earth's crust during periods of intense tectonic activity, and hierarchically organized into two different sets (see Tab. 12.2 p. 176 in [27]): where the atmospheric elements (C, N, O) can be regarded as results of the second set of reactions, involving Si, Al, and Mg as starting elements.In particular, the estimated Mg increment (3.2%, , was produced by collecting information taken from [21][22][23][24][25][26]; more details are reported in [28]).
Successively, between 2.5 and 2.0 Gyr ago, N 2 and O 2 concentrations increased sharply (Great Oxidation Event) in concomitance with the most relevant formation of the Earth's continental crust [18][19][20].Thus, a significant coupling appears between the periods of intense tectonic activity and the sudden increments of CO 2 (and H 2 O), occurred 3.5 Gyr ago, and later, 2.5 Gyr ago, of N 2 and O 2 levels, in the atmospheric composition over the Earth's lifetime [1,19,20] (see Figure 2).
The chemical balances underlying the geochemical evolution of the Earth's crust, ocean, and atmosphere can be considered as indirect evidences of recently hypothesized low-energy nuclear reactions (LENR) [27][28][29][30][31], occurring massively in the Earth's crust during periods of intense tectonic activity, and hierarchically organized into two different sets (see Tab. where the atmospheric elements (C, N, O) can be regarded as results of the second set of reactions, involving Si, Al, and Mg as starting elements.In particular, the estimated Mg increment (3.2%, according to [22]) is equivalent to the carbon content in the primordial atmosphere (particularly high in the form of CO 2 and CH 4 ).The second set of reactions in Eq.( 1), involving Mg as the starting element and C as the resultant, can be regarded as an alternative or a competing mechanism with volcanic degassing [11][12][13][14][15] by which tectonic forces added CO 2 to the atmosphere toward the end of the Hadean period [27,32].
Sci 2019, 1, 2 3 of 12 according to [22]) is equivalent to the carbon content in the primordial atmosphere (particularly high in the form of CO2 and CH4).The second set of reactions in Eq.( 1), involving Mg as the starting element and C as the resultant, can be regarded as an alternative or a competing mechanism with volcanic degassing [11][12][13][14][15] by which tectonic forces added CO2 to the atmosphere toward the end of the Hadean period [27,32]., was produced by collecting information taken from [21][22][23][24][25][26]; more details are reported in [28]).
Interestingly, a comparison between a very rough estimate and experimental evidences seems to support this hypothesis.First, assuming a mean density equal to 3.6 g/cm 3 and a thickness of ~60 km of the Earth's proto-crust, the mass increase in Mg (∼3.5 × 10 21 kg, corresponding to 3.2% of the mass of the proto-crust involved in the reaction), and therefore in C, implies a very high atmospheric pressure.Given a terrestrial surface area of 5.1 × 10 14 m 2 and conjecturing the same gravitational acceleration for the proto-Earth, a tentative value of ~660 atm was obtained for the atmospheric pressure.This very high value, which is plausible and consistent with the conditions prevailing between 3.8 and 2.5 Gyr ago, is corroborated by models presented for a CO2and CH4-rich primordial atmosphere that had ground level pressures of some hundred atm (∼650 atm, as was the value reported in [1]).
Interestingly, a comparison between a very rough estimate and experimental evidences seems to support this hypothesis.First, assuming a mean density equal to 3.6 g/cm 3 and a thickness of ~60 km of the Earth's proto-crust, the mass increase in Mg (~3.5 × 10 21 kg, corresponding to 3.2% of the mass of the proto-crust involved in the reaction), and therefore in C, implies a very high atmospheric pressure.Given a terrestrial surface area of 5.1 × 10 14 m 2 and conjecturing the same gravitational acceleration for the proto-Earth, a tentative value of ~660 atm was obtained for the atmospheric pressure.This very high value, which is plausible and consistent with the conditions prevailing between 3.8 and 2.5 Gyr ago, is corroborated by models presented for a CO 2 -and CH 4 -rich primordial atmosphere that had ground level pressures of some hundred atm (~650 atm, as was the value reported in [1]).
Furthermore, significant neutron emissions have been measured, both at the Earth's crust scale, during earthquake preparation stages (Figure 3) [33][34][35][36], and at the laboratory scale, during crushing tests on non-radioactive rock specimens.In the laboratory experiments, neutron and other forms of energy emissions were measured in correspondence to micro-and macro-fracturing [37][38][39][40][41], with the final considerable reduction in the Fe content consistently counterbalanced by an increase in the content of Al, Si and Mg [29,31].Further evidence supporting the link between seismicity and variations in the atmospheric CO2 is the spatial organization of the CO2 release from the ground in the Himalayas, Nepal, which were apparently controlled by large earthquakes [42].

Atmospheric CO2 and the Carbon Cycle
Carbon dioxide is an integral part of the carbon cycle, in which carbon is exchanged between the Earth's oceans, soils, rocks, and the biosphere at two different rates: the slow carbon cycle, which involves geochemical processes between the atmosphere, oceans, soils, rocks and volcanism; and the fast carbon cycle, which refers to the movement of carbon between the environment and living organisms in the biosphere, including photosynthesis and respiration [43].The slow-rate geochemical processes, including the formation and burial of carbonates, the burial of organic matter (on land or in the ocean), and volcanism have largely determined the flow of CO2 into and out of the atmosphere on multi-million-year time scales.As currently accepted, the reduction of atmospheric CO2 caused by these burial processes appears to be bound by tectonic processes, which return the carbon from the Earth's mantle and crust to the atmosphere through volcanic degassing (which became less frequent as the Earth's mantle progressively cooled).Later, the flow of atmospheric CO2 began to be controlled by other natural processes such as the origin and the expansion of forests, which caused increased burial of organic carbon by photosynthesis, and the respiration of living organisms, which added CO2 back into the atmosphere [44,45].
In the pre-industrial era, the flow of atmospheric CO2 was considered to be largely in balance, with natural sources of CO2 nearly balanced by natural CO2 sinks.Since the Industrial Revolution however, anthropic activity has perturbed the carbon cycle due to the direct addition of carbon to the atmosphere from the burning of fossil fuels and land-use changes (mainly deforestation).According to carbon cycle models [46], about 57% of the anthropogenic CO2 emissions should be In the laboratory experiments, neutron and other forms of energy emissions were measured in correspondence to micro-and macro-fracturing [37][38][39][40][41], with the final considerable reduction in the Fe content consistently counterbalanced by an increase in the content of Al, Si and Mg [29,31].Further evidence supporting the link between seismicity and variations in the atmospheric CO 2 is the spatial organization of the CO 2 release from the ground in the Himalayas, Nepal, which were apparently controlled by large earthquakes [42].

Atmospheric CO 2 and the Carbon Cycle
Carbon dioxide is an integral part of the carbon cycle, in which carbon is exchanged between the Earth's oceans, soils, rocks, and the biosphere at two different rates: the slow carbon cycle, which involves geochemical processes between the atmosphere, oceans, soils, rocks and volcanism; and the fast carbon cycle, which refers to the movement of carbon between the environment and living organisms in the biosphere, including photosynthesis and respiration [43].The slow-rate geochemical processes, including the formation and burial of carbonates, the burial of organic matter (on land or in the ocean), and volcanism have largely determined the flow of CO 2 into and out of the atmosphere on multi-million-year time scales.As currently accepted, the reduction of atmospheric CO 2 caused by these burial processes appears to be bound by tectonic processes, which return the carbon from the Earth's mantle and crust to the atmosphere through volcanic degassing (which became less frequent as the Earth's mantle progressively cooled).Later, the flow of atmospheric CO 2 began to be controlled by other natural processes such as the origin and the expansion of forests, which caused increased burial of organic carbon by photosynthesis, and the respiration of living organisms, which added CO 2 back into the atmosphere [44,45].
In the pre-industrial era, the flow of atmospheric CO 2 was considered to be largely in balance, with natural sources of CO 2 nearly balanced by natural CO 2 sinks.Since the Industrial Revolution however, anthropic activity has perturbed the carbon cycle due to the direct addition of carbon to the atmosphere from the burning of fossil fuels and land-use changes (mainly deforestation).According to carbon cycle models [46], about 57% of the anthropogenic CO 2 emissions should be removed from the atmosphere by the biosphere (vegetation and land) and oceans, which behave as carbon sinks.
As current atmospheric CO 2 levels exceed measurements from the last 800,000 years, according to artic ice core measurements [47], and are rising quickly, anthropogenic perturbation of the global carbon cycle is considered to be the only attributing factor to the dramatic increase in CO 2 as well as that of the other greenhouse gases of the contemporary Earth's atmosphere [48,49].In accordance with this paradigm, the global carbon budget, describing the exchanges of CO 2 between the atmosphere and the other major carbon reservoirs, is currently given by the following balance equation: atm growth = fossil fuel + land use change − ocean sink -land sink (2) where geochemical terms are usually neglected, as their rate is considered too slow to have some relevance on the atmospheric CO 2 concentration over hundred-or thousand-year timescales, or because they became relatively infrequent, like volcanism.However, some doubts remain regarding the balance of this equation, because the ocean sink is estimated by a combination of global ocean biogeochemistry models and the land sink is often estimated from the residual of the other budget terms [48].With regard to the latter point, recent studies suggest that the role of tropical forests may have been previously very poorly quantified, and indicate a terrestrial tropical carbon sink larger than the previous estimates [50,51].Accounting for this finding while balancing the global carbon cycle implies that the currently considered carbon sources are larger [52], and/or that other carbon sources need to be considered in the budget.It must be said that some extra sources, missing in the balance, can also be caused by the human activity, such as the increasing acidification of the oceans, which makes them carbon sources as well.

Data Analysis
When observing the relationship between the anthropogenic CO 2 emissions and the atmospheric CO 2 growth rate (compare diagrams in Figure 4A,C), plotted in GtC/year −1 from 1955 to 2013 (the choice of the period was motivated by the need for comprehensive and reliable data, available online at https://earthquake.usgs.gov/earthquakes/search/and at http://www.globalcarbonproject.org/ carbonbudget/archive.htm#CB20147), some evidences cast some doubts on the belief that anthropogenic emissions effectively drive all atmospheric CO 2 growth [53-55]:

•
The significant acceleration in the anthropogenic emission rate, largely due to China's contribution, observed since 2002 was not reflected in the analogous trend of atmospheric CO 2 , and yet continued its steady growth; • the downward trend of atmospheric CO 2 was seen in some periods, especially from 1988 to 1993, despite the continuous growth of the anthropogenic emissions; and • intensive cyclic fluctuations around the trend line were observed for the atmospheric CO 2 growth rate whereas the increase of the anthropogenic CO 2 emission rate was smoother.
However, it can be argued that the atmosphere, as a part of a complex system which includes oceans and lands, may give a delayed answer to a perturbation, such as the change in CO 2 emission.Instead, there are scientific evidences about changes in atmospheric composition connected to tectonic activity [56], and neutron emissions observed in correspondence to fracturing at the laboratory and Earth's crust scales.Consistently, the hypothesized relationship between LENR and neutron emissions from active faults may be regarded as the principal cause of magnesium depletion and related carbon formation (according to table 12.2, page 176 in [27]) during events connected to tectonic plate formation.The consequent degassing of freshly-formed CO 2 depends on concomitant factors, such as the presence of anomalous heat flux below Earth's crust and crustal thinning.Furthermore, since there are evidences of big tectonic activity (with related extra CO 2 emissions) which didn't bring to any earthquake, it also has to be said that tectonic activity and earthquakes are not synonymous.However, it was worth investigating the possible relationship between the atmospheric CO 2 growth rate and the global seismic-moment release rate (Nm/year −1 , newton-meters per year), although several studies focused on temporary and localized CO 2 emissions connected to seismic activity [57,58].
Accordingly, a comparison of the rates of anthropogenic CO 2 emission, global seismic-moment release (calculated from data provided by the USGS Earthquake Hazards Program [59]), and atmospheric CO 2 growth (refer to xls files in Global Carbon Budget Archive [48]) showed that all the considered time series display an upward trend, linear for atmospheric and anthropogenic data, but quadratic for seismic data (Figure 4A-C).between the atmospheric CO2 growth rate and the global seismic-moment release rate (Nm/year −1 , newton-meters per year), although several studies focused on temporary and localized CO2 emissions connected to seismic activity [57,58].Accordingly, a comparison of the rates of anthropogenic CO2 emission, global seismic-moment release (calculated from data provided by the USGS Earthquake Hazards Program [59]), and atmospheric CO2 growth (refer to xls files in Global Carbon Budget Archive [48]) showed that all the considered time series display an upward trend, linear for atmospheric and anthropogenic data, but quadratic for seismic data (Figure 4A-C).However, it is worth noting that anthropogenic CO2 emissions exhibited low-amplitude fluctuations when compared to those of the atmospheric CO2 growth rate (compare Figure 4A,C), that is, up to one order of magnitude smaller when considering peak-to-peak excursions.However, it is worth noting that anthropogenic CO 2 emissions exhibited low-amplitude fluctuations when compared to those of the atmospheric CO 2 growth rate (compare Figure 4A,C), that is, up to one order of magnitude smaller when considering peak-to-peak excursions.
A further comment results when considering the periodicities hidden in the fluctuations of the time series.The fast Fourier transform (FFT) analysis of residual data, obtained by subtracting the trend component (identified by a simple curve-fitting approach) from the actual data, showed that the low-frequency components (approximately lying in the 0-0.15/year −1 interval) in the anthropogenic emission spectrum prevail over higher frequencies.This was unlike more uniform mixtures of components in seismic-moment release and atmospheric CO 2 spectra, where spectral peaks appeared at high frequencies as well (compare FFT diagrams in Figure 5).A further comment results when considering the periodicities hidden in the fluctuations of the time series.The fast Fourier transform (FFT) analysis of residual data, obtained by subtracting the trend component (identified by a simple curve-fitting approach) from the actual data, showed that the low-frequency components (approximately lying in the 0-0.15/year −1 interval) in the anthropogenic emission spectrum prevail over higher frequencies.This was unlike more uniform mixtures of components in seismic-moment release and atmospheric CO2 spectra, where spectral peaks appeared at high frequencies as well (compare FFT diagrams in Figure 5).As shown in Figure 5A, the anthropogenic time series exhibited a dominant spectral peak at 0.05/year −1 , equivalent to a 20-year period, which did not correlate with the atmospheric CO2 fluctuations as this periodicity is not relevant in the atmospheric spectrum (observe the fourth spectral component of atmospheric CO2 data in Figure 5C).Conversely, the atmospheric fluctuations exhibited a main periodicity of 3.7 years that was almost absent in the anthropogenic emission spectrum.This discrepancy loosens, partly, the bond between anthropogenic emissions and the atmospheric CO2 growth rate.
Instead, the 3.7-year periodicity was relevant in both the atmospheric CO2 growth rate and in the seismic-moment release rate spectra, as well as other periodicities such as the 2.5-year spectral peaks (see Figure 5B,C).Then, residuals are subjected also to coherence analysis [60] to find out more As shown in Figure 5A, the anthropogenic time series exhibited a dominant spectral peak at 0.05/year −1 , equivalent to a 20-year period, which did not correlate with the atmospheric CO 2 fluctuations as this periodicity is not relevant in the atmospheric spectrum (observe the fourth spectral component of atmospheric CO 2 data in Figure 5C).Conversely, the atmospheric fluctuations exhibited a main periodicity of 3.7 years that was almost absent in the anthropogenic emission spectrum.This discrepancy loosens, partly, the bond between anthropogenic emissions and the atmospheric CO 2 growth rate.
Instead, the 3.7-year periodicity was relevant in both the atmospheric CO 2 growth rate and in the seismic-moment release rate spectra, as well as other periodicities such as the 2.5-year spectral peaks (see Figure 5B,C).Then, residuals are subjected also to coherence analysis [60] to find out more systematically on which frequencies the spectral coherence appears between an input x(t) and an output y(t) time series, i.e., on which frequencies the output responds on the input.The spectral coherence Cxy(f) (or normalized cross-spectral density) is defined as: where Gxy(f) is the cross-spectral density between x and y, and Gxx(f) and Gyy(f) the auto-spectral density of x and y respectively.Here, Cxy(f) is calculated to estimate the degree of relationship between the perturbation x (the anthropogenic or the seismic time series) and the answer y (the atmospheric time series) in the frequency domain.
Coherence diagrams of Figure 6 differentiate mainly in the interval 0.2-0.4year−1, where the spectral coherence between seismic and atmospheric data is higher than that between anthropogenic and atmospheric data, consistently with the previous observations.High-coherence values between 0.2 and 0.4 year −1 reflect relevant common cycles between 2.5 and 5 years in the spectrum of both seismic and atmospheric fluctuations, almost absent in the anthropogenic time series.Thus, short-range atmospheric CO 2 fluctuations seems better correlated with seismic than anthropogenic activity.Unfortunately, the narrowness of the considered time window does not allow to grasp possible and, in a sense, expected long-term effects of the seismic activity.systematically on which frequencies the spectral coherence appears between an input x(t) and an output y(t) time series, i.e., on which frequencies the output responds on the input.The spectral coherence Cxy(f) (or normalized cross-spectral density) is defined as: where Gxy(f) is the cross-spectral density between x and y, and Gxx(f) and Gyy(f) the auto-spectral density of x and y respectively.Here, Cxy(f) is calculated to estimate the degree of relationship between the perturbation x (the anthropogenic or the seismic time series) and the answer y (the atmospheric time series) in the frequency domain.Coherence diagrams of Figure 6 differentiate mainly in the interval 0.2-0.4year−1, where the spectral coherence between seismic and atmospheric data is higher than that between anthropogenic and atmospheric data, consistently with the previous observations.High-coherence values between 0.2 and 0.4 year −1 reflect relevant common cycles between 2.5 and 5 years in the spectrum of both seismic and atmospheric fluctuations, almost absent in the anthropogenic time series.Thus, short-range atmospheric CO2 fluctuations seems better correlated with seismic than anthropogenic activity.Unfortunately, the narrowness of the considered time window does not allow to grasp possible and, in a sense, expected long-term effects of the seismic activity.

Conclusions
The presented results derive from geochemical studies on the chemical evolution at the Earth's scale that affected the mantle, crust, and atmosphere during the periods of the most severe tectonic activity, and were corroborated by experimental evidences of neutron emissions during rock fracture and the concomitant changes in element concentrations in the specimens.
It is important to note that the conventional assumptions in relation to the migration of chemical elements do not imply the nearly perfect satisfaction of the mass balances, whereas the chemical balances among the most abundant elements derived from geochemical data are considered as indirect evidences of conjectured LENR reactions.The atmospheric elements (C, N, O) can be regarded as the results of a set of reactions, involving Si, Al, and Mg as starting elements, that are massively triggered by tectonic activity.In particular, this conjecture not only accounts for atmospheric CO 2 formation and its variations over the Earth's lifetime, but could also provide an explanation for some of the observed anomalies in the correlation between the atmospheric CO 2 growth rate and the anthropogenic emission rate.
By examination of the time series, fluctuations in the atmospheric CO 2 growth rate cannot be explained in terms of low-amplitude anthropogenic emission fluctuations (nearly an order-of-magnitude difference).Furthermore, the main periodicities of these two phenomena are different.
Although variations in climate variables are recognized as important drivers of the interannual variability of the atmospheric CO 2 growth rate [61], common cycles are found between atmospheric and seismic variables.In the light of the aforementioned LENR, such atmospheric CO 2 fluctuations may be ascribed to the cycles of the worldwide seismicity.
Obviously, in absence of any causality analysis, the performed spectral analysis does not permit to say anything conclusive about the reciprocal causality relation between these indicators.This study simply aims to open a debate on the models which regulates the atmospheric CO 2 levels, by suggesting more detailed investigations of the oscillations in climate variables and their correlation with other variables connected to Earth's activity.

Figure 2 .
Figure 2. Variation in the atmospheric composition over the Earth's lifetime.During the Archean era, about 15% of the Earth's atmosphere was constituted by carbon dioxide (CO 2 ), and the remaining part was mainly composed by water vapor (H 2 O) (the picture, extracted from [27], was produced by collecting information taken from[21][22][23][24][25][26]; more details are reported in[28]).

Figure 3 .
Figure 3. (A) Seismic activity and neutron flux measurements in the period 1975-1987 (Kola Peninsula, Russia [33]); (B) Typical time correlation between fitting distributions of neutron flux measurements at the Murisengo gypsum mine, and a local seismic swarm (magnitude 3.2 main shock) [36].

Figure 3 .
Figure 3. (A) Seismic activity and neutron flux measurements in the period 1975-1987 (Kola Peninsula, Russia [33]); (B) Typical time correlation between fitting distributions of neutron flux measurements at the Murisengo gypsum mine, and a local seismic swarm (magnitude 3.2 main shock) [36].

Figure 4 .
Figure 4. (A) Time series plots (1955-2013) of annual anthropogenic CO 2 emissions; (B) global seismic-moment release; (C) and the atmospheric CO 2 growth rate.Trend lines are in black.

Figure 5 .
Figure 5. (A) FFT spectra of the de-trended time series for: Anthropogenic CO2 emissions; (B) the global seismic-moment release rate; (C) and the atmospheric CO2 growth rate.Note the discrepancy between the main peaks of anthropogenic (20-year) and atmospheric (3.7-year) spectra, and the peaks shared by the seismic and atmospheric spectra (e.g., at 2.5 and 3.7 years).

Figure 5 .
Figure 5. (A) FFT spectra of the de-trended time series for: Anthropogenic CO 2 emissions; (B) the global seismic-moment release rate; (C) and the atmospheric CO 2 growth rate.Note the discrepancy between the main peaks of anthropogenic (20-year) and atmospheric (3.7-year) spectra, and the peaks shared by the seismic and atmospheric spectra (e.g., at 2.5 and 3.7 years).