A MODEL FOR THE ATTENUATION OF PEAK GROUND ACCELERATION IN NEW ZEALAND EARTHQUAKES BASED ON SEISMOGRAPH AND ACCELEROGRAPH DATA

A combination of weak-motion velocity data from seismographs and strong-motion acceleration data from accelerographs has been used to model the attenuation of peak ground acceleration (PGA) in New Zealand earthquakes. The resulting model extends the PGA attenuation model of Zhao, Dowrick and McVerry [30] to include the variability of rock strength, and also describes the unusually high attenuation in the volcanic zone of the North Island of New Zealand.


INTRODUCTION
A reasonably robust model for the attenuation of PGA in New Zealand has been derived recently by Zhao, Dowrick and Mc Verry [30].In it they express PGA as a function of moment magnitude, distance from source, depth, focal mechanism, tectonic type of earthquake and site ground class.from recorders directly on moderately strong rock (greywacke or limestone).Twenty records were from recorders on weak rock (weathered greywacke or siltstone).The model of Zhao et al. is, therefore, not well suited for providing estimates of PGA at the sites of some important engineering structures, hydro dams for instance.
The model is a notable first for New Zealand and reliably covers several aspects of PGA attenuation, but does suffer somewhat from lack of data from genuine rock sites.This is not surprising as the model is based entirely on data from strongmotion accelerographs, the majority of which are located on the type of site of greatest relevance to New Zealand construction, i.e. alluvium.Only 17% of the data used in the study was from "Class A" sites, where "Class A" was defined by Zhao et al. as either rock-outcrop (11 % of data) or soil layer of up to 3 metres overlying bedrock (6% of data).Importantly only five records, I% of the New Zealand dataset, were from recorders mounted directly on very strong rock (granite, schist or quartz) and three A second difficulty relates to the distance range of the data used.The New Zealand data, 461 recordings from 51 earthquakes, were recorded at source-to-site distances of 10 to 570 km with the bulk of the data lying in the 30 to 200 km range.Two problems with this data distribution are (i) a lack of control on the shape of the attenuation function both in the very important near-field and at distances above 200 km and (ii) the potential for bias at distances above about 200 km.The lack of shape control arises because of the large scatter in the PGA data, and the potential bias because of the non-triggering of many recorders at the greater distances.Geological & Nuclear Sciences, Lower Hutt, NZ, (Member) BULLETIN OF THE NEW ZEALAND SOCIETY FOR EARTHQUAKE ENGINEERING, Vol.32, No. 4, December 1999 Legend Mw he (km) 0 7.0+ ] 0 6.0-6.9 0-20 0 5.0-5.9 6. 6.0-6.9 ] 21-50    6.0-6.9 ]
In contrast to the kinds of site used in strong-motion recording, those selected for the National Seismograph Network (NSN) (Figure 1) are nearly all on rock.In most cases the underlying rock is classified as either very strong (e.g.quartzite) or moderately strong (e.g.Greywacke) and in only a few cases as weak (e.g.siltstone).Hence it is an attractive proposition to use seismic recordings from the NSN to provide the missing rock data for PGA attenuation modelling.
Two other advantages of the NSN data arise from the relatively very high sensitivity of the seismographs.Firstly, the maximum source distance can be increased over that set for the Zhao et al. study,from 500 km to more than 1000 km, and secondly, recordings can be expected from all operational NSN stations for all significant earthquakes on or near the New Zealand landmass, which minimises any bias in the data that might be caused by non-triggered instruments.There is, however, a downside to the high sensitivity of the NSN stations in that they are easily overloaded and so the minimum source distance is about 50 to 150 km, depending of the magnitude of a given event.There is then a potential undesirable feature of largely non-overlapping data sets when the accelerograph and seismograph data sets are combined.
The instruments of the New Zealand accelerograph and seismograph networks are very different from each other and have quite different monitoring purposes.The accelerographs (strong-motion) measure acceleration and are intended to provide information on ground shaking that is strong enough to be damaging to buildings and other structures.Hence they are typically located on alluvial sites in or close to towns and urban areas.Many are located in structures (buildings, hydro dams and bridges) so as to measure the responses of the structures to strong ground shaking.The seismographs (weak-motion) usually measure ground velocity and are intended to provide information on earthquakes.They are much more sensitive than strong-motion recorders and are usually sited on rock well away from urban areas and other sources of seismic noise.
Hence there is a need to show that acceleration waveforms derived from the two types of instrument are sufficiently similar that peak ground accelerations derived from them can be combined for attenuation modelling.This is done in Section 3 where the instruments are described in more detail than above and the results of a period of simultaneous monitoring at one site are given.
Zhao et al. demonstrated that their model was suitable for all of New Zealand apart from the Central Volcanic Region of the North Island, labelled CVR in Figure I.They noted that there was an anomalously high level of attenuation in the CVR but did not have sufficient data to attempt to model it.Recently the high rate of attenuation has been confirmed and modelled for Modified Mercalli Intensity by Dowrick and Rhoades [11].
One reason for a lack of strong-motion data from the CVR is that the high attenuation there means that only rarely have amplitudes been sufficient to trigger strong-motion recorders located within the CVR, and only very rarely are there strongmotion recordings for which the path is completely through the CVR.In this regard the high sensitivity of the seismographs means that there is a significant number of weak-motion records for which the direct path is either partially or completely through the CVR.

Accelerograph (and acceleroscope) recording
Strong-motion recording in New Zealand is carried out with a variety of types of acceleroscope and accelerograph  (16-bit), and GSR-12/FB (12-bit).All are fitted with triaxial servo accelerometers of 2g full-scale capacity, have pre-event memory of at least 4 seconds, and real-time clocks.The sampling interval is 0.0ls for the DCA and 0.004 s for the IDS and GSR instruments.The dynamic properties of the servo accelerometers are critical damping ratio 0.7 and frequency range 0 to at least 30 Hz.
The acceleroscope is a two-component "scratch-plate" type.It gives a trace of the acceleration in the horizontal plane, allowing the amplitude and direction of the maximum horizontal acceleration to be determined.Acceleration is sensed with a damped pendulum and is recorded as a line scribed in a thin layer of smoke-blackened wax on a glass disk of 13 mm diameter.The scriber is a specially sharpened sewing needle.Peak accelerations can be read from the output scratch pattern, but no time information is available.

Seismograph recording
Digital seismograph recording in New Zealand is based on the triaxial Mark Products UC geophone (velocity transducer) and the locally manufactured EARSS digital data recorder [12].
The EARSS incorporates a gain-ranging amplifier, anti-alias filtering, AID conversion and sampling at either 0.01 or 0.02 seconds.The nominal natural frequency of the transducer is 1 Hz and the critical damping ratio 0.7, giving a velocity sensitivity that is essentially constant from 1.5 Hz to about 20 Hz [17].
One site, WEL (Figure 1), is monitored with a Kinemetrics triaxial force balance accelerometer (FBA) in place of the velocity transducer.Characteristics of the FBA are full scale 0.5g, output 5 volts/g, natural frequency 50 Hz and damping 0. 7 of critical.

Digitisation and computer processing
Several methods have been used for the digitisation of the film accelerograms over the last thirty years of monitoring.The earliest films were digitised point-by-point by hand using a travelling microscope, a method that was (thankfully) superseded by a commercial hand digitizer (Hewlett-Packard model 9874A), which in tum was superseded by an automatic curve follower based on a reflectance sensor attached to the pen carriage of a digital plotter.Currently film accelerograms are scanned with a Hewlett-Packard SCANJET scanner at a resolution of 600 d.p.i., and the resulting TIFF files are converted to vector format using SMA SCANVIEW software from Kinemetrics/Systems.
Routine computer processing of accelerograms consists of (i) conversion to standard units of acceleration using static sensitivity values and (film accelerograms only) correction for cross-axis effects [25], and (ii) correction for the dynamic frequency response of the accelerometer pendulums (film recorders only), and band-pass filtering.The dynamic corrections and filtering are carried out in the frequency domain [ 15].Aliasing is prevented by low-pass filtering at 25 Hz, and low-frequency noise is removed by high-pass filtering at, typically, 0. 15 to 0.5 Hz, with a transition bandwidth of 0.15 to 0.2 Hz and a sinusoidal transition function.The high-pass filter frequency is selected visually, on a record-by-record basis, by comparing the Fourier amplitude spectrum calculated from the accelerogram in question with an appropriate noise spectrum [9).The final sampling interval is 0.02 s.
Seismogram processing for the PGA attenuation study commenced with inspection of the velocity traces for clipping and other abnormalities.Traces that were free from abnormalities were then processed in the frequency domain as follows: differentiation to give acceleration time histories, dynamic instrument correction to extend the low-frequency limit to about 0.5 Hz, and high-pass filtering.A high-pass filter frequency of 0.5 Hz was found necessary for suppression of low-frequency noise.Low-pass filtering was not needed at this stage of processing because an anti-alias filter is built-in to the EARSS recorder.
Records from the FBA were treated similarly with the exception that no differentiation step was required.
Several of the seismograph velocity records were clipped, and because the clipped records tended to be the most valuable near-source ones in the seismograph dataset some effort was made to retain them.Fortunately, only peak accelerations were required for the attenuation modelling, and because the peaks in the derived acceleration records tended to occur close to the zero points of the original velocity records, clipping of the velocity records per se was not necessarily a problem.The following procedure was used to guide the retention or rejection of each clipped record.
Firstly, the time of the peak acceleration was located and a few second segment of the velocity trace surrounding that time was plotted for inspection and so that the dominant frequency could be estimated.Then the most likely cause of the clipping was determined, the possibilities considered being either the mechanical capabilities of the lAC transducer (±5 mm maximum displacement from rest position, 0.5 to 20 Hz frequency range) or the voltage input limit at the AID converter oftheEARSS system.
In all cases the cause of the clipping seemed to be the limit set by the voltage range of the AID converter.The dominant frequencies in the clipped records at the times of the peak accelerations were in the range 2 to 5 Hz, and at these frequencies the amplitudes of the recorded motions appeared to be well below the transducer's displacement limit.
For a few records the velocities and frequencies were such that the PGAs were clipped (i.e.adjacent velocity samples had +max.and -max.values).Those records were discarded.For about 25% of the clipped records the degree of clipping was minor.Those were processed in the frequency domain in the same manner as unclipped records.For the remaining records where the degree of clipping was moderate to severe, but accelerations did not appear to be clipped, the frequency domain processing did not seem to cope well with the truncated waveforms and so a simple l::,v/l::,t method of differentiation was used instead.

Comparisons
For a period of 4 months from late November 1994, an EARSS:lAC system and an IDS digital accelerograph were operated together in a concrete bunker at GNS's former Seismological Observatory at Kelburn, Wellington.For operational reasons the instruments had to be located in separate rooms of the bunker, but were less than 2 metres apart.Also in the bunker was the NSN site WEL which was equipped with a force balance accelerometer (FBA) and an EARSS recorder.
During the 4 month period six events were recorded simultaneously on the lAC and IDS systems.All 12 records were processed and the results compared visually using overlays of time history plots and Fourier amplitude spectra.
The results were as follows: • N90E component: excellent agreement for acceleration timehistories, Fourier amplitude spectra (especially.overthe frequency range 0.5 to 10 Hz), and PGAs.Discrepancies between the waveforms and peaks were at most minor, and often were clearly a result of the sampling process.
• NOOE component: there were some discrepancies between both time histories and Fourier spectra, but the correspondence appeared good enough for the purpose of deriving PGAs.
• UP component: although the two instruments were clearly trying to reproduce the same waveforms there were some significant differences between the traces for most of the records.The EARSS:lAC system appeared to have a significantly higher response than the IDS over the frequency range 12 to 15 Hz, and a lower response from 15 to 20 Hz.PGAs from the EARSS:lAC system were consistently higher than those from the IDS accelerograph.
PGAs derived from the two systems are compared in Table I.
Overall the results indicate that horizontal component PGAs derived from the EARSS:lAC system can be used with considerable reliability to supplement data derived from the strong-motion accelerographs.In fact, in some respects the similarity between the waveforms could be considered remarkable given the great differences between the two systems.
Three of the events, 5-2-95, 10-2-95 and 22-3-95, were also recorded by the EARSS:FBA system.Comparisons of PGAs showed (i) in the horizontal directions the EARSS:FBA system gave readings that were on average about 10% smaller than those from the other two systems, and (ii) in the vertical direction the EARSS:FBA system gave PGAs that were on average 5% larger than those from the EARSS:L4C system.
In summary, the above results suggest that horizontal PGAs derived from an EARSS:L4C system are quite adequate for the purpose of PGA attenuation modelling.

NEW ZEALAND EARTHQUAKES STUDIED
The earthquakes considered in the seismogram part of our study were a subset of those used by Zhao et al. for their strong-motion PGA attenuation study (30], i.e. the 25 events, post 1989, for which three-component digital seismogram data were available (Table 2).In common with the Zhao et al.
approach Mw was used as the measure of magnitude, and "depth to the centroid of rupture" as the measure of depth.The locations of the earthquakes are shown in Figure 1 and the distribution of depths and magnitudes in Figure 2(a, b).We also made use of the full Zhao et al. accelerogram dataset including their overseas data.

S. SEISMOGRAM DATA SET
A total of 328 weak-motion records were available from National Network stations, giving a seismograph PGA dataset potentially 70% as large as the Zhao et al. accelerograph dataset.For the period 1990 to 1995 inclusive the two datasets were almost equal in size.
In four of the records the accelerations were clipped and the records were therefore discarded.In a further 28 cases the velocities of at least one component were clipped, but the accelerations did not appear to have been artificially limited, and so the PGA values were retained in the dataset.
A further 50 seismograph records were obtained from a network that was deployed temporarily in the north-eastern part of the CVR, the Taupo Volcanic Zone (TVZ), during the period January 1995 to May 1995.Three major events were recorded by the temporary network, two centred offshore of East Cape on the 5 th and 10 th of February 1995, and one near Wellington on the 22 nd of March 1995 (events 48, 49 arid 50 of Table 2).
PGAs in the seismograph dataset ranged from 2 x 10-6 g to 0.076g, and source distances from 30 to 1320 km (Figure 2(b)).
Not all of the seismograph records were used directly in developing the attenuation model.In order to minimise the risk of bias all records at distances of more than 400 km from source were excluded from the modelling process.The reasons for this are discussed more fully later.Such data were however included in single-event attenuation plots as part of the process of evaluating the resultant models.The final modelling dataset contained 676 values.Of these 72% were from accelerographs and 28% from seismographs, with 40% of the total being from rock sites and 60% from soil sites.

3.
Event reference number as in Zhao et al. [30] Tectonic Type: C = crustal, 1 = inte,face, S = slab Predominant Source Mechanism: N = normal, R = reverse, S = strike-slip.(A mixed event, say partly R and partly S, is defined as predominantly R if the ratio of the components RIS is?: 1.0) Zhao et al. [30] found in their PGA study that only two categories could be separated with statistical significance, "rock" (combining subdivisions AR, AT and AV) and "soil" (combining subdivisions AL, B and C).Postulated "deep" and "soft" subdivisions of classes B and C were found not to be significant, and the scarcity of data from rock sites prevented any more detailed investigation of the "rock" subdivisions.
For the present study the "rock" category was initially subdivided into "very strong", "moderately strong" or "weak" according to the geological nature of the underlying materials.
Brief geological descriptions of the seismograph recording sites also are given in Appendix 1.For the National Seismograph Network eight sites are underlain directly by "very strong" rock, sixteen (the majority) by "moderately strong" rock and four by "weak" rock.
For the temporary array in the TVZ, seven sites were classified as "moderately strong" rock, six as "weak" rock, and six as "soil".However there are uncertainties about some of the TVZ site descriptions.For some it is not clear whether a "rock outcrop" is part of a substantial layer of rock or whether it is just the top of a large boulder.Site TEA V is one such site where the surrounding material is described as Taupo pumice alluvium but the instrument was apparently located on ignimbrite.For at least one other, PKUV, the site appeared to be at the edge of a substantial body of rock, but the wide range of possible shapes for the subterranean part of the body of rock meant that its seismic response class was very uncertain.

Ignimbrite (unwelded) Greywacke (moderately to completely weathered)
In principal many factors can be isolated and built-in to an attenuation model.Zhao et al. [30] modelled the effects of magnitude, distance, source depth, focal mechanism, tectonic type of the earthquake and site ground class.They discussed the high attenuation in the CVR but, because of a lack of suitable data, did not include the CVR effect in their model.Neither did they attempt to model directional effects, once again because a very much larger data set than theirs would have been required for satisfactory results.
The original aim of the seismogram study was to generate additional "rock" class data to supplement that available to the strong-motion PGA model of Zhao et al.As modelling progressed, however, it became very clear that the seismograph rock sites were different from the accelerograph rock sites.PGAs from the seismograph rock sites were on average significantly smaller than those from the accelerograph rock sites.The nature of the underlying rock seemed to be an important factor, and the testing of various approaches suggested that, within the limits of the data available, a satisfactory model could be derived if three ground classes were defined as follows: • strong rock; • weak rock; comprising classes "very strong rock" and "moderately strong rock" as described in section 6 above, comprising the class "weak

Directional effects
Directional effects sometimes seemed to play a significant role.For example, PGAs from the Tikokino earthquake of 11 April 1993 showed a variation in amplitude as a function of direction that was clear in both accelerograph and seismograph data.
Comparing PGAs derived from seismograms recorded at fairly similar epicentral distances at the strong-rock sites MNG,

201
MRZ, OIZ and URZ (Figures 3, 4), the PGA values from sites MNG and MRZ located south-west of the epicentre were close to the apparent trend line for the bulk of the data, the value from site OIZ located to the north-west was a factor of about 6 below the trend line, and that from site URZ located to the north-east was below the trend line by factor of about 3. Note that site KUZ was subject to both directional and CVR effects hence the PGA value from there was very low, and also that the most direct path to site OIZ was through southern-most the tip of the CVR.
There did not seem to be any evidence in the seismogram data for frequency dependence in the variation of attenuation with direction, rather that amplitudes recorded in the low amplitude directions seemed to be reduced across the whole frequency band of interest (Figure 5).
Tikokino earthquake (11 April 1993)  ---:---: . ' .' ' ::I:f :I :::::::::::::;::::::f ::~~~T;:::  Direction-dependent attenuation seemed to be indicated by data from several other earthquakes of the seismograph dataset but, as noted by Smith [26) in studies of MM futensity attenuation, the directions of "high" attenuation varied in different regions of New Zealand.Assuming that the directional effect could be regarded as a relatively high level of attenuation along some paths, the following patterns were noted: for earthquakes centred in the north-west part of the South Island, PGA' s from sites on the east coast of the South Island (ODZ, MQZ, L1Z and KHZ) showed signs of relatively high attenuation, for earthquakes centred near Cape Palliser some sites in the south-west (KHZ, L1Z, but not WVZ) indicated relatively high attenuation, and for earthquakes on the east coast of the North Island, from Castlepoint to Gisborne, recording sites in the north west, excluding those screened by the CVR, suggested relatively high attenuation.
The above patterns are consistent with the orientations of the elliptical isoseismal lines modelled by Smith [26], and in some of the cases where the strikes of the fault ruptures were known, also consistent with the model of Dowrick and Rhoades [11).There were, however, many inconsistencies in the data and this, coupled with our belief that we had insufficient data for a rigorous study of the directional effects, led to a decision not to attempt to model the effects but rather to simply note that they existed.

Effect of the Volcanic Region
It has long been claimed that seismic waves propagating through the volcanic region of the North Island are subject to anomalously high attenuation [ 11, 13 , 18 ,24].Note that here we are using the term "volcanic region" rather than CVR or TVZ because one of the topics for investigation is the boundary of the anomalous zone.Zhao et al. [30] excluded data that might have been affected by the anomalous attenuation from the derivation of their model and simply showed that such data did indeed have a mean value significantly lower than the mean value of the remaining data.Nineteen of the accelerograph records were affected.
Thirty-six records from the weak-motion NSN data set, 11 % of the total, seemed to be affected by the anomalous attenuation.Symptoms were greatly reduced amplitude and less highfrequency content in comparison with "normal" records (Figures 6 and 7).The reduction in amplitude was quite dramatic, as illustrated by PGAs resulting from the Offshore East Cape earthquake of 5 Feb 1995.The most direct travel paths to sites KUZ, WLZ, OIZ and MRZ were through the volcanic region, and the PGAs recorded at those sites were approximately an order of magnitude below those recorded at similar source distances at the "normal" sites (Figure 6).Note that the PGA from site MOA can probably be regarded as higher than normal for the seismograph dataset because, as is discussed later, MOA is underlain by rock of weak strength, and also that sites WCZ and RUZ (Figure 1) were not instrumented at the time of the 5 th February 1995 earthquake.
A detailed explanation of the anomalous attenuation is beyond the scope of the present paper.Suffice it to say that a selective attenuation of the high frequency components of the seismic signal may be a major reason.Low frequency components, 0.5 to 0. 7 Hz (Figure 7) did not appear to be highly attenuated during passage through the volcanic region, whereas higher frequency components did.
Our first task in modelling the effect was to define the boundaries of the anomalous region.We considered three models of the volcanic region proposed previously for other purposes, namely the "CVR", the "whole TVZ", and the "young TVZ", where "CVR" stands for "Central Volcanic Region" and "TVZ" for "Taupo Volcanic Zone" [27).The CVR (Figure 8) is a somewhat arbitrary wedge-shaped zone with its § ~ 203 apex at Mt Ruapehu and the eastern and western sides respectively passing through Whakatane and close to the Coromandel Peninsula.The "young" and "whole" TVZs in contrast have boundaries that closely follow various known volcanic centres.They have common eastern and southern boundaries, but the whole TVZ extends further to the northwest than does the young TVZ.The young TVZ encompasses volcanic centres thought to have been active during the last 340,000 years, and for the whole TVZ those active during the last 2 million years [27]. :::::::::::::::::::::j:::::[:::j::::::~KHZ::::::::::: :::::::::~f.ti()l:Z(-)-~••fr:z::::::_:

Figure 6: Example of high attenuation in the volcanic region of the North Island. The direct travel paths from the 5 February earthquake to sites KJJZ, WLZ, OIZ and MOZ were all through the volcanic region, and the PGAs were clearly very much reduced in comparison to those recorded at locations not affected by volcanic paths. All of the recording sites were on rock.
As a way of selecting the "best" boundaries forthe anomalous region we first derived an attenuation model using records that appeared not to have passed through it.We then used that "normal" attenuation model to estimate PGAs for those records that did appear to be affected by the volcanic region, and examined the ratio "recorded/estimated" PGA as a function of direct path length through each of the model zones.Only those paths which we considered to be well defined were included in the analysis.By "well defined" we mean that the angles of incidence at any of the boundaries were greater than about 30° so that we could safely ignore the effects of refraction at the boundaries.In time a more sophisticated model that takes into account other factors such as refraction will be developed, but that is beyond the scope of the present paper.Records with source-to-site distances greater than 400 km also were excluded.

MOZ Figure 7: Time histories and Fourier spectra from the Off East Cape earthquake of 5 February 1995 illustrating the selective reduction of high frequency components in the seismic signal that had passed through the volcanic region. The effect is clearly evident even in the time-histories. Note the variation in Y-axis scales for the time-history plots.
The results, Figure 9, provided some useful guidance, as follows.
The CVR model (Figure 9(a)) gave a mean PGA ratio that first increased and then decreased as the apparent path length was increased.This seemed less realistic than for the other two models where the PGA ratio steadily decreased with increasing path length.
The points labelled "A" in Figure 9(a), which are associated with the paths labelled "A" in Figure 7, seemed as a group to have somewhat below-average PGAs, indicating at least a moderate length of path within a highly attenuating zone.This suggests that the two TVZs provide a better southern boundary for the highly attenuating zone than does the CVR.
Some of the data points labelled "B" in Figure 9(a) are associated with event 47 (point "B" in Figure 8).
The group average ratio of about 1 suggests a nonvolcanic location for the event, which is a point in favour of the eastern boundary of the TVZ rather than that of the CVR as an eastern boundary to the anomalous zone.Event 47 was well recorded by permanent stations in the New Zealand seismograph network, and also by two additional 3-component EARSS:I.AC instruments and two arrival time detectors that had been deployed temporarily in the eastern Bay of Plenty.Hence the uncertainty in the location of event 47, estimated to be about 5 km in the north-south direction and less than 5 km eastwest, is better than average for events in the Bay of Plenty (T.Webb, personal communication 1999).[27]).The labelled paths and locations, which have corresponding labelled data points in Figure 9, can be used to help define the most likely boundaries of the zone of high attenuation.The reasoning is given in the text.------7![!'~----* --t--------------------------------------+--5-1cr0-~t!.!.\- -,-~--~-----------------------------I e F e el Young TVZ path length (km)

I e e ----t------------------f----------------------
Figure 9: Reduction in PGA with length of path through each of the three volcanic zone models.The estimated (or reference) PGAs were calculated using an attenuation model that did not make any allowance for the high attenuation within the volcanic zones.Problems with the CVR model are (i) the depressed level of mean PGA at O km, (ii) the increase in PGA from O to 20 km, (iii) the comparatively large degree of scatter, and (iv) the ''flattening out" at distances above 70 km.The main problems with the young TVZ model are (i) the large degree of scatter in the data, and (ii) some very low values of recorded PGA at Oto 20 km.Note that the "high" soil site PGA values at about 45 km in Fig. 8(a) and 38 km in (b) and (c) were from one site in one event, suggestive of a site-specific effect.This data point was excluded from the model development.
Other of the data points at "B" in Figure 9(a) were obtained from recording sites between Reporoa and Lake Rotomahana ("C" in Figure 8), and again the group average PGA ratio of about I indicates a small or zero path within the anomalous zone.This further supports the TVZ boundary as the eastern boundary to the anomalous zone.
Most of the points labelled "D" in Figure 9(a) were associated with paths through the wide part of the CVR in the vicinity of Tauranga.The apparent "tailing off'' of the high attenuation effect at path lengths greater than about 70 km could be explained either by a lessening of the high attenuation in the portion of the CVR near Tauranga, or more simply by taking the boundary of the whole TVZ as the northwestern boundary for the anomalous zone.The exact position of the boundary remains uncertain, however, because Dowrick and Rhoades [11] noted high attenuation in the intensities of the 1976 Te Puke earthquake (''TP" in Figure 8).The instrumental epicentre for the Te Puke earthquake was located approximately 2 km west of the whole TVZ boundary, but there were some inconsistencies.The isoseismal pattern [10] seemed to imply better transmission of the seismic waves towards the east into the zone of high attenuation than towards the west.Indeed the highest isoseismal, MMI VII, lay entirely to the east of the epicentre.
The three points labelled "E" in Figure 9(c) (paths "E" in Figure 8) appear to indicate that the young TVZ is not a good model for the north-western boundary.The two paths and points labelled "F' tend to support this view, as do the findings of Dowrick & Rhoades [ 11] which suggest that the zone of high attenuation extends to somewhere between Tauranga and the western boundary of the whole TVZ.
Based on the above our preferred model for the highly attenuating zone is the whole TVZ, even though some of the evidence we have provided is a little tenuous and not entirely consistent.

Development of the attenuation model
In the accelerograph dataset nearly all of the distant records are from digital instruments.Because the non-triggering of some digital instruments could bias the dataset at large distances we have estimated the trigger levels of all of the digital accelerographs and excluded from the analysis those accelerograph records obtained from distances greater than that of the first non-triggered digital accelerograph having a similar triggering level.
Most of the accelerograph records are from weak rock and soil sites within 300 km of source while many of the seismograph records are from weak and strong rock sites at source distances of more than 300 km.In order to minimise any biasing that might arise from such a grouping of the data, i.e., most soil site data at intermediate distances versus most rock site data at long distances, the maximum source distance for data used in the 207 derivation of the model was set at 400 km.Beyond 400 km, the predicted strong motion parameter would be relevant only to unusual engineering applications and only for every large earthquakes, for example, 8.0+, and our data set does not contain any records from such large magnitude earthquakes.
Much New Zealand data is from two types of earthquakes, namely crustal and slab, and a small amount is from subduction zone interface earthquakes.It has been demonstrated that different types of earthquakes can lead to different attenuation characteristics [2,11,29] and so ideally a separate attenuation model should be derived for each type.Another important aspect of attenuation modelling is site effects.As described earlier most of the New Zealand accelerogram data is from soil sites.In the present study we found that data from strong rock, weak rock and soil sites exhibited significantly different PGA attenuation characteristics, and again ideally a separate attenuation model should be developed for each site class.The division into earthquake types and site classes would thus result in six major data groups, strong rock, weak rock and soil for both crustal and slab earthquakes.Such a division of the data would, however, result in a very small number of data points in each group and it would be very difficult to derive a robust attenuation model for each group.
An alternative approach could be to modify an eX1stmg attenuation model derived from a much larger overseas data set, as is being done for attenuation modelling of acceleration response spectra [21].A difficulty with this approach is that the site classes used in the New Zealand attenuation studies are considerably different from those used in some overseas models.For example, rock sites and shallow soil sites were combined into a single rock class in one model [2], and a second model that utilised strong rock and weak rock classifications restricted the source distance to just 60 km [ 5].
The New Zealand dataset has very few records in that distance range (Figure 2(c-d)).
The approach that we have adopted is to combine all the data and use it to derive a single attenuation model, with some of the parameters of the model being applied to a single type of earthquake and some to a single class of site conditions•.For different groupings of the data we aimed to have as many common parameters as possible so that they could be estimated from a large number of data points.
The relative lack of near-source data from even moderate magnitude earthquakes in our dataset meant that we were not confident of being able to support a model with magnitude and distance saturation characteristics, hence we followed the approach of Zhao et al. [30] and adopted a simple Joyner and Boore [16] type approach.Our base model was the soil site model from Zhao et al. [30], i.e. log10 (PGAsL) = A1 Mw + Az log 10 (R) + A3 he+~ + As OR+ At; 81, (1) and (2) where PGAsL is the peak ground acceleration (g) for soil _sites, Mw is the moment magnitude, r (km) is the shortest distance from the rupture surface to the recording site, d is a constant to restrain the near-source PGA prediction and he (km) is the centroid depth of the rupture surface.
Parameter selection was based on the residual analysis from the present data set with respect to the attenuation models of Zhao et al. [30] and regression analysis for the present model was carried out.Statistical analysis was then performed for each parameter and any parameter for which the mean was not larger than zero at a significance level of 5% was excluded.It was thus found that both B and DWR could be eliminated, and for the TVZ data only one of the parameters Bv and Cv could be included.Taking Bv as zero gave a much better fit to the data than taking Cv as zero.This is consistent with the findings of Haines [13] and also consistent with a physical model involving a large anelastic attenuation within the volcanic region.
The final model developed from equations I to 6 is: Where Values of the parameters are as follows: (anelastic attenuation term for strong and weak rock sites only) (additional magnitude term for strong rock sites only) (additional constant term for strong rock sites only) (additional anelastic attenuation for paths through the TVZ) (factor for near-source constraint) Residuals from the modelling are plotted in Figures 10 to 12, some sample fits for individual earthquakes are plotted in Figure 13, and the general form of the model is shown in Figure 14.

DISCUSSION
The total magnitude term for the strong rock class is much larger than for the other site classes.Part of the reason for the large value could be associated with a strong anti-correlation between the coefficient for the additional strong rock magnitude term, AsR. and the strong rock constant DsR, indicating that a smaller pre-defined value for AsR could result in a model with very similar predictions within the magnitude range of the data.This strong correlation suggests that extrapolation outside the magnitude range of the dataset (i.e.Mw 5.08 to 7.41) could result in unreliable predictions.
We attempted to derive a model with magnitude-dependent geometric attenuation to ensure that the large magnitude term for strong rock sites was not caused by the assumption of magnitude-independent attenuation.It was found that the coefficient for the magnitude-dependent attenuation term was not statistically significantly larger than zero and was too small to have any effect on the model's predictions.We• also attempted to fit a model with a magnitude-dependent "d" (equation 2) using fixed coefficients from Campbell [4], and found that the fitted model had a very similar value for the magnitude term to that given above.Figure 10 shows that there is no strong dependence on magnitude or distance for residuals of strong rock site data.These analyses suggest that the large value of the magnitude term is either a result of a particular distribution of our data or a result of physical characteristics of the New Zealand earthquakes.Note that the magnitude term for the soil and weak rock data is also larger than those of Joyner and Boore [16].--------------------' -------~ 5.0 5.5 6.0 6.5 7.0 7.5 Moment magnitude Mw .. ' ' ' . . . .-------------------' ----------' 5.0 5.5 6.0 6.5 7.0 7.5 -.... : .... -~--.; ... : .. ..: .. :. : .: ..... .
6.: ,6.,:     -   .(c) A magnitude 5 event (noting that the "high" strong rock PGA was recorded at site MQZ which often gave high results for events located northwest of the site).(d) An event with magnitude close to 6. (e) A magnitude 7 event (the worst fit for all events in the digital data set).(J) The deepest event in the seismograph dataset (the record from site KUZ showed symptoms of a volcanic path even though the direct path was not through the whole TVZ).
The residual distribution with depth for strong rock sites (Figure lO(c)) apparently has a small trend, with records from very shallow earthquakes (he::; 5 km) being over-predicted and those from deep earthquakes being marginally under-predicted.We do not think this is a real trend because much of it can be explained by the fact that three of the shallowest events (39, 46 and 51, Table 2) were located in the centre of the South Island, and directional effects seem to have resulted in depressed PGA values at recording sites in the sector defined by a line extending north-east of the epicentres and then clockwise to approximately south.Sites ODZ, MQZ, LTZ and KHZ were involved.
Similarly the same three events were associated with all three of the shallow-event (he ::o 5 km ) records that were over-predicted by more than one standard deviation in the weak-rock case (Figure ll(c)).In this case only one recording site, WEL, was involved and it was located north-east of all three events.A fourth over-predicted record, at he= 9 km, also was from site WEL which once again was approximately north-east of the earthquake, event 35.The two common factors make it impossible to determine whether the over-prediction is due to (i) an overall trend in the data, (ii) a site effect, or (iii) a directional effect.There is clearly a need for much more data from weak rock sites.
If a separate depth term was allowed for the strong rock case, then the trend in the residual distribution with depth could be corrected and also the coefficient for the depth term for the strong rock site would be statistically larger than zero.However, this would result in a much larger magnitude term for the strong rock case and an almost perfect anti-correlation between AsR and DsR-A separate depth term for strong rock sites was, therefore, not included in the model presented here.
The remaining very shallow event, the 4 km deep Mw 6.25 Bay of Plenty (CVR) earthquake of 21 June 1992, was well predicted by the complete model including the volcanic path term (Figure 12(c)), whereas all records were clearly substantially over-predicted by the model when the volcanic path term was not included (Figure 13(b)).
Single event plots for the smallest, a mid range, and the largest crustal events, and the deepest event in the seismograph dataset are shown in Figure 13(c-f).In all cases the model, without the volcanic path term, is plotted with heavy lines over the distance range of the data used in its development, i.e. up to 400 km, and with light dashed lines for extrapolations to 1000 km.The fits are good, accepting the usual level of scatter in PGA data, even for distances beyond 400 km.A notable exception however is the fit to the Mw 7 .09Off East Cape earthquake of 5 February 1995.For this earthquake the model under-predicts the non-volcanic path data recorded on rock sites at distances above about 300 km.We do not have an explanation for this and simply note the need for more data from events of similar or larger size.
The two next largest events in the seismograph dataset, Secretary Island, Fiordland (10 August 1993) and Arthur's Pass (18 June 1994), both had a moment magnitude of 6.81.The agreement between predicted and recorded PGAs on rock sites for the Secretary Island event was excellent for distances from 213 100 to 600 km.From 600 to 1200 km the model underestimated the recorded PGAs by a factor of about 2. In the case of the Arthur's Pass earthquake the agreement between the predicted and recorded PGAs was good, apart from those results that may have been affected by directional effects (Figure 13(a)).
The general form of the model is illustrated in Figure 14 with plots for shallow crustal events having strike-slip mechanisms.
The most notable feature is the changing relativity between PGAs on strong rock sites and those on weak rock and soil sites as a function of magnitude.For a magnitude 5 earthquake the PGAs on weak rock are amplified by a factor of about 5.5 with respect to those on strong rock sites, for a magnitude 6 event the amplification factor is 2.4, and at magnitude 7 there is no significant amplification.The form assumed for our model means that the amplifications apply at all source distances.This trend is supported by the recorded data as shown for example in Figure 13.It should be noted however that there is very little rock data at distances less than 50 km, and only 9 records from rock sites at distances less than 100 km from earthquakes of magnitude 6.5 and above.At magnitude 8, a large extrapolation, the model predicts attenuation by a factor of about 2.5 from strong rock to weak rock and soil sites.
Verification of this prediction awaits data.
PGAs predicted for soil sites are very similar to those for weak rock sites for source distances up to about 50 km.At distances beyond 50 km there is significant amplification on going from weak rock to soil and the amount of amplification increases with distance.The model for soil sites (Figure 14) produces attenuation curves that are very similar to those predicted by the model of Zhao et al. [30], even though the parameters of the two models differ.
The predictions for near-source accelerations in large earthquakes are very high.At source distance r = 1 km a magnitude 8 event with strike-slip mechanism could be expected to yield mean PGAs of 1.14g on weak rock and soil sites, and 2.8g on strong rock sites.Such an event could be, for example, a major rupture involving the southern and central segments of the Alpine fault [28].The predictions for a magnitude 7.5 strike-slip event and r = 1 km are 0.8g on weak rock and soil and 1.3g on strong rock at near-source locations.
The southern segment of the Wellington fault is one possible source of such an event.
According to the model, events with reverse mechanism would give rise to PGAs that are 29% higher than those predicted above for strike-slip events.
All of the extrapolations to magnitude 7.5 and above need to be treated with caution as our model, like that of Zhao et al [30], does not allow for the possibility of "saturation" of mean PGA values at short distances in large magnitude earthquakes.It assumes a variation with magnitude that is independent of distance.There are some theoretical grounds for believing that the highest achievable PGAs for rock sites might be about 2g for events having reverse mechanisms, 0.7g for pure strike-slip, and 0.4g for normal mechanisms [19].PGAs on soil too might be limited by non-linear stress-strain characteristics, which are accommodated in our model.Source distance (km) Figure 14: Predicted PGAs for shallow (he= 10 km) events with various magnitudes and strike-slip or normal mechanisms.Note the large amplification in PGA on going from strong rock to weak rock and soil for a magnitude 5 event, the lesser amplification at magnitude 6, the equality at magnitude 7, and the de-amplification at magnitude 8.The thin lines indicate extrapolation beyond the magnitude and distance bounds of the data used in developing the model.The magnitude 8 predictions are extrapolations, as are the very near-source predictions for magnitudes 5 and 6.
Despite the inclusion of 66 near-source records from overseas earthquakes in our dataset we still have insufficient near-source data.In Figure 14 we emphasise those parts of our model that are supported by at least some data, and the near-source gaps are obvious.See also Figure 2(c,d,e).Our model can be considered well constrained near-source only for soil sites and then only for magnitudes in the range 6.5 to 7.There is a wellrecognised shortage of data for magnitudes 7.5 and above and a possibly equally important shortage of near-source data for magnitudes 5 to 6.5.Thus most near-source applications of our model, and indeed of any other of the current PGA attenuation models, should be handled with due caution.

CONCLUSIONS
Seismograph data have proven to be a valuable complement to accelerograph data for modelling the attenuation of peak ground acceleration.Using a combination of seismograph and accelerograph data we have extended the PGA attenuation model of Zhao,Dowrick and McVerry [30] to include the additional site category of strong rock, and also have successfully modelled the relatively high attenuation in the volcanic zone of the North Island of New Zealand.
Three ground classes, namely strong rock, weak rock and soil, were found to give rise to significantly different PGAs.As defined the "strong rock" class included rock types such as unweathered granite, schist, quartz and greywacke, the "weak rock" class included sandstones and mudstones, weathered rock of all types, and bedrock of all types overlain by up to 3 m of soil, and the "soil" class included soils of all types at depths of more than 3 m over bedrock.
PGAs predicted for soil sites were very similar to those predicted by the model of Zhao et al. [30] for all magnitudes, depths and distances.
The PGAs predicted by the model for sites underlain by weak rock types and soils were similar, regardless of magnitude, for source distances up to 50 km.
Beyond 50 km the PGAs on soil sites were greater than those on weak rock sites and the difference increased with distance.
There was a magnitude-dependent amplification of PGA on going from strong rock sites to weak rock or soil sites.At magnitude 7 there was no significant amplification (for source distances up to 50 km), for magnitudes below 7 the amplification factor was greater than one with the degree of amplification increasing as the magnitude decreased, and for magnitudes greater than 7 the amplification factor was less than one, i.e. attenuation.
Very close to the source (i.e.within about 2 km) of earthquakes having strike-slip or normal mechanism the model predicted PGAs for weak rock and soil sites that increased with magnitude, from 0.15g at 7.
215 magnitude 5 to 1.2g at magnitude 8. Near-source PGAs on strong rock sites showed a greater variation with magnitude, from a little under 0.02g at magnitude 5 to 2.8g at magnitude 8.It should be noted however that the largest event in the combined weak-and accelerograph datasets had a magnitude of 7.4, and so the predicted PGAs for a magnitude 8 event are based on extrapolation and therefore must be treated with caution.
PGAs predicted for events having a reverse faulting mechanism were 29% greater than those predicted for strike-slip or normal mechanisms, for all distances and site categories.
The PGA attenuation model is applicable to all of New Zealand including the zone of relatively high attenuation in the volcanic region of the North Island.Within the anomalous zone there appears to be a much higher level of anelastic attenuation than in the rest of New Zealand, with the result that the PGA amplitude is reduced by a factor of 10 for seismic waves passing completely through it at its widest part.The maximum effective width appears to be about 70 km.The extra attenuation is modelled well by a simple function of the length of path within the anomalous zone.
The whole Taupo Volcanic Zone (TVZ) appears to be a better model for the extent of the highly attenuating volcanic zone than either the CVR (Central Volcanic Region) or young TVZ models.
There is an indication that the high attenuation within the TVZ is due to selective attenuation of some frequency components of the seismic signal.
Components of I Hz and above appear to be much more highly attenuated than components below I Hz.
Outside of the TVZ, directional effects were observed to be substantial, but we had insufficient data for reliable modelling of the effects.
The ranges of validity of the model as defined by the data used in its generation are as follows: moment magnitude 5.1 to 7.4, source distance c.10 to 400 km, and centroid depth 4 to 149 km.As is common for PGA attenuation studies there was a relative scarcity of near-source data from large events, i.e. data from within I 0km source distance of events of Mw 7 .5 and greater.Our data set for example contained only one record from rock sites at distances less than 150 km for magnitudes 7.0 and above.There was an equally important lack of near -source data for smaller magnitudes in the range 5 to 6.5.In summary, the near-source constraint of our model should be considered adequate only for the soil ground classification and even then only for the magnitude range 6.5 to 7. All other near-source predictions are extrapolations beyond the range of data used in defining the model and should be treated with due caution.

Figure 1 :
Figure 1: Map showing digital 3-component stations in the New Zealand National Seismograph Network along with locationsof earthquakes recorded by them and used in the PGA attenuation study.The earthquakes are a subset of those used by Zhao et al.[30 ].See Table2for further information on the earthquakes.

Figure 2 :
Figure 2: (a-b) Centroid depth he, focal mechanism and moment magnitude Mwfor the New Zealand earthquakes yielding digital seismograph data for the PGA attenuation study.(c-e) Moment magnitude, site category and type of record for the combined seismograph and accelerograph data sets.Most of the data points for source distances smaller than 10 km are from overseas earthquakes.Data at source distances greater than 400 km were excluded from the modelling process, but were displayed in verification plots.

Figure 3 :
Figure 3: Localions of the Tikokino Earthquake of 11 April 1993 (event 43) and recording sites discussed in the text.The epicentre is indicated by a small circle and the horizontal projection of the fault plane by a small diagonal line.Source directivity effects gave rise to "high" PGA's at sites to the south and south-west of the epicentre and "low" PGA 's at sites to the north and northeast.

Figure 5 :
Figure 5: Time histories and Fourier spectra from the Tikokino earthquake illustrating the reduction of amplitudes over the whole frequency band of the recordings.Note the variation in Y-axis scales for the time-history plots.

Figure 8 :
Figure8: Three possible outlines for the zone of high attenuation (map adapted from Wilson et al.[27]).The labelled paths and locations, which have corresponding labelled data points in Figure9, can be used to help define the most likely boundaries of the zone of high attenuation.The reasoning is given in the text.

FigurelO:
FigurelO: Residuals of the PGA data from strong-rock sites plotted agai.nst(a) moment magnitude M.., (b) source distance r, and (c) centroid depth he.PGA, is the recorded PGA and PGAP is the predicted PGA.A positive residual means that the recorded PGA is greater than the predicted PGA.The apparent over-prediction at centroid depths of 4 and 5 km in plot (c) is probably a result of directivity effects associated with the shallow events 39, 46, and 51.See for example Figure 13(a).

Figure 11 :
Figure 11: Residuals of the PGA data from weak-rock sites plotted against (a) moment magnitude M.., (b) source distance r, and (c) centroid depth he.PGA, is the recorded PGA and PGA, is the predicted PGA.The apparent over-prediction at centroid depths of 4 and 5 km in plot (c) is probably a result of directivity effects associated with the shallow events 39, 46 and 51.

Figure 12 :
Figure 12: Residuals of PGA data affected by paths through or within the TVZ.Results for all rock and soll sites are plotted against (a) moment magnitude Mw, (b) length of path in the TVZ Rv, and (c) depth he• PGA, is the recorded PGA and PGAP is the predicted PGA.

Figure 13 :
Figure 13: Comparisons of recorded and modelled PGAs for 6 New Zealand earthquakes.The plotted curves do not include the volcanic path factor, and the data is from accelerograph and NSN sites only.(a) The Arthur's Pass earthquake of 18 June 1994, showing good agreement apart from depressed values of PGA recorded on the Christchurch side of the epicentre -probably a directional effect.(b) An event located within the volcanic region showing general overprediction by the version of the model not incorporating the volcanic path factor.(c)A magnitude 5 event (noting that the "high" strong rock PGA was recorded at site MQZ which often gave high results for events located northwest of the site).(d) An event with magnitude close to 6. (e) A magnitude 7 event (the worst fit for all events in the digital data set).(J) The deepest event in the seismograph dataset (the record from site KUZ showed symptoms of a volcanic path even though the direct path was not through the whole TVZ).

Table 3 :
Rock strength categories as used in the PGA attenuation study.The mean shear-wave velocities are those associated with the Borcherdt classes.