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MODELING OF WIDE-ANGLE SEISMIC ATTRIBUTES USING THE GAUSSIAN BEAM METHOD

STEPHEN M. STACY1 AND ROBERT L. NOWACK2

ABSTRACT

In this study, observed seismic attributes from shot gather 11 of the SAREX experiment are used to derive a preliminary velocity and attenuation model for the northern end of the profile in southern Alberta. Shot gather 11 was selected because of its prominent Pn arrivals and good signal to noise ratio. The 2-D Gaussian beam method was used to perform the modeling of the seismic attributes including travel times, peak envelope amplitudes and pulse instantaneous frequencies for selected phases. The preliminary model was obtained from the seismic attributes from shot gather 11 starting from prior tomographic results. The amplitudes and instantaneous frequencies were used to constrain the velocity and attenuation structure, with the amplitudes being more sensitive to the velocity gradients and the instantaneous frequencies more sensitive to the attenuation structure. The resulting velocity model has a velocity discontinuity between the upper and lower crust, and lower velocity gradients in the upper and lower crust compared to earlier studies. The attenuation model has Qp-1 values between 0.011 and 0.004 in the upper crust, 0.0019 in the lower crust and a laterally variable Qp-1 in the upper mantle. The Qp-1 values are similar to those found in Archean terranes from other studies. Although the results from a single gather are non-unique, the initial model derived here provides a self-consistent starting point for a more complete seismic attribute inversion for the velocity and attenuation structure.

K ey word s : Refraction Seismology, Seismic Attributes

1. INTRODUCTION

Previous studies have shown that when performing multi-attribute seismic inversions, a starting model consistent with all the seismic attributes is important for the convergence of the inversion (Nowack and Matheney, 1997a,b; Matheney et al., 1997). More detailed models can be obtained in an iterative fashion as more data are incorporated (Lutter and Nowack, 1990; Nowack and Matheney, 1997a,b). In this study, seismic attributes extracted from shot gather 11 of the SAREX experiment are analyzed and modeled to constrain a preliminary velocity and attenuation model along the northern end of the SAREX profile. Shot point 11 is the northernmost shot point of SAREX and was chosen

1 Malcolm Pirnie, Inc., 4646 E. Van Buren St., Suite 400, Phoenix, AZ, 85008-6945 (e-mail: [email protected])

Stud. Geophys. Geod., 46 (2002), 667−690 667 © 2002 StudiaGeo s.r.o., Prague

2 Purdue University, Dept. of Earth and Atmospheric Sciences, 1397 Civil Eng. Bldg., W. Lafayette, IN, 47907 (e-mail: [email protected])

S.M. Stacy and R.L. Nowack

because of the high signal to noise ratio and clear Pn phases in the seismic data. The seismic attributes considered include arrival times, envelope amplitudes and pulse instantaneous frequencies of selected first-arrival phases. Forward modeling was performed using the 2-D Gaussian beam method to constrain a preliminary velocity and attenuation model along the northern end of the SAREX profile starting from prior tomographic results.

The SAREX experiment (Southern Alberta Refraction Experiment) was conducted just prior to the continental scale Deep Probe experiment and was designed to provide detailed resolution of the crustal structure along the Canadian portion of the combined Deep Probe/SAREX profile (Clowes et al., 2002). For SAREX, ten shots were spaced at approximate intervals of 50 km intervals along an 800 km profile from central Alberta to central Montana. The receiver spacing was 1 km in Alberta and 1.25 to 2.5 km in Montana. The Deep Probe experiment had larger shots for offsets out to 2500 km (Gorman et al., 1997; Henstock et al., 1997). Taken together, few refraction/wide-angle reflection experiments have had the receiver coverage and offsets as large as the combined Deep Probe/SAREX experiments (Figure 1). Notable exceptions are Project Early Rise (Iyer et al., 1969) and Russian peacetime nuclear explosion experiments (Morozov et al., 1998). These experiments, however, had much sparser receiver coverage.

The resulting velocity and attenuation from the modeling of the seismic attributes is then compared with the tomographic results of Gorman et al. (2002) for the combined Deep Probe/Sarex profile (henceforth referred to as GMN2) and to other attenuation results in Archean terranes. Although the results obtained here are non-unique, the derived model can be used as a starting model for more complete seismic attribute inversions for the velocity and attenuation structure. As further data are included, more detailed models can then be obtained in an iterative fashion.

2. DATA ANALYSIS

Shot gather 11 of SAREX is shown in Figure 2, where the data have been filtered from

1 to 20 Hz using a causal Butterworth filter. Approximately every other trace has been plotted as a trace normalized seismogram, but all the traces are used for further processing. Clearly identifiable first arrival phases include crustal phases for offsets out to approximately 175 km, and upper mantle Pn phases that are seen for greater offsets. Attribute analysis was not considered for offsets greater than 450 km for the travel times and 400 km for the secondary attributes because of changes in the geological terrane and changes of instrument type. This restricts the analysis to the study of the crust and very upper mantle for the northern part of the SAREX profile. Also, only P-wave arrivals and not S-wave arrivals are considered. More detailed figures of shot gather 11 and other gathers are presented in Gorman et al. (2002) and Clowes et al. (2002) and are not shown here.

As an initial step, travel times of the first arrivals and selected secondary arrivals were manually picked from the data. Interactive plots of individual traces with peak envelopes overlain were used to increase the ability to recognize phase coherence and determine the first arrivals. The observed arrival times are plotted in Figure 3 for a reduction velocity of 8 km/s for the distance range of 0 to 450 km. Arrival time picking uncertainties are estimated to be 0.05 seconds for the crustal phases for distances less than about 175 km

668 Stud. Geophys. Geod., 46 (2002)

Modeling of Wide-Angle Seismic Attributes …

and 0.1 seconds for upper mantle phases. These empirically derived uncertainties are similar to those of GMN2 who estimated uncertainty values in the range of 0.05 to 0.13 seconds for first arrivals. Some of the scatter is related to the signal to noise ratio of the data, and also to laterally varying near surface and crustal structure. Note that several travel times for secondary branches have been picked which are not used for the extraction of secondary attributes, but are important in constraining the velocity profile. Because a simplified 2-D model of the broad scale features is being developed, only a small number of secondary arrival travel times were selected in the 200 − 350 km region.

The travel time branches in Figure 3 include the near offset arrivals for distances less than 10 km, which are associated with the western Canada sedimentary basin (WCSB). Note that the later arrivals at the very near offsets less than 5 km have not been modeled. The upper crustal phases then extend to offsets greater than 115 km. From Figure 3, as well as from reduced plots with reduction velocities near 6 km/s, this branch is nearly straight with an apparent velocity of slightly greater than 6 km/s. This suggests a relatively low upper crustal velocity gradient in this region. For distances greater than 115 km, the upper crustal phase becomes weak and the larger amplitude first arrivals are interpreted to be lower crustal phases with apparent velocities starting near 6.4 km/s. The lower crustal branch also exhibits an arcuateness, which suggests that a velocity gradient occurs in the lower crust. The lower crustal branch also extends as a prominent secondary arrival out to distances past 300 km (Figures 2 and 3). The final primary first arrival phase is the upper mantle Pn phase, which has apparent velocities slightly more than 8 km/s.

Peak envelope amplitudes and instantaneous frequencies are then extracted from the first arrival pulses with picked travel times. An algorithm described by Matheney and Nowack (1995) is used for the extraction of envelope amplitudes and pulse instantaneous frequencies. For a given seismic trace with a measured traveltime, the algorithm computes the analytic signal and from this the envelope amplitude and instantaneous frequencies along the trace. As described by Matheney and Nowack (1995), a damping factor is used to stabilize the instantaneous frequencies when the envelope amplitude gets too small, but has no effect when the envelope amplitude is large. A weighted average of the instantaneous frequencies with the square of the envelope amplitude along the trace is then performed. It can be shown that the instantaneous frequency weighted by the squared envelope in the time domain approaches the centroid of the positive power spectrum in the frequency domain as the length of the weighting window increases (Barnes, 1991; Stacy, 2001; Nowack and Stacy, 2002).

Estimates of the pulse amplitude and instantaneous frequency are then extracted at the first large peak of the envelope amplitude after the measured travel time of the selected pulse. In order to ensure that the estimates are extracted from a pulse with no interference from later arrivals, a check is made for the decay of the envelope amplitude after the peak amplitude. If the decay is not sufficient, then it is assumed that pulse interference is occurring and the estimate is discarded. Also, manual checking for interference is done to reduce the effects of pulse interference with later arrivals.

Figure 4 shows the pulse log-amplitudes for shot gather 11 where the circles are the observed values. For an offset range less than 115 km related to the upper crustal phases, a large but relatively simple decay of the pulse amplitudes is seen. This large amplitude decay is consistent with the relatively low upper crustal velocity gradient inferred from

Stud. Geophys. Geod., 46 (2002) 669


the traveltimes. In the offset range between 120 and 170 km related to the lower crustal phases, there is an increase in amplitudes of about 0.75 log units. This is also consistent with the larger velocity gradient in the lower crust, as well as a mid-crustal interface, inferred from the traveltimes. At about 175 km, there is an approximate 0.5 to 0.75 drop in the log-amplitude related to the crossover with the upper mantle phase. This suggests a lower velocity gradient in the upper mantle compared to the lower crust consistent with the traveltimes. Although there is scatter in the data, there is also a suggestion of a slight increase in the pulse amplitudes with distance for the Pn phase.

Figure 5 shows the pulse instantaneous frequencies for shot gather 11 where the circles are for the observed first arrival pulses. For distances less than 115 km related to the upper crustal phases, the instantaneous frequency values decay from 14 to 10 Hz. The gaps in the data are where either the amplitudes are low or pulse interference is inferred. For the distance range between 120 and 170 km, which is related to the lower crustal first arrival phases, the instantaneous frequencies decrease to between 7.5 and 9 Hz. This is associated with an increase in amplitudes shown in Figure 4, which suggests that this increase in amplitudes is a geometric effect related to the velocity structure. A second gap in the instantaneous frequencies is related to interference effects at the crossover distance between the lower crustal and Pn phases. The instantaneous frequencies for the Pn phase have only a small drop of about 1 Hz or less at the crossover distance and then are relatively flat with a slight decrease with distance.

3. MODELING OF TRAVEL TIMES

Forward modeling of the travel times was performed to constrain the velocity

structure, which was then refined by modeling of the secondary seismic attributes. The GMN2 tomography results were simplified and used as a starting velocity model, which was then refined by forward modeling using the attribute data from shot gather 11. The velocities are converted to a flat earth for the modeling using an Earth flattening transformation (Aki and Richards, 1980). Travel times were calculated using the ray method for a receiver spacing of 1 km for out to 450 km offset. The calculated travel times are then compared to the observed first arrival travel times as well as to selected back-branch travel times. In Figure 3, the observed travel times are plotted as circles and the calculated phases are plotted as plus signs. Calculated reflected phases are not plotted in Figure 3, but are overlain on the seismograms in Figure 6. A good match is obtained for the crustal phases, while the match for the Pn phases is not as good due to lower signal to noise and possibly small-scale lateral heterogeneities. In this figure, prominent first-arrival phases including the upper crustal phases, the lower crustal phases, the PmP and the Pn are shown and match the observed data reasonably well. The calculated secondary PmP arrivals, however, do not travel as far as the observed secondary PmP arrivals. The extent of the secondary PmP arrivals is related to the gradient of the lowermost crust. It may be that the lower crustal gradients are somewhat lower than the gradients in our model. Lateral variations may also have an effect on the extent of the secondary PmP arrival, but the extent of the effect of lateral heterogeneities is not accounted for in the simplified 2-D model presented here. A seismic attribute inversion would better separate the lateral heterogeneities from the vertical ones.



The resulting velocity model from forward modeling of the travel times and secondary seismic attributes is shown in Figure 7 and Table 1. However, these results are non-unique based on attribute data from a single gather. The velocities for the shallow crustal depths shown in Table 1 are associated with the Western Canada Sedimentary Basin (WCSB) and are constrained by well-log information (Clowes et al., 2002). The WCSB is modeled using four layers where the top layer is between 0.62 and 0.79 km thick and has a small vertical velocity gradient as well as a slight lateral velocity gradient. The next layer is a 0.07 km thick layer that has a vertical velocity gradient from 2.75 km/s to 2.76 km/s. The third layer is 0.69 km thick and has velocities that increase from 5 km/s to 5.05 km/s. The fourth layer in the WCSB is a low-velocity zone, which has a thickness of 0.6 km and a vertical velocity gradient that increases from about 3.63 to about 3.65 km/s. The total thickness of the modeled sedimentary basin varies depending on the surface topography, but has an average thickness of about 2 km.

Below the WCSB, the upper crust of the velocity model shown in Figure 7 consists of two layers. The first is a 0.7 km thick layer with a vertical velocity gradient that increases from 6.076 to 6.082 km/s. The depth below sea level at the bottom of this layer is about 2 km. The second layer has a thickness of 11 km and velocities that increase from 6.09 to 6.1 km/s. There is then a velocity discontinuity at the base of the upper crust, which may correspond with the Conrad discontinuity along the northern part of the profile.

The lower crust in the model shown in Figure 7 consists of a combined layer with three velocity gradients. The first gradient has a thickness of 5 km and velocities that increase from about 6.38 to 6.45 km/s. The lowermost crust has velocities that increase from about 6.45 km/s at 18 km depth to about 6.99 km/s at the Moho.

Similar to the models of Henstock et al. (1998) and GMN2, the Moho in the model shown in Figure 7 dips to the south, and the velocity gradients in the lower crust and upper mantle layer vary laterally. Similar to GMN2, our model has a laterally constant velocity at the base of the model in the mantle at a depth of about 87 km. The upper mantle in our model has velocities that increase from about 8.05 km/s at the Moho to 8.37 km/s at a depth of 87 km.

4. MODELING OF SECONDARY ATTRIBUTES

Secondary seismic attributes were modeled using the 2-D Gaussian beam method

(Červený et al., 1982; Červený, 1985; Nowack and Aki, 1984; Nowack, 2002). The Gaussian beam method was used for the forward modeling since it allows for more accurate modeling of the Pn branch in the presence of interfaces in comparison to the ray method (Nowack and Stacy, 2002; Stacy, 2001). In order to determine a reasonable source pulse for use in the calculation of Gaussian beam synthetics, an iterative matching of observed near offset pulses was performed. The shallow Qp-1 values for the western Canada sedimentary basin (WCSB) are assumed for the source pulse matching. The WCSB values used are similar to those obtained for northwestern Alberta by Zelt and Ellis (1990) who found Qp-1 values in the sedimentary layer of about 0.01. An initial source pulse was obtained by attenuating the source pulse to select near offset trace distances and then matching the observed pulse shapes and widths (Stacy, 2001). Based on the initial source pulse modeling, Gaussian beam synthetic seismograms were computed using a Gabor source wavelet,



2( ) exp ( 2 ( ) / ) cos ( 2 ( ) )m i m is t f t t f t tπ γ π= − − − + ν ,

where is 15.5 Hz, mf γ is 4, ν is 0.764π− and is the pulse arrival time. itFor the 2-D Gaussian beam modeling, an initial grid of ray endpoints was spaced at

1.5 km intervals out to offsets of 600 km. Prominent rays considered include rays through the WCSB, the upper and lower crust, and the upper mantle. The upper mantle phases include the direct Pn, as well as underside reflections from the Moho, which were found to be important for the modeling of seismic attributes of Pn phases (Nowack and Stacy, 2002). The receivers were spaced every ten km with a minimum receiver offset of 5 km. The individual Gaussian beams were then summed to obtain the synthetic seismograms. Each trace had 2048 samples with a time sampling of 0.0122 s. Effective plane phase fronts at the receiver were used to specify the beam parameters. Also, the beam parameters were chosen to minimize the discretization error (Červený, 1985).

Gaussian beam synthetic seismograms are shown in Figure 8 for the velocity model in Figure 7 and the attenuation model in Figure 9. The trace-normalized synthetic seismograms are plotted over the distance range of 0 to 450 km and are reduced in time by 8 km/s. In general, the phases calculated in the synthetic record section closely resemble those seen in the observed data in Figures 2 and 6. The calculated upper crustal arrivals decay in a similar fashion to the phases identified on the observed record section, while the lower crustal and upper mantle phases also closely resemble the observed phases. Note that the secondary PmP arrivals extend to further offsets using Gaussian beams than the traveltimes for these pulses shown in Figure 6 and computed using ray theory.

Figure 9 shows the Qp-1 model resulting from the modeling of the secondary attributes in this study. The dashed and solid lines show the Qp-1 values for offsets of 0 and 500 km and are also given in Table 1. The shallow layers of the WCSB have Qp-1 values of 0.0111 for the top two layers and 0.01 for the bottom two layers corresponding to Qp values of 90 and 100. The upper crust has Qp-1 values of 0.004 and 0.00364, corresponding to Qp values of 250 to 275. The lower crustal layers have a Qp-1 of 0.0019 corresponding to a Qp of 525. The upper mantle has vertically varying Qp-1 values that decrease from 0.00182 (Qp = 550) at the Moho to 0.000476 (Qp = 2100) at the base of the model at about 87 km in depth. The dip in the Moho results in laterally varying, upper mantle Qp-1 values.

Peak envelope amplitudes and instantaneous frequencies were extracted from the synthetic seismograms using the method of Matheney and Nowack (1995). The observed and calculated log-amplitudes are shown in Figure 4 by circles and x’s, respectively. The calculated pulse amplitudes were scaled such that the amplitude of the trace at an offset of 15 km is equal to the observed amplitude at the same offset.

A good match between the observed and calculated amplitude decay curves is seen for offsets less than 115 km. The lower crustal amplitudes between 120 and 170 km have more scatter than the upper crustal phases, but the calculated amplitudes still appear to match the observed trend in the data with the rapid increase in amplitude due to the larger velocity gradients in the lower crust. Though the derived lower crustal velocity gradient may still be too large, the amplitudes of the lower crustal first arrivals have been modeled. Finally, the amplitude of the calculated Pn decreases compared to the lower crustal phases



and then slowly increases with offset. The observed amplitudes again have significant scatter but show a similar trend.

The observed and calculated instantaneous frequency values are shown in Figure 5 by the circles and x’s, respectively. The calculated instantaneous frequencies for the upper crust have a steep decay from 14 to 10 Hz resulting from large Qp-1 values in the upper crust (see Figure 9). The lower crust has calculated instantaneous frequencies that are relatively constant with a slight decrease over the distance range from 120 to 170 km. Finally, the calculated upper mantle phase slightly increases between 200 and 225 km offset and then only slightly decreases to about 7.5 Hz for greater offsets. This results from interference between the diving wave and the whispering gallery phases prior to the separation of the diving wave (Červený and Ravindra, 1971; Aki and Richards, 1980; Nowack and Stacy, 2002) and causes the instantaneous frequency curve for the upper mantle phase to decay somewhat less rapidly than if only the diving wave were calculated for this distance range.

5. DISCUSSION

Figure 10 shows a comparison between the simplified velocity profile from this study

for shot gather 11 and vertical slices obtained from the travel time inversion results of GMN2. For the near offsets, Figure 10a shows a vertical velocity slice from this study at the left edge of the simplified model beneath the shot and is shown by a thick, solid line. The near offset velocity slices for GMN2 are located at model positions (M.P.) –26 km (thin solid line), M.P. 24 km (thin dashed line) and M.P. 74 km (thin dot-dashed line) with respect to our model. In general, the velocities from this study approximately compare with those found by GMN2 for model positions between –26 and 74 km. The boundary between the upper crust and the lower crust, however, is 5 − 10 km shallower in this study than in the GMN2 study. Also, the upper crustal velocity gradient is less with a velocity discontinuity between the upper and lower crust possibly related to the Conrad discontinuity in this region. Our model has a much lower velocity gradient in the lower crust compared to GMN2. Evidence for a lower velocity gradient in the lower crust is also seen in the wide-angle secondary branches that extend to 300 km in Figures 2 and 6. The Moho depth from this study and the near offset model positions of GMN2 are similar at about 37 km depth. The velocity gradient for the upper mantle velocity gradient in this study is slightly larger than in the near offset velocity slices from GMN2.

Figure 10b shows a comparison for intermediate offset velocity slices from this study and from GMN2. The velocity slices are located at model position 174 km for this study (thick solid line) and model positions 124 km (thin solid line), 174 km (thin dashed line) and 224 km (thin dot-dashed line) from GMN2. The velocity gradients for the upper crust from this study are considerably less steep than for either of the other three velocity slices displayed. Because this study focuses on just one shot gather, there are fewer constraints on the upper crustal velocity gradient as offset increases to the south and the resulting simplified model is non-unique. The lower crustal gradient of this study matches that of model position 174 km from GMN2. The Moho for this study is, however, somewhat shallower than the Moho for the velocity slices from GMN2 for these offset ranges. Part of the difference in the Moho depth can be attributed to the larger velocities in the lower crust in two of the three velocity profiles from GMN2 in this distance range compared to



the results from this study. The upper mantle velocity gradient for model position 174 km from this study is similar to the gradients for the velocity profiles from GMN2.

Figure 10c shows a comparison of far offset velocity slices from this study and from GMN2. The velocity profile from this study is located at 324 km offset (thick solid line) and those from GMN2 are located at 274 km (thin solid line), 324 km (thin dashed) and 374 km (thin dot-dashed) relative to shot point 11. As with the previous figure, the upper crust for this study has a lower velocity gradient than those for the GMN2 model. The lower crust, however, has similar velocities until a depth of about 25 km. Between 30 km depth and the Moho, the velocities in this model are slower than those of the GMN2 model. This causes the modeled Moho of this study to be shallower than the Moho of GMN2 for this distance range. All the velocity slices now have similar upper mantle velocity gradients at this offset range. However, again the modeling of the seismic attributes from this study was from a single shot gather and the resulting simplified model is non-unique.

Figure 9 shows the Qp-1 model from this study along with the Qp-1 model of Zelt and Ellis (1990) shown as horizontal lines and the upper mantle Qp-1 models of Der et al. (1986) for two different frequencies of 3 and 10 Hz shown as vertical dot-dashed lines. Zelt and Ellis (1990) estimated one-dimensional Qp profiles for the Peace River Arch (PRA) region in northwestern Alberta, Canada, which is approximately 3 degrees north and 4 degrees west of the Southern Alberta Refraction Experiment. Despite being nearly 500 km away from the SAREX data area, the PRA is still in an Archean province east of the Rocky Mountain Front, and thus should have a similar attenuation structure. Zelt and Ellis (1990) estimated the Qp-1 of the upper crust to be between 0.002 and 0.005 (Qp values between 200 and 500). The upper crust for this study is within this range, with values between 0.00364 and 0.004 (Qp values between 250 and 275). The lower crust and the upper mantle in the Zelt and Ellis (1990) model have maximum Qp-1 values possibly as large as 0.00167 (Qp = 600) and minimum values as small as 0.000286 (Qp = 3500). In this study, the lower crust has a Qp-1 value of 0.0018 (Qp = 550), which is slightly larger than the maximum found in Zelt and Ellis (1990). The upper mantle for this study is variable with depth, however, is in the range of the Qp-1 model of Zelt and Ellis (1990) as shown in Figure 9. Der et al. (1986) provided average Qp-1 values as a function of frequency in the upper mantle. For 3 and 10 Hz, these values ranged from 0.000668 to 0.000898 in the upper mantle lid (Qp values between 1115 and 1500) and are shown with the results from this study in Figure 9.

6. CONCLUSIONS

In this study, a preliminary model for crustal and upper mantle velocity and

attenuation in southern Alberta has been obtained from prior 2-D tomographic results using wide-angle seismic attributes from shot gather 11 of the SAREX experiment. The 2-D Gaussian beam method was used to model seismic attributes, which include travel times as well as pulse amplitudes and instantaneous frequencies of selected phases. The resulting velocity model includes a four layer western Canada sedimentary basin (WCSB), an upper crust with a low velocity gradient, a mid-crustal velocity discontinuity, and a vertically and laterally varying lower crust and upper mantle with a Moho dipping to the south. In addition to travel times, amplitudes and instantaneous frequencies of first arrival



phases are used to constrain velocity and attenuation structure, with the amplitudes being more sensitive to the velocity gradients and pulse instantaneous frequencies more sensitive to the attenuation structure. Structural effects are also important in the modeling of seismic attributes of refracted waves for sharp interfaces with large velocity increases. For this study, only a non-unique, preliminary velocity and attenuation model has been derived for the northern end of the SAREX profile based on seismic attributes from shot gather 11. However, this can be used as a starting model for a more complete seismic attribute inversion using data from the entire profile, where a self-consistent initial model is important for the convergence of a multi-attribute inversion.

Acknowledgements: The authors would like to thank Kris Vasudevan for providing the SAREX

data for this study. The authors would also like to thank A.R. Gorman and R.M. Clowes for providing access to their tomographic velocity models for the Deep Probe/SAREX profile. Comments by L.W. Braile, H.J. Hinze and the reviewers significantly improved the manuscript.

Table 1. Velocity and depth values for the velocity model shown in Figure 7. Profiles are located at 0, 250 and 500 km offset. Negative depths are above mean sea level, while positive depths are below mean sea level.

Velocity Model

0 km Profile 250 km Profile 500 km Profile

Depth [km] Vel. [km/s] Depth [km] Vel. [km/s] Depth [km] Vel. [km/s]

-0.70 2.31 -0.77 2.39 -0.87 2.47 -0.08 2.33 -0.08 2.41 -0.08 2.49 -0.08 2.76 -0.08 2.76 -0.08 2.76 0.01 2.76 0.01 2.76 0.01 2.76 0.01 5.00 0.01 5.00 0.01 5.00 0.70 5.05 0.70 5.05 0.70 5.05 0.70 3.63 0.70 3.63 0.70 3.63 1.30 3.65 1.30 3.65 1.30 3.65 1.30 6.08 1.30 6.08 1.30 6.08 2.00 6.08 2.00 6.08 2.00 6.08 2.00 6.09 2.00 6.09 2.00 6.09 12.99 6.10 12.99 6.10 12.99 6.10 12.99 6.38 12.99 6.38 12.99 6.38 17.97 6.45 17.97 6.45 17.97 6.45 17.97 6.45 17.97 6.45 17.97 6.45 35.14 6.96 40.01 6.96 44.87 6.97 37.13 6.99 42.00 6.99 46.86 6.98 37.13 8.06 42.00 8.05 46.86 8.05 87.00 8.37 87.01 8.37 87.00 8.37



Table 2. Depths and 1/Qp for the model shown in Figure 10. Profiles are located at 0 and 500 km offset and then are linearly interpolated. Negative depths are above mean sea level, while positive depths are below mean sea level.

1/QP Model

0 km Profile 500 km Profile

Depth [km] 1/QP Depth [km] 1/QP

-0.70 0.0111 -0.86 0.0111 0.01 0.0111 0.01 0.0111 0.01 0.0100 0.01 0.0100 1.30 0.0100 1.30 0.0100 1.30 0.0040 1.30 0.0040 2.00 0.0040 2.00 0.0040 2.00 0.0036 2.00 0.0036 13.0 0.0036 13.0 0.0036 13.0 0.0019 13.0 0.0019 37.1 0.0019 46.9 0.0019 37.1 0.0018 46.9 0.0018 37.9 0.0017 47.8 0.0017 38.9 0.0015 48.8 0.0015 39.9 0.0014 49.8 0.0014 40.9 0.0013 50.8 0.0012 42.9 0.0011 51.8 0.0012 44.8 0.0010 52.8 0.0011 46.8 0.0009 53.8 0.0010 51.8 0.0008 57.7 0.0008 56.7 0.0007 61.7 0.0007 61.7 0.0006 65.7 0.0006 66.6 0.0006 69.6 0.0006 71.6 0.0005 73.6 0.0005 76.5 0.0005 77.5 0.0005 81.5 0.0005 81.5 0.0005 87.0 0.0005 87.0 0.0005



DEEP PROBE / SAREX EXPERIMENTAL LAYOUT

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Fig. 1. Map of the experimental layout for the Deep Probe and SAREX seismic experiments. The white stars with black borders and the white line extending from northern New Mexico northward into Canada are the respective shot point and receiver locations for the Deep Probe experiment. The Deep Probe shot points are labeled SP. The smaller black stars and the black line are the respective shot points and receiver locations for the SAREX experiment. The SAREX shot points that have been labeled (i.e. shots 1,3,6, 8 and 11) are labeled S. The SAREX shot points and receivers have been slightly shifted to the east in order to see all receiver locations. Also shown are the regional topography and political boundaries (modified from Henstock et al., 1997). Shot point 11 is used for wide-angle seismic attribute modeling and is the northernmost of the SAREX shotpoints.



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Fig. 2. Trace normalized seismograms for shot point 11 of SAREX for distances from 0 − 450 km plotted with a reduction velocity of 8 km/s. A 1 − 20 Hz causal bandpass filter has been applied. Approximately every other trace is plotted to increase clarity of observed arrivals, though all traces were processed to pick arrival times and a subset of secondary attributes based on the picking criteria.



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Fig. 3. Observed (circles) and calculated (crosses) travel times for shot gather 11 of SAREX plotted with a reduction velocity of 8 km/s between the offset range of 0 − 450 km. All first arrivals and select secondary arrivals are plotted.



OBS. VS. CALC. AMPLITUDES

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UD

E

OFFSET (KM)

Observed =

Calculated =

Fig. 4. Observed (circles) and calculated (x’s) log-amplitudes for first arrivals from shot gather 11 of SAREX. The calculated amplitudes are scaled such that the amplitude of the first arrival on the trace with an offset of 15 km is equal to an observed amplitude measurement taken from a trace with an offset of 15 km.



0 50 100 150 200 250 300 350 400

5

6

7

8

9

10

11

12

13

14

15

INS

TA

NT

AN

EO

US

FR

EQ

UE

NC

Y (

HZ

)

OBS. VS. CALC. INST. FREQUENCIES

OFFSET (KM)

Observed =

Calculated =

Fig. 5. Observed (circles) and calculated (x’s) instantaneous frequencies for first arrivals from shot gather 11 of SAREX. The initial calculated values of the instantaneous frequencies are based on the modeling of seismic pulses at near offsets.



SA

RE

X S

HO

T G

AT

HE

R 1

1, 1-2

0 H

ZS

N

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

OF

FS

ET

(K

M)

TIME-X/8 (S)

Fig. 6. Trace normalized seismograms for shot point 11 of the SAREX experiment for distances from 0 − 450 km plotted with a reduction velocity of 8 km/s. Approximately every other trace is plotted. The calculated travel times are shown by dashed lines.



M.P 0 = Top

M.P. 250 = Middle

M.P. 500 = Bottom

0

20

40

60

80

100

5 6 7 8

DE

PT

H (

KM

)

VELOCITY (KM/S)

9

VELOCITY MODEL

Fig. 7. The simplified 2-D velocity model used for the calculation of 2-D Gaussian beam synthetic seismograms in this study. The top (northern) profile is located at zero km offset from SAREX shot point 11, the middle, dashed profile is at 250 km offset, and the lower solid line is at 500 km offset. The upper crust below the WCSB is composed of an 11 km thick layer with a nearly constant velocity of 6.1 km/s. The lower crust is composed of three velocity gradients with velocities from 6.34 km/s at 13 km depth to about 7 km/s at the Moho. The Moho dips towards the south and has an approximately constant velocity increase across it. The velocity in the upper mantle increases from 8.05 km/s at the Moho to about 8.37 km/s at the bottom of the model at 87 km.



0.0

2.0

4.0

6.0

8.0

10

.0

12

.0

14

.0

0.0

50

.01

00

.01

50

.02

00

.02

50

.03

00

.03

50

.04

00

.04

50

.0

TIME - X/8 (S)

OF

FS

ET

(K

M)

NS

GA

US

SIA

N B

EA

M S

YN

TH

ET

IC S

EIS

MO

GR

AM

S

Fig. 8. Trace normalized synthetic seismograms computed with the 2-D Gaussian beam method with a reduction velocity of 8 km/s. The source pulse has an average frequency of 15.5 Hz.



0 0.002 0.004 0.006 0.008 0.01 0.012

90

80

70

60

50

40

30

20

10

0

Zelt and Ellis (1990) = horiz line

DE

PT

H (

KM

)

INVERSE Q MODEL COMPARISONS

1/Q p

Der et al. (1986) = dot-dashed

3 Hz

10 Hz

Fig. 9. The 1/Qp model obtained by modeling of seismic attributes from shot point 11 from SAREX. The dashed line shows the inverse-Q below the shot point at 0 offset and the solid line is the inverse-Q model for an offset of 500 km. The inverse-Q model of Zelt and Ellis (1990) is shown by the solid horizontal lines with vertical bars. The 1/Qp estimates from Der et al. (1986) for 3 and 10 Hz for the upper mantle lid are shown by the vertical dashed-dot lines at depths from 45 to 75 km.



NEAR OFFSET VELOCITY PROFILE

COMPARISON

0

20

40

60

80

100

5 6 7 8

VELOCITY (KM/S)

9

DE

PT

H (

KM

)

M.P. 0 = thick solid

G.M.P. -26 = thin solid

G.M.P. 24 = thin dashed

G.M.P. 74 = thin dot-dashed

Fig. 10a. Comparison of the near offset velocity slice used in this study at model position (M.P.) zero km offset (thick solid) and those from Gorman et al. (2002) for model positions (G.M.P.) –26 km (thin solid), 24 km (thin dashed) and 74 km (thin dot-dashed).



INTERMEDIATE OFFSET VELOCITY

PROFILE COMPARISONS

0

20

40

60

80

1005 6 7 8 9

VELOCITY (KM/S)

DE

PT

H (

KM

)

M.P. 174 = thick solid

G.M.P. 124 = thin solid

G.M.P. 174 = thin dashed

G.M.P. 224 = thin dot-dashed

Fig. 10b. Comparison of the intermediate offset velocity slice used in this study at model position (M.P.) 174 km (thick solid) and those from Gorman et al. (2002) for model positions (G.M.P.) 124 km (thin solid), 174 km (thin dashed) and 224 km (thin dot-dashed).



FAR OFFSET 1-D VELOCITY

PROFILE COMPARISONS

0

20

40

60

80

1005 6 7 8 9

VELOCITY (KM/S)

DE

PT

H (

KM

)

M.P.324 =thick solid

G.M.P.274=thin solid

G.M.P.324=thin dashed

G.M.P.374.=thin dot-dashed

Fig. 10c. Comparison of the far offset velocity slice used in this study at model position (M.P.) 324 km offset (thick solid) and those from Gorman et al. (2002) for model positions (G.M.P.) 274 km (thin solid), 324 km (thin dashed) and 374 km (thin dot-dashed).



Received: December 21, 2001; Accepted: September 23, 2002

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