JournalofGeophysicalResearch: SolidEarth RESEARCH ARTICLE 1.12/213JB1621 Key Points: A first regional-scale 3-D attenuation model for Northern California High values in the SFB area indicating potentially strong ground motion Generally low values in the western fault zones Supporting Information: Figure S1 Text S1 Correspondence to: G. Lin, glin@rsmas.miami.edu Citation: Lin, G. (214), Three-dimensional compressional wave attenuation tomography for the crust and uppermost mantle of Northern and central California, J. Geophys. Res. Solid Earth, 119, 3462 3477, doi:1.12/213jb1621. Received 21 AUG 213 Accepted 1 APR 214 Accepted article online 14 APR 214 Published online 3 APR 214 Three-dimensional compressional wave attenuation tomography for the crust and uppermost mantle of Northern and central California Guoqing Lin 1 1 Division of Marine Geology and Geophysics, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA Abstract I present a frequency-independent three-dimensional (3-D) compressional wave attenuation model (indicated by quality factor Q p ) for the crust and uppermost mantle of Northern and central California. The tomographic inversion used t values measured from amplitude spectra of 8,988 P wave arrivals of 3247 events recorded by 463 network stations through a 3-D seismic velocity model. The model has a uniform horizontal grid spacing of km, and the vertical node intervals range between 2 and 1 km down to 4 km depth. In general, the resulting Q p values increase with depth and agree with the surface geology at shallow depth layers. The most significant features observed in the Q p model are the high Q p values in the Sierra Nevada mountains and low Q p anomalies in the western fault zones. Low Q p values are also imaged in Owens Valley and Long Valley at shallow depths and the Cape Mendocino region in the lower crust ( km depth). An overall contrast of Q p values across the fault is observed in the creeping, Parkfield and Cholame-Carrizo sections of the San Andreas Fault. The new 3-D Q p model provides an important complement to the existing regional-scale velocity models for interpreting structural heterogeneity and fluid saturation of rocks in the study area. 1. Introduction The northern portion of California is one of the most seismically active and most extensively studied regions in the world. It spans from the Klamath Mountains in the north to the Tehachapi Mountains in the south, and from the Pacific-North America plate boundary to the Lake Tahoe-Reno area (Figure 1). The area comprises multiple subregions by their geological settings, the active fault zones in the west, the Sierra Nevada to the east and the Great Valley in the middle. Several fault systems make great contributions to the ongoing seismic activity, including the famous San Andreas Fault, the Maacama Fault, the Hayward Fault, the Calaveras Fault, the Green Valley Fault, and the Rinconada Fault. The geological features and the tectonic development of Northern California have been reviewed in great detail by Ernst [1981] and Benz et al. [1992] among others. Attenuation of seismic waves provides important independent constraints on Earth properties because their sensitivity to rock composition, fluid content, temperature, and other properties is distinct from that provided by P and S wave velocities. Tomographic inversions have been applied for the determination of the three-dimensional (3-D) attenuation structure in a way similar to velocity tomography. Generally, the high-frequency decay rates of direct wave amplitude spectra are used to determine the whole path attenuation, quantified by the frequency-independent attenuation operator t values. The t values from a set of earthquakes recorded by seismic stations are then inverted for the 3-D attenuation structure, indicated by the inverse of quality factor Q, by tracing the raypaths through a given velocity model, preferably a 3-D model [Eberhart-Phillips and Chadwick, 22]. Attenuation tomography has been applied to areas in Northern and central California, such as the Medicine Lake Volcano [Evans and Zucca, 1988], the aftershock region of the 1989 Loma Prieta earthquake [Lees and Lindley, 1994], the Geysers geothermal field [Zucca et al., 1994], and the San Andreas Fault Observatory at Depth (SAFOD) site in Parkfield [Bennington et al., 28]. However, no regional-scale 3-D attenuation model for the northern and central portions of California is available as yet. In this study, I present a frequency-independent 3-D model of the P wave attenuation, in terms of Q p, for the Northern and central California crust and upper mantle using seismic data archived at the Northern California Earthquake Data Center (NCEDC). The Q p model covers a region of 48 km by 84 km and extends to 4 km below sea level. It represents a regional-scale image of the structure that is difficult to LIN 214. American Geophysical Union. All Rights Reserved. 3462
Journal of Geophysical Research: Solid Earth 1.12/213JB1621 resolve in local studies and provides a useful complement for understanding the structural heterogeneity and fluid saturation of rocks in the study area. 2. Data Set Figure 1. Map of selected geological and geographic features in Northern and central California. Abbreviations are HRC, Healdsburg-Rodgers Creek Fault; GV, Green Valley Fault; SFB, San Francisco Bay; HF, Hayward Fault; ZF, Zayante Fault; SF, Sargent Fault; RLF, Reliz Fault Zone; RF, Rinconada Fault zone; SAF, San Andreas Fault; and SSJV, Southern San Joaquin Valley. Map is produced using a geographic information system database of geologic units and structural features in California by Ludington et al. []. The red straight lines indicate the profile locations for the model cross sections shown in Figure 12. The seismic data used in this study are obtained from the NCEDC and are recorded by the seismic stations of several regional networks, including the U.S. Geological Survey Northern California Seismic Network, the University of Nevada Reno Northern Nevada Seismic Network, and the California Department of Water Resources. I request first-arrival picks and waveform data for events between 199 and 21 in the study area. I only use events between magnitude 2.1 and. for the tomographic inversion to exclude smaller events that may have low signal levels and larger events that are usually characterized with complex radiation patterns. The data set consists of over 33, events (red dots in Figure 2) recorded by 463 seismic stations (blue triangles in Figure 2). 3. Tomographic Inversion Method I apply the simul2 inversion algorithm [Thurber, 1993; Eberhart-Phillips, 1993; Thurber and Eberhart- Phillips, 1999] to solve for variations at 3-D grid nodes. The simul2 algorithm and its earlier version simulps have been successfully applied to determine the 3-D models with different scales in various tectonic regions, such as the 1989 Loma Prieta aftershock region [Rietbrock, 1996], the shallow Hikurangi subduction zone in New Zealand [Eberhart-Phillips and Chadwick, 22; Eberhart-Phillips et al., 28], the Southern California crust [Hauksson and Shearer, 26], and the SAFOD site in Parkfield [Bennington et al., 28]. The simul2 algorithm is a damped least squares, full matrix inversion method intended for velocity and attenuation inversions. With the t values and 3-D velocity structure available, one can invert for the attenuation model by relating t to along the raypath between event i and station j using the following equation, tij = 1 ds + tstation ij (x, y, z) vp (x, y, z) (1) where vp is the P wave velocity model and ds is an element of path length. The local site effect can be described by a constant tstation operator when only the high-frequency decay rate is of interest [Anderson and Hough, 1984] and was included in the inversion of this study. The simul2 algorithm solves equation (1) for iteratively since the inversion is nonlinear. It uses a combination of parameter separation [Pavlis and Booker, 198; Spencer and Gubbins, 198] and damped least squares inversion to solve for the model perturbations. The appropriate damping parameters are usually selected using a data misfit versus model variance trade-off analysis. During the attenuation inversion, velocity model and earthquake locations are not changed. The full resolution matrix for the solution can be calculated to evaluate the quality of the models. LIN 214. American Geophysical Union. All Rights Reserved. 3463
1.12/213JB1621 4 38 36 1 km 4. Data Processing and t Determination In this study, the vertical component recordings are used to determine t values from P wave spectra. The amplitude spectrum is calculated for a 2.6 s time window around each P arrival time by using a multitaper approach by Prieto et al. [29]. A corresponding noise spectrum is also computed for a 2.6 s window right before the signal segment. I follow the techniques and notation in Rietbrock [21] and Eberhart-Phillips and Chadwick [22] for the determination of t values. Assuming an f 2 source model [Brune, 197], the velocity amplitude spectrum A ij (f) of event i at station j can be described by 2 f A -124-122 -12-118 ij (f) =2πfΩ ci ij f 2 ci + f 2 exp[ πft ij ] (2) Figure 2. Event and station distributions in the study area enclosed by where Ω ij is the long-period displacement spectral level and includes a the pink polygon. Red dots represent the 33, events between magnitude 2.1 and., for which t values are determined. Blue triangles stand for the 463 recording stations from the regional seismic networks. geometrical spreading factor, f ci is the source corner frequency of event i, and t is the frequency-independent attenuation operator. These unknown parameters are determined in an iterative spectra-fitting procedure. The best ij fitting corner frequency is defined as the frequency that minimizes the difference between the observed and calculated velocity spectra, fit = 1 N N [ log(aij ) log(d ij ) ] 2 j = 1 (3) where N is the number of observations for event i, A ij is the calculated, and D ij is the observed velocity spectrum. The final t ij and Ω ij values are calculated with the best fitting corner frequency. I also assign weights of, 1, 2, 3, and 4 to each observation according to the individual fitting error compared with the overall misfit, where represents the best fitting and 4 for the worst. I only use measurements with the signal-to-noise ratio above 3 in a continuous 1 Hz wide frequency band between 1 and 3 Hz. This frequency range is selected based on amplitude-frequency characteristics, and other factors, and is similar to those used in other studies [e.g., Schlotterbeck and Abers, 21; Eberhart- Phillips and Chadwick, 22; Hauksson and Shearer, 26]. Source corner frequency is grid searched between 2 and 2 Hz. Figure 3 shows examples of amplitude spectra and t values for an event. After the determination of t values, I select events with at least eight t values with weights smaller than 3 and separated by 2 km as the master events for the input of the tomography inversion. This results in 3247 events and 8,988 t values. The minimum t used in the inversion is.1, and maximum is.17, which are similar to the values in the Southern California attenuation study by Hauksson and Shearer [26]. The mean and standard deviation of the t values are.39 and., respectively. The master events are shown by the black dots in Figure 4. It is apparent that the ray coverage along the Great Valley in the middle part of the study area is not as good as other areas, therefore resulting in poor Q p resolution in this region.. Three-dimensional Q p Model Setup.1. 3-D Velocity Structure and Earthquake Relocation During the attenuation inversion, t values are inverted for Q p variations through 3-D ray tracing of a given velocity model, usually a 3-D model. Thurber et al. [29] and Lin et al. [21] have recently developed LIN 214. American Geophysical Union. All Rights Reserved. 3464
1.12/213JB1621 Amplitude Amplitude Amplitude Time (seconds) t * =.429 f c = 8.9 weight=1 PGH 1 2 1 2 4 Frequency (Hz) Amplitude Amplitude Amplitude Time (seconds) Time (seconds) 1 1 t * =.428 f c = 8.9 weight=2 t * =.1 f c = 8.9 weight=2 1 1 1 2 1 2 Spectra 1 3 Spectra 1 3 Spectra 1 2 1 3 1 4 HDL 1 4 BRV 1 2 1 2 4 1 2 1 2 4 Frequency (Hz) Frequency (Hz) Time (seconds) Time (seconds) Time (seconds) 1 1 t * =.463 f c = 8.9 weight=1 1 1 t * =.397 f c = 8.9 weight= 1 1 t * =.67 f c = 8.9 weight= Spectra 1 2 1 3 Spectra 1 2 1 3 Spectra 1 2 1 3 1 4 HJG PSR 1 4 PHP 1 2 1 2 4 1 4 1 2 1 2 4 1 2 1 2 4 Frequency (Hz) Frequency (Hz) Frequency (Hz) Figure 3. Examples of (top) traveltime series and (below) amplitude spectra along with the computed t values, corner frequencies, and assigned weights. regional 3-D P velocity models covering Northern and central California. Both studies use the finite difference, regional-scale version of the double-difference tomography algorithm tomodd [Zhang and Thurber, 26]. In this work, I use the model by Lin et al. [21] for the 3-D ray tracing, which covers the entire California state using stitched" subregion models with 1 to 2 km horizontal node spacing and 2 to 1 km node spacing in depth. The key advantage of the statewide model is the improved resolution in near-surface layers owing to the inclusion of abundant controlled source data and the better constrained deeper crustal structure because of the inclusion of arrival times at large epicentral distances from earthquakes in Southern California. During the simul2 inversion, variations in Q p do not alter traveltimes or hypocenters. Thus, the hypocenters are fixed in the inversion at their input locations without any changes. In this study, the master events were relocated by the 3-D velocity model before the attenuation inversion, starting with the double-difference earthquake relocations by Waldhauser and Schaff [28]..2. Initial Q p Model Based on the distributions of the master events, seismic stations and raypaths, I identified the parameterizations used in the inversion through a variety of tests. The horizontal grid spacing for the final attenuation model is km (squares in Figure 4). I use the same vertical nodes as in the 3-D velocity model of Lin et al. [21] with the intervals ranging between 2 and 7 km from 1 to 27 km depth and additional layers at 3 and 4 km depths (relative to mean sea level). The inversion grids are rotated 36 counterclockwise LIN 214. American Geophysical Union. All Rights Reserved. 346
1.12/213JB1621 Figure 4. Master events (black dots) and gridding nodes (orange squares) used in the attenuation tomography inversion. The Cartesian coordinate is rotated 36 counterclockwise with respect to latitude and longitude, with the X axis pointing to the southwest direction and Y axis to the northwest. The origin is located at (38., 121. ) (shown by the blue star at the center of the map). Gray lines show raypath coverage in the study area. The pink and red straight lines indicate the profiles for the model cross sections shown in Figures 1 12. with the X axis pointing to the southwest (SW) direction and Y axis to the northwest (NW). The coordinate origin is located at (38., 121. ). Note that in this study all depths are relative to mean sea level. It has been recognized that 3-D model inversions usually depend on the initial models, especially when starting with one-dimensional (1-D) models. In order to obtain a robust Q p model, I first searched for an optimal 1-D model. I started with uniform half-space models with Q p values varying within a wide range between 1 and 1 at the interval of. I ran a series of single-iteration inversions and chose the one that gives the minimum data misfit as the best constant Q p value. As shown in Figure a, a Q p value of 4 gives the minimum root-mean-square (RMS) of data misfit. For the range of Q p between 1 and 1, the RMS varies from.91 to.24 s. Values beyond this range significantly increase the data misfit and destabilize the inversion process. Next I used 4 as the starting Q p value to run another set of single-iteration series and then the layer average values of the resulting model as the starting model for the next iteration. This process was repeated a few times until the layer average attenuation values of the inverted model were not significantly different from the input model and they fit the data equally well. The RMS of data misfit was reduced from.24 to.19 s during this process. This final 1-D model was used as the starting model for the final attenuation inversion shown in this paper. Figure b shows examples of the above 1-D models. 1.9 (a) (b) Normalized RMS.8.7.6. damping = 4 1 2.4.3 2 4 6 8 1 Starting constant Iterative models Model used for the final inverion 3 2 4 6 8 Figure. (a) Initial constant Q p determined by the RMS of attenuation operator t residuals. The RMS reaches the minimum value at Q p = 4. (b) Examples of 1-D Q p models. Dashed line shows the constant Q p value of 4. Dotted ones are examples of the 1-D models during the model selection. Thick line is the starting 1-D model for the inversion of the final 3-D tomography model. LIN 214. American Geophysical Union. All Rights Reserved. 3466
1.12/213JB1621 Normalized data misfit 1.9.9.8.8.7.7 damping =.7.2.4.6.8 1 Normalized model variance Figure 6. Trade-off curve between data misfit and model variance for attenuation inversion. The optimal damping parameter for Q p inversion is.7..3. Model Parameterizations Damping parameters are usually applied to stabilize the inversion process [e.g., Eberhart-Phillips, 1986, 1993]. I selected the optimal damping for Q p by running a series of single-iteration inversions with a large range of damping values and plotting the data variance versus model variance trade-off curves, similar to the approach applied to the velocity model inversions [e.g., Lin et al., 27; Lin and Thurber, 212; Lin, 213]. I chose.7 as the simul2 damping value for Q p, which produced a good compromise between data misfit and model variance (Figure 6). During the tomographic inversion, I applied distance weighting factors, which are 1. for distances closer than 1 km,. beyond 14 km, and linearly tapered between them. This distance weighting is commonly used for body wave tomographic studies and similar to the attenuation study for Southern California by Hauksson and Shearer [26]. In order to estimate the robustness of the model, I also compute the resolution matrix during inversions. 6. Final Model Results The tomographic inversion is convergent after five iterations. I compute the RMS of the t residuals for the master events resulted from both the starting 1-D and final 3-D models. The residual RMS drops from.19 to.12 s after the inversion (Figure 7). This amount of reduction is comparable with other regional/local-scale attenuation studies [e.g., Eberhart-Phillips and Chadwick, 22; Hauksson and Shearer, 26; Bennington et al., 28; Nakajima et al., 213]. Normalized Histogram.18.16.14.12.1.8.6.4.2.2.1.1.2 residual (s) Figure 7. The t residual distributions for the starting (gray) and final (black-white) Q p models. The root-mean-square of the residuals drops from.19 to.12 s for the master events. 6.1. Resolution Test To assess the model quality, I performed a checkerboard resolution test similar to those for the velocity model inversions [e.g., Thurber et al., 29; Lin et al., 21; Lin and Thurber, 212]. I computed synthetic t values through the starting 1-D model with ±2% Q p perturbations across two horizontal grid nodes and alternating high and low Q p at different depths. Event hypocenters, station locations and t raypaths have the same distributions as the real data. I also applied the same inversion parameters, such as the damping parameter, as in the real data inversion. Figure 8 shows map view and cross-section comparisons between the true and inverted Q p models. The model is considered to be well resolved where the checkerboard images are recovered. The pink contours enclose LIN 214. American Geophysical Union. All Rights Reserved. 3467
1.12/213JB1621 (A1) Depth=1. (km) Depth=4. (km) Depth=8. (km) (A2) Depth=1. (km) Depth=4. (km) Depth=8. (km) 3 3 3 3 3 3 - a a - - - - - -3 b b -3-3 -3-3 -3 - - - Depth=14.(km) Depth=2. (km) Depth=27. (km) - - - Depth=14.(km) Depth=2. (km) Depth=27. (km) 3 3 3 3 3 3 - - - - - - -3-3 -3-3 -3-3 - - - (B1) b (C1) b a a 1 1 2 2 3 3 3 4 1 2 3 4 6 7 8 9 1 11 12 13 1 2 3 4 6 7 8 9 1 11 12 13 14 16 17 18 (B2) Distance (km) b Distance (km) (C2) b a a 1 1 2 2 3 3 3 4 1 2 3 4 6 7 8 9 1 11 12 13 1 2 3 4 6 7 8 9 1 11 12 13 14 16 17 18 Distance (km) Distance (km) (%) -2-18 -16-14 -12-1 -8-6 -4-2 2 4 6 8 1 12 14 16 18 2 Figure 8. Checkerboard test for the Q p model. (A1) Map view of the true model. White lines show the profile locations for the cross sections in B1, C1, B2, and C2. Note that these two profiles are not parallel or perpendicular to the grid coordinates; therefore, the Q p perturbations are not exactly alternating across grids. (A2) Map view of the inverted model. (B1, C1) Cross sections of the true model along profiles a-a and b-b, respectively. (B2, C2) Cross sections of the inverted model along the same profiles. The pink contours in A2, B2, and C2 enclose the areas where the diagonal element of the resolution matrix is greater than.2. Black lines in map views denote coast line, state boundary, and surface traces of mapped faults. - - - the well-resolved regions where the diagonal element of the resolution matrix is greater than.2 (1. represents the best resolution and. not resolved at all). Note that the values of the resolution throughout the grid space could be significantly increased by decreasing the damping parameter, but the inversion results may be less reliable. The model is generally well resolved at depths of 4 km and greater, where abundant crossing rays are available. The resolution at shallow and deep layers is limited. The Q p model is best resolved in the western fault zones owing to the great seismic activity, especially along the San Andreas Fault. The Sierra Nevada is also relatively well resolved, but strong smearing is seen near Long Valley. It is not surprising that the Great Valley in the middle of the study area is very poorly resolved due to the lack of events and seismic stations in this area. Cross sections along two profiles a-a and b-b (shown in the map view) are also provided to show vertical smearing. The model resolution is generally good above km depth along a-a, but slightly poorer along b-b, which is near the edge of the study area. LIN 214. American Geophysical Union. All Rights Reserved. 3468
1.12/213JB1621 (a) Depth=1. (km) (b) Depth=4. (km) 36 36 27 27 18 18 9 9-9 -9-18 -18-27 -27-36 -36 18 9-9 -18 18 9-9 -18 4 63 1 8 1 398 631 1 (c) Depth=8. (km) (d) Depth=14. (km) 36 36 27 27 18 18 9 9-9 -9-18 -18-27 -27-36 -36 18 9-9 -18 18 9-9 -18 1 8 1 398 631 1 (e) Depth=2. (km) (f) Depth=27. (km) 36 36 27 27 18 18 9 9-9 -9-18 -18-27 -27-36 -36 18 9-9 -18 18 9-9 -18 1 398 631 1 Figure 9. 6.2. Map Views I present the final 3-D Q p model in both map views and cross sections. Figure 9 shows the map view slices of the Q p model at different depths from 1 to 27 km below sea level. The most striking features of the Q p model are the prominent low anomalies in the southwest portion of the study area and the elevated values in the Sierra Nevada mountains on the northeast (NE) side. At 1 km depth, Q p varies between 3 and 2 in the fault systems along the western shoreline. Slightly higher Q p anomalies ranging from 1 to 3 are observed in the Sierra Nevada. A low Q p body is observed at Owens Valley (x = 12 km and y = 24 27 km). The attenuation contrast between the fault zones along the coastline and the Sierra Nevada is clearly seen at 4 km depth. Great Q p variations start to show at this layer. Strong attenuation difference across the San Andreas Fault (SAF) in the southwest portion of the study area near Parkfield is visible with the SW side (>3) higher than the NE side (<1). The Q p value at Owens Valley is slightly lower than the nearby regions. However, the lowest Q p anomaly (6 7) in this area occurs in its northwest area of Long Valley caldera, which is surrounded by high Q p anomalies (ranging from to 11) in the Sierra Nevada Mountains and is still visible at the next depth layer. These single-node anomalies should be analyzed carefully. Given the resolution values in these areas, they may represent local attenuation variations smeared at the coarse single nodes. At 8 km depth, the high Q p bodies in the northeast portion are well correlated with the Sierra Nevada Mountains. In contrast, low Q p values ( ) are observed in the Maacama Fault Zone, the Green Valley and Calaveras Fault zone in the northwest region. Very low Q p anomalies ( 12) are also seen in the creeping, Parkfield and Cholame-Carrizo sections of the SAF. The attenuation contrast across the SAF in these sections becomes stronger with the Q p varying from 12 on the SW side of the SAF to 2 on the NE side. The highest Q p (up to ) at LIN 214. American Geophysical Union. All Rights Reserved. 3469
1.12/213JB1621 NW SE A shoreline SFB SAF ZF RF A 1 2 x=12 B MF Parkfield B 1 2 x=6 C C 1 2 x= D D 1 2 x=-6 E Long Valley E 1 2 x=-12 3 2 1 - -1 - -2 - -3 VE=3 63 1 8 1 398 63 1 8 Figure 1. Cross sections of the Q p model along the five profiles in the NW-SE direction shown in Figure 9f. The color bar is in the common logarithmic scale (i.e., log 1 ). The black dots represent the double-difference relocated earthquakes from Waldhauser and Schaff [28] within ±3 km of the profile. The white contours enclose the area where the diagonal element of the resolution matrix is greater than.2. Note that the vertical exaggeration is 3. Abbreviations are SFB, San Francisco Bay; SAF, San Andreas Fault; ZF, Zayante Fault; RF, Rinconada Fault zone; and MF, Maacama Fault. this depth takes place in the area between the SAF Peninsular and Santa Cruz Mountains sections and the Hayward Fault, indicating potentially stronger ground motion in this area. Similar attenuation structure is seen at 14 km depth, but the attenuation contrast becomes weaker. The Q p model is relatively uniform at the next two depth layers of 2 and 27 km. At 2 km depth, very low Q p anomalies are seen in the north part of the Great Valley. The most striking features seen at these two depths are the prominent low Q p anomalies of 3 4 near the Cape Mendocino region, the westernmost point of California. Throughout the entire depth range, the Sierra Nevada is dominated by high Q p values, whereas the Great Valley is barely resolved due to the lack of seismicity. 6.3. Cross Sections Attenuation variations with depth can be more clearly seen in cross sections through the new Q p model. I show two types of cross sections through the Q p model, one parallel to the SAF in the NW-SE direction (shown by the letters in Figures 4 and 9f), and the other perpendicular to the SAF in the SW-NE direction (shown by the numbers in Figures 4 and 9f). Figure 1 shows cross sections of the Q p model along five profiles in the NW-SE direction parallel to the SAF sliding from the SW to the NE side of the study area. The most Figure 9. (a-f) Map views of the Q p model at different depth slices. The white contours enclose the areas where the diagonal element of the resolution matrix is greater than.2. Black lines denote coast line, state boundary, and surface traces of mapped faults. The color bar is in the common logarithmic scale (i.e., log 1 ). Major geological features are marked in Figure 9a. Pink and red lines in Figure 9f show the profile locations for the following cross sections, same as those in Figure 4 but in the Cartesian coordinate. LIN 214. American Geophysical Union. All Rights Reserved. 347
1.12/213JB1621 complex Q p structures occur in cross sections A-A and E-E, which cut the western fault zones and the Sierra Nevada, respectively. Profile A-A along the shoreline is subparallel to the SAF and shows the most complex structure among all the five cross sections. The most significant feature along this profile is the low Q p values near the surface and high Q p anomalies at depth in the San Francisco Bay (SFB). The majority of the seismicity near the SAF is the aftershock sequence of the 1989 Loma Prieta earthquake. The next profile B-B is between the active fault zone and the Great Valley. The Q p model is well resolved throughout this cross section because of the uniformly distributed seismicity. Low Q p anomalies are observed in the lower crust (>2 km depth) of several fault zones, including the Cape Mendocino region, the Green Valley Fault, the Greenville Fault, and the SAF creeping, Parkfield and Cholame sections. The majority of the Q p model is poorly resolved in cross section C-C along the Great Valley due to the lack of seismicity. The Q p structure along profile D-D between the Great Valley and the Sierra Nevada starts to show strong variations with low Q p (9 4) in the Great Valley (y = 33 8 km) and high Q p anomalies (2 9) in the Sierra Nevada (y =8-33 km). The last profile cuts through mainly the Sierra Nevada where high Q p anomalies dominate. Along with the active seismicity in Long Valley, complex Q p structure is observed (y = 2-24). Low Q p values (8 ) are resolved between and 8 km depth, and high anomalies ( 1) are seen below that. The highest Q p ( 126) along this profile is observed between and km depth to the southeast side. In Figure 11, I show the Q p model along the profiles in the SW-NE direction moving from the northwest to southeast side of the study area. In the first cross section 1-1 through the Klamath Mountains, Lake Shasta, and Mount Shasta at the north edge of the study area, the attenuation structure is relatively uniform with the Q p varying from near the surface to in the lower crust (>2 km depth). The most notable feature is the low Q p body ( 32) in the Cape Mendocino region (x = 8 3 km). The seismicity is rather sparse along this cross section. The second profile 2-2 cuts through the Maacama Fault zone, the Great Valley, and the Sierra Nevada. The majority of the seismicity is focused beneath the Maacama Fault zone coinciding with a slightly high Q p zone between 2 and 6 km depths. In the second half of this cross section, the Q p contrast between the Great valley and the Sierra Nevada can be clearly seen. Beginning from cross section 3-3, the Q p structure becomes more complex, consistent with the complicated geological structure along this profile. The most significant features in this section are the high Q p anomalies between the SAF and the Hayward Fault. The Q p values beneath the SFB are slightly higher than the nearby Green Valley Fault Zone near the surface but greatly elevated (up to 1) between 6 and 2 km depths. Another high Q p body occurs below the Sierra Nevada and reaches to the highest values of 14 near the California-Nevada state boundary. The Q p model is not resolved in the Great Valley in the middle section. In the next cross section farther to the southeast (4-4 ), the most complex Q p structure is again near the western fault zones. Very low anomalies ( ) are seen at shallow depths in the active fault zones, including the Zayante Fault, the San Andreas Fault, and the Calaveras Fault. In contrast to these low Q p values, high anomalies are seen between 6 and 17 km depths. The high Q p body southwest of the SAF is about km deeper than the one between the SAF and Calaveras Fault. High Q p anomalies are again observed under the Sierra Nevada. In the last cross section -, the seismicity mainly concentrates over the complex fault zones in the Sierra Nevada, including the Hilton Creek and Long Valley fault zones. A high Q p body is visible southwest of the seismicity in the Sierra Nevada. As seen in the map views, the attenuation contrast across the SAF is visible along this profile with higher Q p on the SW side and lower anomalies on the other side between and km depths. 6.4. The t Terms station As indicated by equation (1), the local site effect can be described by a constant t operator. In this study, station t station terms were computed during the Q p inversion by applying a relatively large damping parameter compared with the Q p damping in order to avoid projecting resolvable shallow attenuation structure into the station corrections. The resolved t values range from.2 to.3 and do not show correlations with station station elevations (Figure S1 in the supporting information). The areas with low near-surface Q p (e.g., fault zones along the western coastlines) are dominated by positive station terms, whereas negative values are more common in the areas with high near-surface Q p (e.g., the Sierra Nevada Mountains). This observation is related to the fact that 3-D tomographic inversion tends to overestimate near-surface velocities in the low velocity areas and underestimate velocities in the high velocity areas [e.g., Lin et al., 27; Hauksson and Shearer, 26], which can also be seen in the resolution test (Figure 8). It may also be caused by the relatively coarse grid spacing and uneven ray coverage used in the inversion. LIN 214. American Geophysical Union. All Rights Reserved. 3471
1.12/213JB1621 SW NE 1 2 y=24 1 2 y=12 1 2 y= 1 2 y=-12 1 2 y=-24 1 - -1 - VE=2 63 1 8 1 398 63 1 8 Figure 11. Cross sections of the Q p model along the five profiles in the SW-NE direction shown in Figure 9f. The color bar is in the common logarithmic scale (i.e., log 1 ). The black dots represent the double-difference relocated earthquakes from Waldhauser and Schaff [28] within ±3 km of the profile. The white contours enclose the area where the diagonal element of the resolution matrix is greater than.2. The vertical exaggeration is 2. Abbreviations are SAF, San Andreas Fault; MF, Maacama Fault; SFB, San Francisco Bay; HF, Hayward Fault; GF, Green Valley Fault; WTDPF, West Tahoe Dollar Point Fault; ZF, Zayante Fault; CF, Calaveras Fault; WWRF, West Walker River Fault; RF, Rinconada Fault zone; HCF, Hilton Creek Fault; and LVF, Long Valley Fault. 7. Discussion Generally, the Q p values in this study increase with depth and the range of variations is similar to other regional-scale studies [e.g., Hauksson and Shearer, 26]. Although the model resolution may not be comparable to local studies, the Q p structure agrees with the geological features very well, with high Q p anomalies in the mountain ranges, such as the Sierra Nevada Mountains, and low Q p values in the valleys, such as Owens Valley and Long Valley. In order to illustrate this, I show cross sections along two profiles a-a and b-b in Figure 12. These profile locations are very close to those for the geological units across the Coast Ranges and the SAF in the Parkfield-Cholame sections by Zoback et al. [22], based on the compilation of seismic, gravity, magnetic, heat flow, and geological data by Page et al. [1998]. In Figure 12a, the new Q p model is shown across the Santa Cruz Mountains, SFB, East Bay Hills, and the northern Diablo Range (profile a-a in Figures 1 and 9f). The lowest Q p values (<1) take place near the surface between the San Gregorio Fault and the SAF, which are consistent with the marine sedimentary rocks there. The relatively low Q p values from LIN 214. American Geophysical Union. All Rights Reserved. 3472
1.12/213JB1621 (B) (A) 1 2 3 1 2 3 4 6 7 8 9 1 11 12 13 Distance (km) 1 9 1 398 631 1 1 2 3 3 4 1 2 3 4 6 7 8 9 1 11 12 13 14 16 17 18 Distance (km) 79 1 126 9 2 1 316 398 1 631 794 Figure 12. Cross sections of the Q p model along profiles a-a and b-b shown in Figure 9f across the (a) Coast Ranges and the (b) San Andreas Fault near Parkfield and Cholame. These profiles are very close to those in Zoback et al. [22, Figure 9]. Again, the black dots represent the double-difference relocated earthquakes from Waldhauser and Schaff [28], and the white contours enclose the area where the diagonal element of the resolution matrix is greater than.2. Abbreviations are SGF, San Gregorio Fault; SAF, San Andreas Fault; and SFB, San Francisco Bay. the surface to 1 km depth in this area agree with the location of the thickened oceanic crust suggested by Page et al. [1998]. The most striking feature along this cross section is the very high Q p (>1) beneath the SFB, which is covered by Quaternary alluvium and marine deposits near the surface and constructed as Franciscan Complex by Holbrook et al. [1996]. The high Q p values suggest potentially stronger ground motion in this area. The high Q p deeper than 2 km depth may reflect the mantle. From the Hayward Fault to the Calaveras Fault and the northern Diablo Range, very low Q p anomalies are correlated with the Franciscan Complex, the Great Valley Sequence, and the Quaternary alluvium in the Great Valley (Figure 1). The lowest values ( 1 1) in this area coincide with the Great Valley Sequence, where the aggregate stratigraphic thickness is at least 12 km [Irwin, 199]. In Figure 12b, the Q p model is shown across the San Andreas Fault near Parkfield and Cholame. The most significant feature along this profile is the Q p difference between the SW and NE sides of the SAF. The Salinian Block between the Rinconada Fault and the SAF shows the highest Q p anomalies in the upper and middle crust along this profile. The San Luis Range between the Hosgri and Rinconada Faults is predominantly Franciscan Complex, including bodies of greenstone and serpentine, and shows Q p values comparable to those in the adjacent Salinian Block. High Q p values at about 1 km depth from the Hosgri through the SAF may represent the brittle-ductile transition zone. From the SAF to the San Joaquin Valley, very low Q p anomalies again coincide with the metasedimentary rocks of the Franciscan Complex, the Great Valley Sequence, and the Quaternary alluvium in Great Valley [Irwin, 199]. Although the model is poorly resolved below 3 km depth, the very high Q p body between 12 and 18 km distance may be the expression of the mantle wedge. Some major features of the new 3-D Q p model are summarized in the following sections. 7.1. Low Q p Regions The active fault zones in the western part of the study area, which are primarily dominated by Franciscan assemblage, generally show low Q p anomalies throughout the entire depth range. The Maacama Fault zone, the Healdsburg-Rodgers Creek Fault, the Green Valley, the Greenville Fault, and the Calaveras Fault in the northwest region always show low Q p anomalies (with the lowest values ranging from 3 at 1 km to 213 LIN 214. American Geophysical Union. All Rights Reserved. 3473
1.12/213JB1621 14 12 1 8 6 4 2 3 4 6 7 8 Vp (km/s) 3 7 12 18 32 Figure 13. Q p versus V p values at the well-resolved inversion nodes. Points are colored by grid depths. Pink dashed line marks V p at 7.2 km/s. at 14 km depth), which are consistent with the Franciscan terrain and may also reflect the presence of pore fluids in these fault zones [Winkler and Nur, 1979; Tompkins and Christensen, 1999]. The Parkfield region in the central portion of California is probably the most extensively studied area in California and is also dominated by very low Q p values. Although the model presented in this paper cannot be compared with the fine resolution in some previous studies, similar features are observed. Abercrombie [2] used borehole data to invert for Q values on each side of the San Andreas Fault near Parkfield. She found that the Q p value on the NE side of the SAF is about between.6 and.9 km and the attenuation (i.e., Q 1 ) on the NE side of the fault (Q NE 1) is approximately twice that on the SW side (Q SW 2) above km depth. Those values greatly agree with what is resolved in this study. Bennington et al. [28] inverted 3-D Q models for the SAFOD site in Parkfield. Both their model and the one in this study observe an attenuation contrast across the SAF with the SW side dominated by higher Q p values and NE side by lower Q p values. The high Q p is interpreted as reflected in the Salinian basement rocks, and the low values are caused by the metasedimentary rocks of the Franciscan terrain. The Q p contrast becomes insignificant below 2 km depth (Figure 12b). Low Q p anomalies are also commonly observed in the geothermal fields and calderas, such as the Geysers geothermal field and Long Valley caldera. Zuccaetal.[1994] studied the seismic velocity and attenuation structure of the Geysers geothermal field and observed the decrease of Q p with depth within the reservoir (i.e., above 1. km depth). Romero et al. [1997] observed low Q p in Geysers correlated with Franciscan melange and high Q p corresponding to metagraywacke units ( km study area). However, given the grid spacing and depth intervals used in this study, it is difficult to image such detailed structure at very shallow depths. The Sierra Nevada mountains in the eastern side of the study area are dominated by high Q p anomalies with the exception of Long Valley caldera, where the low Q p anomalies of 7 67 are surrounded by high Q p ranging from to 11. Ponko and Sanders [1994] observed high attenuation (i.e., low Q p ) beneath Mammoth Mountain and the resurgent dome in Long Valley caldera and interpreted due to presence of compressible fluid. Sanders et al. [199] also observed low Q p anomalies along the southern rim of Long Valley caldera at 4 km depth. The Q p values in Long Valley are expected to be low by the volcanic flow rocks and marine sediments and may also be affected by presence of fluid and high heat flow. The low Q p anomalies at 4 and 8 km depths in this study greatly agree with these results. The Franciscan assemblage spans the entire Coast Ranges and covers the Cape Mendocino region in the north. One of the interesting features in the limited-resolved deeper layers (at 2 and 27 km depths) is the low Q p anomalies observed near the Cape Mendocino region (Figures 9e and 9f). Beaudoin et al. [1994] inverted the crustal velocity structure in this area and interpreted the upper km depth as Coastal Belt Franciscan and Gorda crust between and 21 km depth. Verdonck and Zandt [1994] also put constraints on the top of the basaltic layer of the Gorda plate at 18 2 km depth. The low Q p values observed in the current study are consistent with the Franciscan assemblage above km depth and may be associated with the subducting Gorda plate at deeper layers. 7.2. High Q p Blocks The most significant feature in the resolved model is the Q p contrast between the western fault zones and the Sierra Nevada mountains. High Q p anomalies are observed dominating in the Sierra Nevada throughout LIN 214. American Geophysical Union. All Rights Reserved. 3474
1.12/213JB1621 the entire depth range, particularly above km depth. Corresponding to the relatively uniform V p structure within the Mesozoic arc plutons [Fliedner et al., 2], high Q p anomalies are observed ranging from at 1 km to at 14 km depth and the Q p values are relatively uniform at 8 and 14 km depths. One of the striking features observed in the Q p model is the high Q p block in the SFB area between and km depth (in cross sections A-A and a-a ). This block extends from the SAF to the Hayward Fault and has very little seismicity (Figure 12a), which may be due to the competent blueschist facies equivalents under high-pressure and low-temperature conditions in the Franciscan terrain [Page et al., 1998]. The Loma Prieta aftershock region (A-A in Figure 1) falls within this region. Lees and Lindley [1994] investigated the attenuation variations in the aftershock region of the Loma Prieta earthquake. They also observed low Q p near the surface and high Q p in the fault zone at depths of 1 18 km, similar to what is observed in this study, but with a coarser structural feature because of the relatively large grid spacing in this study. Along with the high Q p block in the SFB, the Salinian block on the western side of the SAF is another area with high Q p values observed in the western fault zone, which is interpreted as a piece of Sierra Nevada arc transported northward by the SAF [e.g., Whidden et al., 1998]. The block mainly consists of granitic rocks and is inherently more resistant mechanically than the Franciscan Complex and often shows high Q p anomalies [Page et al., 1998]. 7.3. Q p -V p Relationship In general, the new 3-D Q p model shows similar patterns as the velocity models for Northern California by Thurber et al. [29] and Lin et al. [21]. Figure 13 presents the Q p values versus the P wave velocities by Lin et al. [21] at the well-resolved Q p inversion nodes. At shallow depths (< km), especially near the surface, where the velocity variations are the most heterogeneous, Q p values are observed to range between 3 and 2. For V p between 6 and 7.2 km/s, the Q p displays significant variations even when the velocity is relatively uniform, which may be caused by temperature and fluid content. The Q p -V p relationship for V p < 7.2 km/s does not show a linear relationship as presented in previous studies [e.g., Olsen, 2; Olsen et al., 23] but seems to be better fit by an exponential curve. An exponential relationship between Q p and V p is observed for the upper mantle (1 6 km depth) of the Tonga/Fiji region [Roth et al., 2]. Similar relationship for the crustal data in this study may indicate that this kind of relationship is not a unique feature for mantle materials. Roth et al. [2] showed that their Q p -V p relationship is consistent with laboratory experiments assuming the attenuation anomalies are mainly caused by temperature variations. This should be investigated with more details for the crustal data. Values at deeper layers (2 and 27 km depths) do not fit with this curve, probably due to the limited number of points at these depths. Seismic attenuation also depends on temperature of rocks, which is roughly proportional to the heat flow. Hence, a spatial correlation between heat flow and attenuation is usually expected. I compared the Q p model at 1 km depth with the heat flow data at the borehole locations obtained from the U.S. Geological Survey in the study area. A general increase of well-resolved Q p with reduced heat flow can be seen, although no simple correlation between the heat flow and attenuation can be summarized. The best correlation occurs along the San Andreas Fault from the SFB to Cholame, where high heat flow is prominent with the corresponding low Q p values. Similar correspondence is also observed in the Maacama Fault zone. The cold Sierra Nevada is dominated by low heat flow and high Q p anomalies. Although the Q p values near Long Valley do not correlate well with the surface heat flow, they both show similar anomalous distributions. Areas that do not show clear correlations between the Q p and heat flow usually have limited Q p resolutions. 7.4. Frequency Dependence of Q The Q p model presented in this study is assumed to be frequency independent and therefore should not be directly compared with frequency-dependent models. The frequency dependence of Q in the frequency range of this study (1 3 Hz) is usually expressed by Q = Q f η [e.g., Anderson and Given, 1982; Toksoz et al., 1987], where f is the central frequency of the frequency-dependence band and η is a constant between (equivalent to frequency independence) and 1, but could also be negative sometimes. Adams and Abercrombie [1998] showed that the attenuation can be strongly frequency dependent between 1 and 1 Hz and can be assumed frequency independent above 1 Hz. If we assume the range of the frequency dependence is 1 1 Hz (the central frequency f =. Hz) and η=., then the Q p values obtained in this work are about 2.3 times as large as Q. Erickson et al. [24] determined frequency-dependent crustal attenuation for Northern California using Lg surface waveforms in the frequency range of. 16 Hz. Their results show that Lg Q is 6 (±22)at12Hz.Ford et al. [28] determined 1-D Lg regional attenuation for Northern LIN 214. American Geophysical Union. All Rights Reserved. 347
1.12/213JB1621 California by comparing different analysis methods and investigating its frequency dependence. These Lg Q values can be compared with Q s, but not directly with Q p values. Q p Q s ratio is also an important parameter to study fluid saturation. While most of the attenuation studies concentrated on Q s, a variety of Q p Q s values between.7 and 2. have been estimated for different areas in California [e.g., Abercrombie, 1997; Aster and Shearer, 1991; Olsen, 2; Olsen et al., 23]. However, a robust 3-D Q s or Q p Q s inversion for the current study is difficult to achieve because the majority of the seismic stations in the study area are vertical component stations, and there is no reliable V s model for 3-D ray tracing for Northern California, although Lin et al. [21] presented a coarse 3 3 km S wave velocity model based on USArray and Southern California Seismic Network recordings.hauksson and Shearer [26] provided a detailed discussion on the frequency dependence of attenuation for Southern California. 8. Conclusions In this paper, I present a regional-scale frequency-independent 3-D Q p model for Northern and central California by inverting t values using the simul2 tomographic algorithm. The main difference between this study and previous ones is the large spatial scale of the new Q p model. It images the attenuation structure of the crust and uppermost mantle to reveal some features that are difficult to resolve in local studies. It extends to greater depths due to the inclusion of substantial data at large epicentral distances and a statewide 3-D velocity model. The resolved Q p values generally increase with depth and agree with the surface geology at shallow depth layers. The most significant features observed in the Q p model are the high Q p values in the Sierra Nevada mountains and low Q p anomalies in the western fault systems. Low Q p values are also imaged in Owens Valley and Long Valley at shallow depths and the Cape Mendocino region in the lower crust and uppermost mantle. It is unfortunate and not surprising that the model lacks resolution in the Great Valley due to the absence of stations and events there. An overall contrast of Q p values across the fault is observed in the creeping, Parkfield and Cholame-Carrizo sections of the San Andreas Fault. This model provides a first-order measurement of the attenuation in Northern California and serves as an important complement to the 3-D velocity model about rock properties and structure heterogeneity. It can also be used as a starting point for future frequency-dependent attenuation studies. Acknowledgments I thank the NCEDC and the seismic networks for maintaining the seismic data and making them available and Clifford H. Thurber for his simul2 program. I am grateful to Michael Pasyanos and an anonymous reviewer for their constructive and detailed comments. Figures were made using the public domain GMT software [Wessel and Smith, 1991] and Matlab. References Abercrombie, R. (2), Crustal attenuation and site effects at Parkfield, California, J. Geophys. Res.,, 6277 6286. Abercrombie, R. E. (1997), Near-surface attenuation and site effects from comparison of surface and deep borehole recordings, Bull. Seismol. Soc. Am., 87, 731 744. Adams, D. A., and R. E. Abercrombie (1998), Seismic attenuation above 1 Hz in Southern California from coda waves recorded in the Cajon Pass borehole, J. Geophys. Res., 13, 24,7 24,27. Anderson, D., and J. Given (1982), Absorption band Q model for the Earth, J. Geophys. Res., 87, 3893 394. Anderson, J. G., and S. E. Hough (1984), A model for the shape of the Fourier amplitude spectrum of acceleration at high frequencies, Bull. Seismol. Soc. Am., 74, 1969 1993. Aster, R. C., and P. M. Shearer (1991), High-frequency borehole seismograms recorded in the San Jacinto Fault zone, Southern California Part 2. Attenuation and site effects, Bull. Seismol. Soc. Am., 81, 181 11. Beaudoin, B., M. Magee, and H. Benz (1994), Crustal velocity structure north of the Mendocino Triple Junction, Geophys. Res. Lett., 21, 2319 2322. Bennington, N., C. Thurber, and S. Roecker (28), Three-dimensional seismic attenuation structure around the SAFOD site, Parkfield, California, Bull. Seismol. Soc. Am., 98, 2934 2947. Benz, H. M., G. Zandt, and D. H. Oppenheimer (1992), Lithospheric structure of Northern California from teleseismic images of the upper mantle, J. Geophys. Res., 97, 4791 487. Brune, J. N. (197), Tectonic stress and the spectra of seismic shear waves from earthquakes, J. Geophys. Res., 7, 4997 9. 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Stuart (28), Three-dimensional attenuation structure of the Hikurangi subduction zone in the central North Island, New Zealand, Geophys. J. Int., 174, 418 434. Erickson, D., D. E. McNamara, and H. M. Benz (24), Frequency-dependent Lg Q within the continental United States, Bull. Seismol. Soc. Am., 94, 163 1643. Ernst, W. G. (1981), The Geotectonic Development of California, 76 pp., Prentice-Hall, Upper Saddle River, N. J. Evans, J. R., and J. J. Zucca (1988), Active high-resolution seismic tomography of compressional wave velocity and attenuation structure at Medicine Lake Volcano, Northern California Cascade Range, J. Geophys. Res., 93,,16,36. Fliedner, M. M., S. L. Klemperer, and N. I. Christensen (2), Three-dimensional seismic model of the Sierra Nevada arc, California, and its implications for crustal and upper mantle composition, J. Geophys. Res.,, 1,899 1,922. LIN 214. American Geophysical Union. All Rights Reserved. 3476