34 Chapter 3 Isotropic scattering and crustal imaging with wide-angle prestack migration 3.1 Introduction Earthquake seismologists may be reluctant to believe that one can successfully image crustal faults using only P, P, isotropic scattering characteristics and earthquake sources, as I do here. For instance, Aki (1992) shows that P, S conversion for seismic waves is much greater than S, P.Thus, the dominance of S,waves in the coda of seismograms raises concern about the validity of dealing with only P, P scattering in imaging crustal reectors. In spite of this, successful P, P scattering applications of this type abound in oil-related seismic imaging for fracture detection and reservoir characterization (e.g., Mittet et al., 1997). I believe this is the rst time P, P scattering is used for crustal targets with wide-angle prestack migration of earthquake recordings.
35 3.2 Crustal imaging method 3.2.1 Wide-angle prestack depth migration I carry out the search for scattering structures and reectors, like steeply-dipping faults and thrust faults, ramps, and detachments, with the assumption that these scatterers include a component that radiates isotropically (e.g., Lay, 1987; Lynnes and Lay, 1989; Revenaugh, 1995c). Under this simple assumption, which isvalid for structures that cause variations in Lame parameter (Aki and Richards, 198, Vol. II, p. 728-734; Sato, 1984; Wu and Aki, 1985; Tarantola, 1986; Wu, 1989; Ikelle et al., 1992; Tura and Johnson, 1993), the search for crustal structures using earthquake seismograms becomes practical. Ignoring the reection angle at the image point leads to my treatment of the data as a P, P isotropic scattering problem. The strength of the scattered waves I image depends on Lame parameter perturbations, which under asymptotic assumptions behave like point explosions (Wu, 1989). Forward-scattered and backscattered waves will have the same phase and amplitude. I thus image variations in the Lame parameter due to its independence of reection angle. This imaging is as signicant as impedance imaging, since it is proportional to the relationship between compressional and shear velocities. The V P /V S ratio is often used to estimate the lithology of subsurface rocks from sonic logs (e.g., Schon, 1996, p. 25-212) or seismic reection proles (e.g., Musacchio et al., 1997). Experimental work shows wide ranges of V P /V S ratios within fault zones, on the
36 basis of seismic velocity and density measurements made on samples from exhumed faults. For instance, McCaree and Christensen (1993) showed, for the mylonite zone of the Brevard fault in the southern Appalachians, that the compressional reectivity will normally be stronger than the shear reectivity. This stronger compressional reectivity appears to be related to a wider distribution of compressional versus shear velocityvalues, creating stronger P,wave reection coecients and impedance variations. Hence, deep fault zones may well exhibit a V P and signature that I can image. See Appendices A and B for further details about fault and elastic properties (Lame parameter perturbations), respectively. The depth migration method I use is a backprojection of assumed primary reection amplitudes into a depth section, based on traveltimes through an assumed velocity model. Because the backprojection requires knowledge of the source wavelet for deconvolution by crosscorrelation with each seismic trace (Louie et al., 1988; Le Bras and Clayton, 1988), I roughly approximate this by crosscorrelating with a boxcar function.5 s long, close to the central period of the expected reection arrivals. The net eect of this is to smooth the migration (through low-pass ltering of the data), center the reection pulses near zero phase, and avoid operator aliasing (Lumley et al., 1994). This ltering also minimizes phase dierences arising from our lack ofknowledge of focal mechanisms. I obtain images of subsurface reectors by summing cross-correlated data at traveltimes computed through one-dimensional velocity models, ignoring lateral velocity variations. The Kirchho depth migration process I use is similar to that
37 of Louie et al. (1988). The migration is a backprojection of assumed primary reection amplitudes into a depth section. It has been identied by Le Bras and Clayton (1988) as the tomographic inverse of the acoustic wave equation under the Born approximation in the far eld, utilizing WKBJ rays for downward continuation and two-way reection traveltime for the imaging condition. Traveltime versus distance matrices are computed from assumed velocity proles with Vidale's (1988) nite-dierence solution to the eikonal equation. I obtain the nal depth imaging result by stacking the migrated partial images from each event. One of the major problems in Kirchho depth migration is image resolution. When I apply this method to data with limited observation geometry, artifacts or false images appear and make the results dicult to interpret. In this case, sparse receiver coverage causes artifacts along elliptical trajectories in the migrated depth section. Defocusing of P, S and S, P converted energy by the P, P migration also contributes to image degradation, as well as upward sweeping smiles (i.e., lateral smearing of discontinuous reections into synforms) produced by strong noise. 3.2.2 Migrations of acoustic synthetic seismograms To illustrate my reconstruction of scattering structures, I begin with a 2-D synthetic example. Fig. 3.1 shows the southern California velocity prole of Hadley and Kanamori (1977), which I use to image a 2-D model of a dipping mid-crustal reector (an impedance contrast) from 16 randomly-placed \earthquake" point
38 4 16 Receivers Region of point sources Near offset = 3 km; far offset = 19 km Velocity Depth km/s km 5.5.-5.5 Dipping reflector 6.3 5.5-16. 6.7 16.-32. 7.8 32.-... Distance, km 2 L1 L2 M Figure 3.1: Southern California velocity model used for the computation of 2-D acoustic synthetic seismograms and 2-D Kirchho depth imaging. The dipping reector (impedance contrast due to a density change) is the imaging target for the 2-D synthetic example and is not present in the migration velocity models. L1, L2, and M (Moho) stand for crustal layer interfaces. Densities on the left and right sides of the dipping reector are 1 and 25 kg/m 3, respectively.
39 sources. I compute synthetic record sections with the fourth-order nite-dierence solution of the full-wave 2-D acoustic wave equation described by Vidale (199). The record sections I utilize comprise up to 2 km in epicentral distance and 3 s duration to include wide-angle reections for 16 dierent source locations on the 2-D line. There is no muting or further preprocessing. Fig. 3.2 shows the progressive migration of the synthetic 2-D record sections. The migration utilizes the velocity model to compute the Kirchho two-way traveltime imaging condition. Even the migration of seismograms from just one event (Fig. 3.2a) shows the crustal layering interfaces (L1, L2, and M, where M stands for the Moho). After 8 events are included (Fig. 3.2b), the dipping structure begins to appear as well. With 16 events, the intersections between structures are clear (Fig. 3.2c, white arrows), and the dipping structure is resolved. Note how apparent phase changes along the dipping reector result from incomplete cancellation of Kirchho arcs, with the completeness of cancellation varying along its length. The velocity model used to compute traveltimes was not smoothed and contains discontinuities. (This is the same velocity model used to generate the synthetic seismograms.) Image quality could be improved, for instance, by using velocity gradients and a smoothed version of the velocity model for traveltime calculation. In addition, dip ltering (Hale and Claerbout, 1983) after migration may make the elliptical artifacts less distracting. Artifacts also result from not muting the direct arrivals from the synthetic seis-
4 Distance, km 5 a) L1 L2 M 4 1 Event b) L1 L2 M 4 8 Events c) L1 L2 M 4 16 Events Figure 3.2: Demonstration of progressive migration imaging the 2-D dipping re- ector shown in Fig. 3.1. The reectivity cross sections result from 2-D Kirchho depth migration of progressively larger numbers of synthetic seismograms. L1, L2, and M (Moho) stand for crustal layer interfaces. There is no vertical exaggeration. Black is reconstructed positive reectivity, white is reconstructed negative reectivity, and gray shows little reectivity.
41 mograms (P g in the real seismograms). As the direct arrivals have the minimum arrival time at any oset, they backproject to the shallow parts of the images. This is not too important for me as muting could improve imaging of the top of the model, and I am more interested in deep structures. For the sake of illustration, note how Fig. 3.2c shows a light band above L1 that is due to unmuted direct arrivals. The L1 boundary, in fact, appears to have been reconstructed from forward-scattered reections with arrival times just behind the rst arrival. Fig. 3.3 shows the same progressive migration as that in Fig. 3.2, but for the case of sparse synthetic seismograms. I only used one fth of the data used to generate Fig. 3.2. Note how despite data sparsity the migration coverage is good enough to dene the crustal layering interfaces. However, this simple test illustrates the loss of resolution due to inadequate receiver spacing and migration coverage. Artifacts distort the images by pulling the structure out along the Kirchho elliptical trajectories (Kirchho impulse responses) discussed in Chapter 1. Zelt et al. (1996) addressed this and other limitations of wide-angle prestack migration. This depth imaging method, backed up by more detailed velocity models than I use here, has imaged the ne structure of steeply-dipping faults along with the detailed seismic stratigraphy of near-horizontal sedimentary rocks (e.g., Pullammanappallil and Louie, 1994; Chavez-Perez et al., 1996). Picking reections observed in the seismograms (Pullammanappallil and Louie, 1993), or an optimization based on coherency criteria without requiring picks (Pullammanappallil and
42 Distance, km 5 a) L1 L2 M 4 1 Event b) L1 L2 M 4 8 Events c) L1 L2 M 4 16 Events Figure 3.3: Same as that in Fig. 3.2 for the case of sparse 2-D synthetic seismograms. The reectivity cross sections result from 2-D Kirchho depth migration of progressively larger numbers of synthetic seismograms. L1, L2, and M (Moho) stand for crustal layer interfaces. There is no vertical exaggeration.
43 Louie, 1997), can also yield highly detailed velocity results. Statistical assessments and validity checks of migrated images, with special consideration of artifacts and resolution, can be created in the manner of Louie and Pullammanappallil (1994). 3.2.3 Migrations of elastic synthetic seismograms Elastic synthetic seismograms For tests of 3-D Kirchho reconstruction, I use a fourth-order nite-dierence solution of the elastic wave equation to compute P, SV seismograms (Levander, 1988). Line sources are the seismic excitation. I do not do any conversion from a line source to a point source (e.g., a widely used conversion of 2-D to 3-D consists of multiplying the seismic trace by the square root of t and convolving it with the inverse of the square root of t; Vidale and Helmberger, 1987). This is based on the fact that, even for simple layered models, Igel et al. (1993) have shown that such techniques fail to give accurate 3-D source representations and seismograms. There is thus source directivity due to the vertical-motion line sources I use. Iaminterested in acoustic images or -images. contributions are isotropic (Wu, 1989) and come from local P,wave energy, mostly P, P reections and transmitted P,wave arrivals (Fig. 3.4). This is clearly not the case when one tries to obtain density images or rigidity images (-images). For instance, variations lead to anisotropic scattering and one needs to take S,waves into account (Fig. 3.4) to correctly image such variations. Fig. 3.5 shows that in the presence of, back and forward scattered events will constructively interfere upon migration,
44 P Backscattering P P-P Reflection P-P λ µ + - P-P First arrival Forward scattering P-P P-S Figure 3.4: Vertical-component elastic synthetics for a two-layer model showing the early P,wave coda for variations in Lame parameters ( and ) during back and forward scattering. Note the absence of a forward-scattered S,wave for the scattering component.
45 P-P Σ λ P-S λ Back Scatter Forward Back Scatter Forward P-P P-S Σ µ + µ - Figure 3.5: Dynamic range enhancement for through Kirchho summation of reected (P, P ) and converted (P, S) arrivals. P, P arrivals, as well as P,S, tend to cancel out during the summation process for the case. Incidence angles are about 6 degrees for backscattered arrivals and 12 degrees for forward scattered arrivals.
46 while for a they tend to cancel out. The search for requires only the use of P,waves, whereas the search for requires the use of P, and S,waves. Thus, the search for structures becomes practical with an acoustic processing scheme. This is true, as we will see in the following tests, even for the case of elastic synthetic data. See Appendix C for further details about how I computed Figs. 3.4 and 3.5, and the equivalence between the \inverse acoustic backscattering view" (e.g., Weglein, 1985; Carrion, 1987; Matson, 1996) and the \traditional view" (from the Zoeppritz equations; e.g., Aki and Richards, 198, Vol. I, p. 153; Shuey, 1985) of reections and reection coecients. Trace balancing In industry practice, trace amplitudes are equalized before stack or migration. That is to say, amplitudes are normalized so that the root-mean-square amplitude over a selected time window is the same for all traces. In addition, amplitude is usually scaled by the square root of t (e.g., Shearer, 1994) to compensate for amplitude decay with time in seismic stacks and migrations. I do trace equalization for receiver amplitude balancing and approximate spherical divergence correction (i.e., the amplitudes are normalized so that the meansquared amplitude over the P g, S g part of the trace is the same for all traces). The basic idea is that when the data are trace equalized before stack, the eect of noisy traces on the stack is small and precise data editing is not crucial (e.g.,
47 Anderson and McMechan, 1989). This is useful for the earthquake case because it is roughly equivalent to energy normalization for varying magnitudes and station responses. If noise were small, my procedure would lead to a perfect spherical divergence correction. However, I expect that there is more noise than signal. Thus, trace equalization boosts late arrivals in a practical manner, keeping the noise at the same level for all the traces. Clipped and saturated records and record sections Clipped and saturated records are quite common in (short-period) earthquake data. I regard them as sign-bit recordings (O'Brien et al., 1982) that will acquire dynamic range through Kirchho summation. Based on these working assumptions, the crustal imaging technique proceeds as follows: 1) the record sections I use comprise up to 2 km in epicentral distance and 3 s duration to include wide-angle reections between rst compressional, P g, and rst shear, S g, arrivals, and I mute outside the window between P g and S g traveltime branches to extract only compressional arrivals, mostly P g, P m P and S, P converted energy. 2) Preprocessing includes trace equalization for receiver amplitude balancing (i.e., the amplitudes are normalized so that the mean-squared amplitude over the P g -S g window of each trace is the same for all traces; this is roughly equivalent to energy normalization for varying magnitudes plus spherical divergence correction). 3) I obtain images of subsurface reectors by summing data at traveltimes computed through one-dimensional velocity models, ignoring lateral velocity variations. [Traveltime
48 versus distance matrices are computed with Vidale's (1988) nite-dierence solution to the eikonal equation; static shifts due to surface topography and source depth are taken into account in the migration.] 4) I obtain the nal depth imaging result by 3-D Kirchho prestack summation of the migrated partial images for each event. The Kirchho depth migration process I use is similar to that of Louie et al. (1988). The usefulness of using such an acoustic scheme to process verticalcomponent earthquake data is that it leads to practical -images. This is relevant because even with the use of elastic iterative migration schemes (e.g., Mittet et al., 1997) -images appear very similar after several iterations. Migrations for a simple crustal model Fig. 3.6 shows a simple at-layer crustal velocity model contrived for the computation of 2-D elastic synthetic seismograms and 3-D Kirchho migration imaging. It is somewhat similar to the southern California velocity model of Hadley and Kanamori (1977). Its interfaces and property variations are located at 5.5 (), 16 ( or V P ), 24 () and 32 km (all; considered to be the general case for ). Note the pure perturbation for the 16 km interface. (See Appendix B for further details about model properties.) Fig. 3.7 shows the epicentral location of the \earthquake sources" I use (vertical-motion line sources) and of the migration prole. Note that the sources are about 1 km away from the migration prole. There are ve sources of an assumed Ricker wavelet with 1 Hz central frequency,
49 48 km 5.5 km 16 km 24 km 32 km 2 km 16 km recording array 15 km 15 km line sources Layer 1 Layer 2 Layer 3 Layer 4 Moho Layer 5 β α ρ all α, km/s β, km/s ρ, kg/m 3 Layer 1 Layer 2 Layer 3 Layer 4 5. 5. 6. 6. 2.9 3.5 3.5 3.5 3 3 3 36 Layer 5 7. 4.1 42 Figure 3.6: Crustal velocity model contrived for the computation of elastic synthetic seismograms. The receiver array (black inverted triangles) depicts the distance range of SCSN station locations used (Wald, 1996; Fig. 3.7). The table shows material properties.,, and, stand for P,wave velocity, S,wave velocity, and density, respectively.
5 5 km N Migration profile Sources Receivers Figure 3.7: Source-receiver location map for the migration of elastic synthetic seismograms. Receivers show some of the SCSN station locations used (Wald, 1996), with the migration prole used for depth imaging. All ve sources (synthetic events) having increasing epicentral depths are located away from the migration prole.
51 located at depths of 2.8, 1.8, 2, 28 and 37 km. Fig. 3.8 (bottom) shows a depth section obtained by migration of records from the synthetics for the locations (Fig. 3.8, top) of the Southern California Seismic Network (SCSN). Black shows positive reectivity, white shows negative reectivity, and gray shows little reectivity. Of course, buried sources are problematic. That is why I consider the model shown in Fig. 3.6 to be a conservative test, in terms of the source-receiver conguration, for this 3-D wide-angle prestack migration technique. This is one of the worst situations one would expect to nd: sources at all crustal depths and a small number of events and seismograms. Fig. 3.9 shows the migrated images separately for each source, and the summation of all contributions without and with dip ltering (Hale and Claerbout, 1983). Note how the contributions from individual events (1-5) depict sign changes along the interfaces. This is easier to see from source 1 at the deepest interface, where Kirchho trajectories from dierent receivers at very dierent azimuths contribute to constructing the interface image. In addition, source 3, which lies between the two interfaces (16 and 32 km) I want to image, shows sign changes along those boundaries due to stretching along Kirchho trajectories. The easiest way to explain sign changes between interfaces is with the location of the buried sources. The 16 km interface is illuminated mostly with forward scattered energy, whereas the 32 km interface is illuminated with backscattered energy. The polarity of a reection from an interface between two very distinct media depends upon whether the incident wave arrives from above or below the interface
52 5 km 34.15 Latitude N 34.6 4 Figure 3.8: View of the SCSN station locations (above), with depth section from migration of records from ve synthetic events (Fig. 3.7) having increasing epicentral depths. The dip-ltered image results from acoustic processing of verticalcomponent elastic synthetic seismograms (near oset = 15 km; far oset = 175 km)., and stand for S,wave velocity, P,wave velocity and density interface depths, respectively. Black is reconstructed positive reectivity, white is reconstructed negative reectivity, and gray shows little reectivity.
53 Distance, km 5 1 Distance, km 5 5 + + 4 Distance, km 5 4 Distance, km 5 + 4 Distance, km 5 4 2 3 4 4 Distance, km 5 4 Distance, km 5 4 Sum of 1-5 Sum of 1-5 dip filtered Figure 3.9: Migrated images depicting crustal reectivity for each source and the horizontal summation of all contributions without and with dip ltering (Hale and Claerbout, 1983). Note how the contributions from individual events (1-5) produce sign changes along the interfaces. The most prominent ones are depicted with black arrows and ellipses for the negative case, and white arrows and ellipses for the positive case.
54 (and, of course, upon the media stinesses and polarity of the incoming pulse); the amplitudes of all image points derived from a forward-scattered ray haveto be multiplied by -1 before being added in. If this is not done, energy from sources above and below a reector would tend to cancel instead of adding constructively (Zhiming et al., 1984). Multiplication of the amplitudes by -1 is done in reversetime migration. [Reverse-time migration is computationally very expensive. It is generally the most expensive technique in current migration practice (Zhu and Lines, 1997).] The exception is point Lame parameter diractors, which have the same reectivity for all directions of incidence (e.g., Hu et al., 1988; Zhu and Lines, 1997). I do not do a sign correction based on incidence because the migration algorithm I use treats the problem as a P, P scattering case for lots of isotropic point diractors, with the same reectivity for all directions of incidence. Note that I assume these diractors are not between distinct media, but only diractors upon a smooth velocity background. The traveltime calculation includes turning rays when the velocity prole has steep enough gradients. This allows one to image structures having dips greater than 9 degrees, without multiplying by -1. However, I have problems dealing with post-critical angle reections, or refractions. Those events tend to blur the images because I do not apply any correction for their 9 degree phase shift. This shows at the upper portion of the images because of minimum traveltime for refracted events.
55 Clear elliptical Kirchho trajectories and artifacts due to buried sources and the station distribution (\acquisition footprint") appear in all images shown in Fig. 3.9. They all can be explained in terms of inadequate receiver coverage and incomplete summation (similar to that seen in Fig. 3.3), the Fresnel zone of forward and backscattered waves (note, for instance, how interfaces disappear just away from the projected location of the sources; this is due to a loss of lateral resolution of the image), phase shifts due to refraction (e.g., Clayton and McMechan, 1981), errors in computing traveltimes from deeper events (due to buried sources), and variations of incidence angle. Due to the earthquake source-network receiver conguration of my problem, reected rays can have avery large incidence angle. These rays can prevent proper imaging for two reasons. First, the arrivals with a postcritical angle of incidence will undergo a phase change (Aki and Richards, 198, Vol. I, p. 155-163) which can blur the migrated image. Second, arrivals of rays with larger incidence angles will undergo wavelet stretching in the migrated section. This will smear the migrated image and hinder resolution. The wavelet shape change caused by the postcritical reection phase change is not visually obvious to the interpreter (e.g., Qin, 1994; for the cross-well imaging case) and does not signicantly aect the migration results. To alleviate the rst problem, rays with suciently large incidence angles can be simply eliminated. A Kirchho migration scheme like this, with an incidence angle constraint, was implemented by Qin and Schuster (1993) and Qin (1994) for the cross-well imaging case. I do not include an incidence angle constraint, for reasons
56 of simplicity and generality. One can always remove some of these unwanted eects from the images, for plotting and stacking purposes (Fig. 3.9), by practical postmigration low-pass or dip ltering to enhance visibility and resolution (Hu et al., 1988; Mittet et al., 1997). Despite imaging artifacts and inherent problems with sparsity of station coverage and data sampling (spatial aliasing), note how Figs. 3.8 and 3.9 image the approximate depths of the interfaces (dotted lines), shown in Fig. 3.8, where () occur. Defocusing of P, S and S, P converted energy by the P, P migration also contributes to image degradation, as well as to the denition of reectors by distorted pieces. This is a very good result because I image what I am searching for: interfaces due to isotropic scattering. (See Appendix B for some ranges of for this and other cases discussed below.) One way of visualizing how migrations of each event contribute to the nal depth section is through a common-image gather in the imaging volume. This has proven useful in the oil industry and related research (e.g., Nemeth, 1994; G.T. Schuster, personal communication) during data analysis and interpretation. Fig. 3.1 shows the imaging volume of the 5 events used. Note the horizontallycoherent energy in the image plane that contributes to the prominent 16 and 32 km interfaces. To further test the validity ofmy images, I must determine which imaged structures are real and which are artifacts produced from the imaging of noisy data. One test is a simple resampling analysis, which is done by imaging the data
57 4 S Image Plane 16 km interface 32 km interface N Depth section Figure 3.1: Imaging volume showing migrations of all traces from each of the 5 sources used, on the left face of the volume. The left face represents the image plane, over which horizontal summation produces the nal depth section on the right face. Note the horizontally coherent energy that contributes to the 16 and 32 km interfaces in the nal depth section.
58 after destroying trace-to-trace coherence by randomly ipping the signs of data traces. The images of resampled data allow us to observe mostly the problems with poor station distribution and coverage, the inadequate number of sources and the eects due to Kirchho operator aliasing. Fig. 3.11 depicts the same images shown in Figs. 3.8 and 3.9 for the horizontal summation of all contributions without and with dip ltering, and their migration artifacts. The latter are equivalent to migration of random noise. Compare Figs. 3.11a, c with Fig. 3.11b, d to visually separate out artifacts from the signal of coherent reectors. Note that artifacts in Figs. 3.11a, c may appear negated in Figs. 3.11b, d. The images are most prominently dierent at the 16 and 32 km interfaces. We can see examples of a coherent reector and of a migration artifact in Figs. 3.11c, d. The coherent reector (black ellipse in Fig. 3.11c) does not look the same in the noise estimate (white ellipse in Fig. 3.11d), whereas the artifact (black circle in Fig. 3.11c) looks alike and negated (white circle in Fig. 3.11d). Noise analysis Another test is to compare my depth section for the horizontal summation of all contributions with dip ltering and its migration artifacts (Fig. 3.12a, b) with the equivalent where I have substituted pure gaussian noise (signal-to-noise ratio of ) for the synthetic seismograms (Fig. 3.12c, d). I conducted this empirical noise analysis using ltered gaussian random noise for the data, in the same manner as LeBras and Clayton (1988). The results are very encouraging. The migration
59 Distance, km 5 a Distance, km 5 b 4 Distance, km 5 4 c Distance, km 5 d 4 4 Figure 3.11: a) Same depth section as that in Figs. 3.8 and 3.9. The image has contributions from all 5 sources used. b) Depth section based on a simplied resampling analysis. This image depicts migration artifacts and is an approximation to migration of random noise. Compare with (a) to visually separate out artifacts from signal (coherent reectors). c) Same image as in (a) and in Fig. 3.8 after dip ltering to enhance the main reectors. d) Same image as in (b) after dip ltering to enhance the main reectors. Compare with (c) to visually separate out artifacts from signal.
6 Distance, km 5 a Distance, km 5 b 4 4 Distance, km 5 c Distance, km 5 d 4 4 Figure 3.12: a) Same depth section as that in Fig. 3.9 after dip ltering to enhance the main reectors. The image has contributions from all 5 sources used. b) Depth section based on a simplied resampling analysis after dip ltering to enhance migration noise. This image depicts migration artifacts and is equivalent to migration of random noise. Compare with (a) to visually separate out artifacts from signal. c) Same image as in (a) for a data set of pure gaussian noise with no signal (signal-to-noise ratio of ) after dip ltering to enhance its general features. d) Same resampling image as in (b) for a data set of pure gaussian noise with no signal after dip ltering to enhance its main features. Compare with (c) to visually separate out artifacts from signal.
61 of pure noise does not suggest any of the crustal interfaces and thus provides further validation to the results of Fig. 3.9. Note, however, the similarity to the images of resampled data (Figs. 3.12b, d), emphasizing the usefulness of the simple resampling analysis to depict artifacts produced from the imaging of noisy data. Sensitivity tovelocity changes Velocity errors have a great impact on the focusing aspects of migration (e.g., De Vries and Berkhout, 1984; Black and Brzostowski, 1994; Maeland, 1996, 1997). They can simply shift the depth of imaged reectors or completely blur the images. Their inuence can be analyzed with a simple test. Fig. 3.13 shows two extreme cases for the eects of +/- 2% average velocity errors. Compare Fig. 3.13a and c with b to visually separate out the eects due to velocity changes in this case. They both blur the depth images and hinder resolution and continuity of the crustal interfaces. In addition, they do not introduce continuous nor very coherent false structure. Use of S,waves If it were our objective, one could also try prestack depth migration of the S,waves contained in the seismograms. This has been attempted before, for instance, by Balch et al. (1991) for the cross-borehole imaging case and by Jackson et al. (1991) for multicomponent common-receiver gather migration of single-level walkaway seismic proles. To illustrate how simple this idea is, Fig 3.14 shows the
62 Distance, km 5 4 a Distance, km 5 4 b Distance, km 5 4 c Figure 3.13: a) Depth section as that in Fig. 3.8 for the case of a + 2% velocity perturbation in all layers (dip ltered). b) Same depth section as that in Fig. 3.8 (dip ltered). c) Depth section as that in Fig. 3.8 for the case of a - 2% velocity perturbation in all layers (dip ltered).
63 depth migration of records from the same 5 events I used to obtain the image shown in Fig. 3.8, using the southern California velocity model of Fig. 3.1. For this case, I used the S,wave velocities shown in Fig. 3.6. The record sections I use also comprise up to 2 km in epicentral distance as in the P,wave case, and 3 s duration to include (slower velocity) rst shear (S g ) arrivals, wide-angle shear reections and surface and converted waves. I mute all arrivals before the S g traveltime branch to extract mostly shear and surface wave arrivals. Fig. 3.14 does not image any crustal interfaces. This was expected because there are no isotropic scatterers for the S,wave case (Wu, 1989). The most reective regions of the images are due to the projected location of the sources in the left uppermost 2 km or so. 3.2.4 Low-velocity fault zones Fig. 3.15 shows the simple example I decided to test to try to image a low-velocity fault zone. It corresponds to the same material properties of the fault zone model of Igel et al. (1997) used to simulate SH, and P, SV trapped-wave propagation in fault zones. This paper is, to the best of my knowledge, the only one that has dealt with the P, SV case. I deal, however, with the less realistic case of a atlayer, low-velocity fault zone, whereas Igel et al.'s fault zone model corresponds to a vertical, strike-slip fault. I do not attack the vertical fault case for reasons of computational practicality.
64 Distance, km 5 a Distance, km 5 b 4 4 Distance, km 5 c Distance, km 5 d 4 4 Figure 3.14: Migrated depth sections for S,waves. a) Migrated depth section without dip ltering. b) Resampled migrated section without dip ltering. c) Migrated depth section with dip ltering. d) Resampled migrated section with dip ltering.
65 Line sources @ 3, 5, 6 km 3 km 1 km 2 km 16 km: receivers Vp = 5.2 km/s Vs = 3. km/s ρ =25kg/m 3 (1) 2 m Fault Zone 2 km Vp = 4.85 km/s Vs = 2.8 km/s 3 (2) 1 km ρ = 25 kg/m Vp = 5.55 km/s Vs = 3.2 km/s ρ = 25 kg/m3 Line sources @ 13, 14, 15 km λ, λ % µ, µ % υ, υ % Upper interface Lower interface 13.7 13.3-29.5-28.6 Figure 3.15: Velocity model and material properties for two horizontal low-velocity fault zone models at 1 km depth. Receivers (black inverted triangles) depict the distance range of SCSN station locations of Fig. 3.7. Fault zone (1) is a 2 m thick at layer. Fault zone (2) is a 1 km thick at layer. The table shows perturbations (in percentages; computed with the expressions presented by Sato, 1984, eq. 8) of the two Lame parameters and Poisson's ratio.
66 Fig. 3.15 shows the simple crustal velocity model I used for the computation of the 2-D elastic synthetic seismograms and P,wave traveltimes. There are ve sources with an assumed Ricker wavelet of 3 Hz central frequency, located above and below the low-velocity fault zones at depths of 3, 5, 6, 13, 14 and 15 km. The source-receiver conguration and epicentral location of the \earthquake sources" is the same as that in Fig. 3.7. Fig. 3.16 shows the migrated images for the summation of all six contributions with dip ltering. Note how one can only image, in comparison to the resampled image, distorted pieces (due to Kirchho trajectories) of the fault zones (Figs. 3.16a, c). This is, however, very encouraging due to the inherently complex low velocity zones and perturbations of equivalent magnitude for the two Lame parameters. (See Appendices A and B for additional information about fault properties and perturbations in Lame parameters.) In addition, the source-receiver conguration is much worse (fewer distinct source locations and worse illumination) than that used for Fig. 3.8. 3.3 Discussion and Conclusions I image crustal fault zones by searching for isotropic scatterers with a wide-angle Kirchho prestack migration scheme. This provides a practical 3-D imaging tool that works for interfaces, despite limitations with the synthetic seismograms, the simplied velocity model used (which makes the computations feasible on a basic workstation), undesirable eects of buried sources, and the poor, irregular,
67 2 Distance, km 5 Distance, km 5 2 Fault Zone (1) a 2 Stretched Fault Image Image of Multiple Fault Zone (2) c Distance, km 5 Distance, km 5 2 b d Figure 3.16: Migrated depth sections for the low-velocity fault zone models of Fig. 3.15. a) Migrated depth section (dip ltered) for Fault Zone (1). b) Resampled migrated section (dip ltered) for Fault Zone (1). c) Migrated depth section (dip ltered) for Fault Zone (2). d) Resampled migrated section (dip ltered) for Fault Zone (2). The white dashed line depicts the 1 km depth level where the upper interface of both fault zones is located. White ellipses show pieces of the imaged fault zones (a, c) and artifacts (b, d), whereas black ellipses show multiples (a, c) and artifacts (b, d).
68 and sparse data sampling of the station distribution of the SCSN. Clear elliptical Kirchho trajectories and artifacts due to buried sources and the station distribution appear in all images. However, they all can be explained in terms of inadequate receiver coverage and incomplete summation. 2-D acoustic synthetics and 2-D Kirchho migration make allowance for the reconstruction of dipping scattering structures. For the case of 2-D elastic synthetics and 3-D Kirchho migration, interface details and properties are obscured by phase changes, but structure is interpretable. A simple but eective resampling analysis allows identication of real structures against imaging artifacts. Based on this simple procedure, I found that migrated random noise will not mimic synthetic structures. Both fault-zone concepts studied (i.e, the low-velocity fault zone of Igel et al., 1997, and the more general, high P,reectivity, case of McCaree and Christensen, 1993) produce results one can interpret. Finally, due to their scattering radiation characteristics, the use of shear waves does not allow us to image crustal fault zones. This was expected because there are no isotropic scatterers for this case.