Applications of the various focusing algorithms have a degree of success that depends on the beam geometry used. A zone of low-velocity material is found in the upper 100 km beneath the region of the Salton Trough.
Introduction to Method of Inversion
After the discussion of the method, there will be a section presenting the results of different algorithms acting on beam distributions that are highly anisotropic and inhomogeneous. Any particular row of LTL can be identified with the basic back-projection reconstruction of the particular block associated with that row.
Ray Weighting
In this approach, the delays for each block are divided into different inertial azimuth regions, the average is found for each region, and then these regional determinations are averaged to arrive at an estimate for the entire block.
D eblurring
When the beam set is anisotropic yet homogeneous, wavenumber deconvolution will work correctly as long as the scattering function can be determined. Furthermore, if C = 1/2 is taken, the operation represented by equation (1.3) can be rewritten as a linear combination of the second derivative operator and the identity operator.
Iteration
The main faults of Southern California and the subdivisions of the Transverse Ranges referenced in the text. This contributes to a vector that parallels the trend of the San Andreas Fault (N40W) with a magnitude of 35 mmjyr (Sieh and Jahns, 1984). Compensates for the age of the San Andreas Fault and the opening of the Gulf of California.
Determined seismic estimate of Moho pos1t10n (a) (Hearn, 198-!b) and calculated Yariation at Moho position (b). These are located in the Peninsular Ranges and Southern Coast Ranges regions. That the mantle is active in surface processes is supported by the maintenance of the large bend (Kosloff, 1978; kinematic model above).
In the eastern Transverse Ranges, this is supported by the location of the Transverse Range Anomaly north of the San Andreas Fault. However, development of a bend in the San Andreas fault requires convergence to the west of the pole (which, curiously enough, "is where the transverse ranges currently lie).
Comparison of \lethods
Application of Tomographic Schemes
When the beam directivity is fairly homogeneous, direct beam weighting works well, as seen in Figure l.Sa. 7 a is in the same format as Figure 1.4, but the nearest-neighbor detection filter has been used.
Resolution and Error Estimations
The covariance of the model parameters (ie, the coin of the slowness estimates, cov (s) = ssT) is commonly used to estimate the effects of n01se on the model through the relationship cov (s) = a2(LTLt1 (Jackson, 1972). The response of the inversion method to random noise using of a slightly inhomogeneous set of rays.
Data Reduction
This is followed by a description of the details of the inversion tomographic method needed in this specific application. The problem statement is identical to that most commonly used in the generalized inverse problem (see, for example, Aki et al (1977) for a discussion that is particularly relevant to the geometry of teleseismic arrivals).
Details of the Specific Inversion Algorithm Used
It is a measure of the variety and number of hits experienced by a block, and is determined by retracing rays from the stations shown in Figure II.3 through the structure shown in Figure IJ.5 according to the ray information which is given in Figure 11.1. In most parts of the inversion space, the beam coverage is not sufficient to justify the use of such small blocks.
Estimations of Resolution and Error
It is difficult to estimate a priori the error in travel times due to these sources, but the range of errors IS. To test the sensitivity of the inverse to noise, a direct inversion is performed on a random distribution of time delays that are input as if they were data, and the output is examined. A Gaussian distribution is used for the input function, although values greater than three standard deviations from the mean are not included, so that very different lag values are not allowed.
The RMS delay caused by this inversion is only 2.2% of the input signal. However, it is possible to use the variance of the inversion to quantify the sensitivity of the inversion as a whole to noise. For the Southern California beam geometry, the noise inversion results are shown in Fig. IUJ.
Later it will be found that the coherent structure is reconstructed with a degree of success that depends on the geometry of the problem, but accounting for at least go% of the signal. This testifies to the robustness of the inversion even in the presence of significant amounts of noise. Considering that the expected noise level in the actual data is small, we can safely say that noise-related artifacts in the inversion are not a major problem.
Application of Tomographic Algorithm to Test Structures
The ray set and inversion method used on the test structures are the same as those used in the inversion of the actual data. This is shown in Figure II.10 and should be compared with the point responses in the basic back projection, Figure II.8. The amplitude of the reconstructed block is 66% of the amplitude of the actual anomalous block.
A much more difficult and illustrative example is the reconstruction of a deviating cube with a non-deviating interior (Figure II.ll). This contrasts with the good reconstruction of the vertical planes, where the amplitude reaches 80%. The specific ability to detect and resolve thin horizontal structures at any depth is tested by inverting an anomalous horizontal plate located in the 10th and 17th layer of blocks.
The results sho\Yn in Figure II.l2 clearly indicate that this structure is difficult to constrain vertically and that this ability decreases as the depth to the producing anomaly increases. This pattern is well reproduced by the inversion throughout the portion of southern California that is reasonably sampled (Figure II.13). This figure also illustrates that in poorly sampled regions the inversion does not reconstruct the anomaly to a JeyeJ comparable to the reconstruction produced in very heavily sampled regions.
Resu lts
Reconstruction of actual travel time delays using binning, deconvolution, and five iterations. Comparison of the strong anomaly under the cross-sections (Figure II.l4) and the shock quality map (Figure II.7) shows that this anomaly is in a well-sampled region and the resolution should be good. In particular, Figure II.l5 has a thin, wedge-shaped anomaly that is embedded under the cross-range region, and the inverse of the synthetic delays does very well in reconstructing this structure.
Inversion of a simple structure designed to simulate the main features seen in the inversion of actual delays (Figure II.l2). As in the case of the actual delays, binning, deconvolution and five iterations were applied. The test structure differs from Figure II.l5 only in the position of the cross-range anomaly, which is positioned two blocks (60 km) to the south.
This station delay map by itself gives no indication of the depth in the anomalous region. First, the Transverse Range anomaly at about 100 km depth is remarkably similar in outline to the map appearance of the Transverse Ranges themselves (Figure II.20). Similarity of cross-range anomaly at 100 km depth to physically defined cross-ranges.
Discussion
The primary observation is that little convergence occurs across the San Andreas fault, including the portion near the transverse regions. A review of the literature on the Cenozoic history of the San Andreas fault system is then presented. This relative motion roughly parallels the sections of the San Andreas fault north and south of the Great Bend.
Transverse series considerable convergence can be attributed to the Banning Beach of the San Andreas fault (\1atti et al., 1984). This suggests that the borderland south of the western Transverse Ranges is moving along with the Pacific plate. We feel that this satisfies the geology better (Davis and Lagoe, 198-1) than appeals to the geometry of the San Andreas-Garlock junction.
The current kinematics and observed net displacements of the San Andreas Fault are major limitations. Tractions at the base of the lithosphere due to the flow field shown in Figure III.8. Most of the slip on the north San Andreas remains on the San Andreas Fault south of the big turn.
Barrows, A.G., 1979, Geology and fault activity of the Valyermo segment of the San Andreas fault zone, Ca. Sieh, I<.E., and Jahns, R., 1984, Holocene activity of the San Andreas fault at Wallace Creek, California, Geol.
The Kinematic \fodel of the Crust
L ate Cenozoic llistory of the San Andreas Fault
Three Dimensional, Constant Viscosity Dynamic Modeling
The mantle is considered to be bounded by a no-slip boundary at the surface of the half-space. The shear pulls at the base of the lithosphere are given by 1J du.jdz, where v. An agreement in outline of the physiographic Transverse Ranges and the Transverse Ranges anomaly at a depth of approximately 100 km.
In particular, the transverse strand strike anomaly should be discussed in terms of activities occurring in southern California. 1\V direction of flow produced by the Salton Trough- TransYerse Ranges circulation model (Figure IIL8) south of the big bend. The conditions for thermal instability at the base of the lithosphere were greatly improved in this new environment (Yuen and Fleitout (19 4) haYe analyzed similar conditions over a rising plume).
Veldon, R.J., 1984a, Quaternary deformation due to the junction of the San Andreas and San Jacinto faults, southern California, Abs.
A \ ' fodel for the Recent D evelopment of Southern California
