A region of southern California was selected for study to show the application of the wavenumber filtering methods on gravity data. Figure 9 shows the region and some of its tectonic features, including the Transverse Ranges and portions of the California Continental Borderland, the Peninsular Ranges and the Mojave Desert. Applying the wavenumber filtering method to this data will help deliniate structure, show where gravity anomalies are affected by faults, and separate shallow features from deep seated ones. Of special interest in this study is the western Transverse Ranges, including the Santa Ynez and Santa Monica Mountains, the northern Channel Islands, and the Ventura and Santa Barbara Basins. Paleomagnetic data collected in recent years (Jones and Irwin, 1975; Jones and others, 1976; Kamerling and Luyendyk, 1979; Greenhaus and Cox, 1979; Crouch, 1979; Luyendyk and others, 1980; Hornafius, 1984; Hornafius and others, 1984; Kaplan and others, 1984) have shown that portions of southern California have undergone appreciable lateral motion and rotation. It is not clear, though, whether the region has moved as a single terrane or as many individual pieces. Also not clear is whether the basins and mountain ranges were formed as a result of rotation, rifting or other tectonic events. Analysis of the gravity data may give new insight on these problems.
The Transverse Ranges of southern California form a province of east-west trending mountains and basins which cut across the predominant north-northwest to south-southeast trend of the rest of western North America. The province can be divided into three regions. The eastern region includes the San Bernardino and Little San Bernardino Mountains and is bounded on the west by the San Andreas fault. The central region contains the San Gabriel Mountains and is bounded by the San Andreas fault on the northeast and the San Gabriel and Sierra Madre faults on the southwest. To the west of the San Gabriel Mountains are the western Transverse Ranges. Within this region are the Santa Ynez Mountains, Santa Monica Mountains, and the Ventura Basin. Not everyone agrees on the western extent of the western Transverse Ranges. In particular, the northern Channel Islands, Anacapa, Santa Cruz, Santa Maria and San Miguel, appear to be a continuation of the Santa Monica Mountains but also appear to be continuations of the northwest-southeast ridges of the California Continental Borderland. There is geological evidence to support both theories (ie, referenes) However, paleomagnetic data shows that Anacapa and Santa Cruz have rotations similar to the Santa Monica Mountains and not similar to San Clemente, Santa Catalina, and San Nicholas islands (Kamerling and Luyendyk, 1979).
A tectonic problem of the Transverse Ranges is that the province is cut by two major strike-slip faults, the San Andreas and the San Gabriel - Sierra Madre. It is believed that there has been 240 km of right lateral motion on the southern San Andreas fault and 60 km of motion on the San Gabriel - Sierra Madre faults. Yet the three regions are now aligned. This seems to suggest that either the formation of the three regions of the Transverse Ranges were due to different geologic conditions that now simply line up, or that the Transverse Ranges are a recent feature and have not yet been offset by the faults. A third possiblity is that the cause of the Transverse Ranges is located at depth and is not offset by the motion between the Pacific and the North American plates. Evidence of a high-velocity body in the mantle under the Transverse Ranges cutting across the San Andreas and San Gabriel faults has been reported by Hadley and Katamori (1977), Raikes (1980), Walck and Minster (1982), Hearn (1984), and Humphreys and others (1984). However, this does not explain the paleomagnetic data of the western Transverse Ranges.
In this study the wavenumber filtering method is used to aid in the analysis of the gravity data of southern California. The complexity of the region makes it difficult to see possible tectonic features in the unfiltered gravity maps. This chapter describes the preparation of the data for filtering, including the method of gridding irregularly spaced data into an evenly spaced matrix, and the filters used to help enhance and/or isolate specific features.
Two types of gravity data are used in this study. Land-based stations are from a compilation by the Regional Geophysics branch of the USGS. Within the region of study, there are 13,942 land based stations of complete Bouguer gravity anomaly values. These stations are on a Woollard and Rose (1963) datum used by Chapman (1966). The complete Bouguer anomaly was calculated at a density of 2.67 grams per cubic centimeter. There are 5182 stations offshore of free air anomalies from the Defense Mapping Agency, St. Louis, Missouri. Figure 10 shows the location of all gravity stations with respect to the location of the matrix. The scale of this map and all vector contour maps is 1 inch to 40 kilometers.
The wavenumber filtering method requires that the data be in matrix form. Thus the irregularly spaced gravity stations must be interpolated into an evenly spaced grid. The FFT subroutine used in these programs requires that the number of rows and columns of the data set be a power of 2. To cover the region of interest best, a matrix of 128 columns and 64 rows was selected. The distance between the rows and columns is 2.5 kilometers. Since the size of the smallest feature that can be seen in any contour map of a data matrix is twice the grid spacing, this matrix will show features greater than 5 kilometers. Because large scale structure is of primary interest in this study, this grid spacing is acceptable.
The matrix was created from the irregularly spaced gravity stations using a modification of the polynomial surface fitting routine in Braile (1979). A description and listing of the gridding program GRID_USING_POLY_FIT is contained in Appendix A. The polynomials were 5th order except in regions of few data points, where the order was allowed to drop to 4th or 3rd order. The grid was prepared in a UTM coordinate system. All columns are parallel to a Central Meridian of 118 degrees west. All rows are perpendicular to the Central Meridian. The UTM coordinate of grid location (1,1), the lower left corner, is (320,3740). To limit overshoot around the edges, data up to 20 kilometers outside the matrix were used in the calculations of the polynomials.
Once the matrix has been created, the program SETUP is used to to begin the filtering process. This program reflects the matrix along its right hand side and then along its top. This new matrix is four times as large with 256 columns and 128 rows. The mean is determined and removed from the matrix. The matrix then is converted from the spatial domain to the frequency domain. The results are written to a file to be used for all filtering. The program FILTER takes the output from SETUP and performs the various types of filtering techniques. After filtering only the lower left quadrant, that of the original region, is saved and contoured.
Figure 11 is a color contour map of the gridded data. This contour map was created on a Grinnell image processing video screen and then photographed by a Loge/Dunn Instruments 631 color camera system. The color table has 15 equal intervals ranging from red in regions of high gravity to white to blue in regions of low gravity. Each contour represents approximately 13 1/3 milligals. Map B1 in Appendix B is a vector contour plot of the same matrix. Also included on this map are the selected geological features shown in figure 9.
The contour map of the original data is very complex with many anomalies of different size and amplitude. In this study, large scale features are of the most interest. It is desirable to see the effects of faults, to distinguish the boundaries of various terranes, and perhaps even to see lower crust - upper mantle structure. The map's complexity makes analysis difficult with small near surface features hiding the relationship of deeper features. To suppress these small wavelength - high wavenumber anomalies and enhance long wavelength features one should perform low-pass band-pass filtering and upward continuation filtering. To separate and deliniate anomalies one should perform first and second vertical derivative filtering. First and second horizontal derivative filtering would show where the gravity field is affected by faults and boundaries. High pass band-pass filtering would remove any regional trend. Multiple band-pass filtering would show the location of anomalies of corresponding sizes. Anomalies of specific orientations can be found by performing numerous strike-pass filtering. All of these filtering techniques have been carried out on the original data set and are presented in the next section. Maps B2 to B35 in Appendix B are vector contour maps of the data filtered in various ways.
To remove the high frequency anomalies in the hope of seeing deeper structure, the data were filtered by progressivly narrower low-pass band-pass filters (figures B2 to B5). In low-pass filters, only frequencies below the selected limit are passed and all higher ones are cut. The upper frequency limit is set to 1/2, 1/4, 1/8, and 1/16 of the Nyquist frequency. Since the Nyquist wavelength is two times the station spacing or 5 kilometers, these band-pass filter maps show anomalies with wavelengths greater than 10, 20, 40, and 80 kilometers respectively. Note that on each successive map more of the small features have disappeared. The contours become less angular and more rounded as the band-pass filter cuts out more of the high frequencies. Both the 0 to 1/2 Nyquist map (B2) and the 0 to 1/4 Nyquist map (B3) look very similar to the original data (B1). All of the major features remain. Only the noise has been removed. Thus, most of the important geological features are contained in the lower fourth wavenumbers. In figure B4 many features have become very circular and smoothed. The Santa Monica Mountains and the Channel Islands show up as two distinct anomalies. The San Fernando Basin is no longer apparent. It is also clear that the Los Angeles Basin is a minor anomaly compared to the Santa Monica and the Santa Cruz Basins. The San Gabriel Mountains are also only minor features and the San Bernardino Mountains do not appear at all. By the 0 to 1/16 Nyquist map (B5), most of the features have been lost, and the filtered data no longer seem to represent the real data. This is because not enough wavenumbers remain to accurately portray the matrix. Almost all of the frequency content, especially in the Y direction, has been filtered out.
The regional trend of the area may also disguise features. Regional trends may be due to thickening of the continent or variations in the upper mantle. Band-pass filtering was performed on the data in a way to remove any regional trend. Instead of passing all wavelengths greater than a specific value, only wavelengths between certain values were passed. The range of frequencies used here are 1/16 to 1/2 (figure B6), 1/16 to 1/4, (figure B7), and 1/8 to 1/2 of the Nyquist (figure B8) For figures B6 and B7 all frequencies less than 80 kilometers are assumed to be the regional trend. Although figure B8 has too much of the low frequency content removed, structure shows up well in the other two. In these filtered maps, it becomes apparent the San Gabriel Mountain anomaly covers only a small portion of block between the San Andreas and San Gabriel faults. The geological map (Jenkins and Strand, 1969) shows the anomaly occurs in a region of Pelona Schist. The northwest and southeast ends of the block have no anomaly associated with it. In figure B6 an anomaly that was otherwise hidden becomes clearer between the Elsinore and San Jacinto faults. The anomaly of the Santa Ynez Mountains is also more visible in these maps. One could try to corrolate these small anomalies to the small scale geology, but in this study large scale features are of more interest. In band-pass filtering one must be careful not to choose too small a range of wavenumbers or aliasing will occur.
Upward continuation also suppresses the high frequency anomalies, so the data set is filtered by progressivly higher upward continuation filters. The data set was upward continued to 2.5, 5, 10, and 25 kilometers (figures B9 to B12). As can be seen with each progressive upward continuation, more of the smaller features have disappeared leaving only larger trends. The 2.5 kilometer map shows little change from the map of the original data. Only noise and very small features have disappeared. Even more apparent in the upward continuation maps than on the band-pass maps is the lack of gravity anomaly in the San Gabriel Mountains. Both the 5 and 10 kilometer maps (B10 and B11) show contours passing directly through the mountains. The ease with which the anomaly is filtered out indicates that the mountain range is a shallow feature and has no root. Also note that the Santa Ynez Mountains anomaly filters out rather easily, but the Santa Monica Mountains-northern Channel Islands anomaly remains strong. By the 25 kilometer map (B11), individual terranes or provinces are no longer distinguishable. Once the data have been upward continued to this level, it is questionable whether the map represents any aspect of the geology. Too many of the wavenumbers have been suppressed. Perhaps this map may show a regional trend that indicates the continent thickening from west to east, but nothing more. Unlike the band-pass filter, even when most of the wavenumbers have been surpressed, such as at elevations greater than 25 kilometers, the data remain stable, but little information can be seen.
Downward continuation filtering is typically performed to delineate boundaries. The shape of the anomalies should become sharper as the depth of the bodies causing the anomalies is reached. To prevent downward continuation filtering from becoming unstable, the smaller wavelengths need to be removed. It is assumed that these smaller anomalies are due to features shallower than the downward continuation level. In figures B13 and B14, data that had first been band-pass filtered 0 to 1/2 Nyquist was then continued downward to a depth of 2.5 and 5 kilometers, respectively. This band-pass filter removed all wavelengths less than 10 kilometers. Note that the 5 km depth map (B14) shows some unstability in places. Downward continuations to levels greater than 5 kilometers shows data that is completely cluttered. This indicates that many of the remaining anomalies are due to features above the downward continuation level. More of the high wavenumbers should be filtered out before performing downward continuation. Figures B15 to B17 show data that has been band-pass filtered 0 to 1/4 Nyquist and then continued downward to a depth of 2.5, 5 and 10 kilometers. This band-pass removed all anomalies with wavelengths less than 20 kilometers. The 10 km depth map (B17) is somewhat unstable. This indicates that much structure occurs above 10 kilometers. Analysis of the downward continuation maps shows broad large amplitude anomalies with very sharp boundaries. From these maps a very distinct change in the gravity anomaly from positive to negative is apparent along the southern side of the Santa Monica Mountains and the northern Channel Islands. This indicates a sharp change in density across this region. Also apparent is a change in density on the north side of the Channel Islands passing into the Santa Barbara Channel. A sharp boundary is not seen north of the Santa Monica Mountains. Figure B18 shows downward continuation of a data set 5 kilometers where the regional trend has been removed by first performing a 1/16 to 1/2 band-pass. In this map the negative anomaly associated with the Ventura Basin is shown to be quite continuous the entire length of the western Transverse Ranges.
Derivative filtering is also performed to help deliniate structure in the data. Calculating the first and second vertical derivative may help separate multiple anomalies. Higher frequencies are enhanced at the expense of lower frequencies. However, if the data contain noise or small errors, the derivative filters will only accentuate that noise. This is quite apparent on the map of the first vertical derivative of the original data (B19). No structure can be seen. By first surpressing the highest frequencies, such as by performing an upward continuation or band-pass filter, the noise is removed. When vertical derivatives are taken, features become apparent (B20 to B23). These maps show the size and shape of the small negative anomaly over the San Fernando Basin separate from the rest of the Ventura Basin. The San Gabriel anomaly shows up as having two lobes.
Horizontal derivative filters in the X and Y directions can be used to accentuate areas of great changes, perhaps indicating boundaries between terranes. First horizontal derivative filters show regions of high gradient (figures B24 to B27). Second horizontal derivative filters show regions of high curvature (figures B28 to B31). One can also take the first derivative in the X direction and then in the Y direction (figures B32 and B33). Where the gradient and/or curvature is greatest, one would suspect a boundary. Figures B24 and B25 show high gradients occuring between the ridges of the Borderland and only a minor one between the Palos Verdes ridge and the Los Angeles Basin. No maximum occurs along the San Andreas Fault, but one does occur along the San Jacinto Fault. Figures B28 and B29 show very high gradients on the south side of the Santa Monica Mountains-Channel Islands and minor ones to the north and south of the Oakridge Fault.
Strike-pass filtering can be used to isolate certain anomalies that are oriented in a specific direction. Any number of orientations could be analyzed, but most would not show anything significant. In the geology of this region, there are two major trends: features parallel to the San Andreas and features parallel to the Transverse Ranges. To see what gravity anomalies are related to these trends, the gravity matrix has been strike-pass filtered accordingly. Figure B34 shows anomalies with an orientation between 60 and 120 degrees with respect to the matrix, parallel to the Transverse Ranges. The only anomalies that show up in this map is that of the Santa Monica Mountains and Channel Islands, and to a lesser extent, the Santa Ynez Mountains. This map shows that the gravity anomalies of the San Gabriel and San Bernardino Mountains do not really have an east-west orientation. Figure B35 show anomalies with an orientation between 145 and 165 degrees, parallel to the San Andreas. It shows that many anomalies are parallel to the San Andreas fault, including the San Gabriel Mountains, and the California Continental Borderland. The positive anomalies associated with the Catalina Rigde, San Clemente Ridge, and Palos Verdes, and the negative anomalies of the Santa Cruz, Santa Monica and Los Angeles Basins show to be oriented parallel to the San Andreas fault. This does not mean that the San Andreas fault influenced the formation of these features, but that the controlling factor of the San Andreas, the northwest motion of the Pacific plate with respect to the North American plate, was also the controlling factor of the Borderland.
Gravity of a region of southern California has been filtered in various ways using the wavenumber filtering method to isolate and enhance tectonic features. Maps of the filtered data has been presented in Appendix B. In the next section, the filtered gravity data is analysed further with respect to the tectonics of southern California.
From the filtered gravity maps, it appears that the three regions of the Transverse Ranges are quite different. The gravity of the San Bernardino Mountains is not the same as the that of the San Gabriel Mountains or that of the western Transverse Ranges. The San Bernardino and Little San Bernardino Mountains have only a small gravity anomaly associated with them. The gravity of these mountains blend in well with the gravity anomalies in the Mojave Desert. The orientation of the anomaly of the San Gabriel Mountains seems to be controlled by the San Andreas and San Gabriel faults. The major anomaly of the San Gabriel Mountains correlates well with an outcrop of Pelona Schist. This small positive anomaly disappears quickly when filtered, indicating the feature is shallow and that the mountains have no root, agreeing with seismic data from Roller and Healy (1963) and Mellman (1972). The western Transverse Ranges shows three parallel east - west gravity anomalies. The northern feature is a minor positive anomaly associated with the Santa Ynez Mountains. The southern feature is a very strong positive anomaly associated with the Santa Monica Mountains - northern Channel Islands. Between the two is a minor negative anomaly associated with the Ventura Basin. The three regions of the Transverse Ranges each have their own unique gravity anomaly pattern. These differences in gravity signature support theories that the western Transverse Ranges were formed by very different processes than the rest of the province.
From careful analysis of the filtered data, boundaries between areas of similar gravity have been drawn (figure 12). In the northern half of the region, a distinct change of gravity occurs as one passes across the San Andreas fault. To the south, however, the change occurs at the San Jacinto fault. The southern San Andreas fault is not apparent in the gravity. This is especially clear in the low-pass filtered maps B2 to B4 and the upward continued maps B9 to B11. A boundary can be drawn along the San Gabriel fault, separating the San Gabriel Mountains from the western Transverse Ranges. A significant change in gravity can be seen at this boundary in most of the band-pass and vertical derivative filtered maps (such as maps B2, B3, B6, B7, and B20 through B23). Another boundary can be drawn along the Elsinore fault. In the band-pass filtered maps B6 and B7, where the regional trend has been removed, it appears that the boundary along the Elsinore fault continues northward to the boundary along the San Gabriel fault.
In the California Continental Borderland, boundaries can be drawn separating the positive anomaly ridges from the negative anomaly basins. Band-pass filtered maps B2, B6 and B7 show that the Palos Verdes ridge extends well offshore both to the north and south. These filtered maps also show the northern tip of the San Clemente Ridge extending almost to the northern Channel Islands. The Newport - Inglewood fault does not appear to be a significant tectonic boundary. The fault shows up in the gravity only in the horizontal first derivative maps such as B26 and B27.
Boundaries for the western Transverse Ranges show up quite well in band-pass, downward continuation and horizontal derivative filtered maps. From maps B13, B14 and B15, a boundary can be drawn along the southern side of the Santa Monica Mountains and northern Channel Islands. These maps also indicate a northwest to southeast break between the Channel Islands and the Santa Monica Mountains. From the shape of the boundaries, it appears that the Channel Islands were once tucked against the south side of the Santa Monica Mountains, but have since been faulted to the northwest. The northern boundary of the Santa Monica Mountains are not as clear. Some evidence of a boundary just south of the Oakridge Fault can be seen in maps B18, B23 and B26. Also in these maps a boundary is visible between the Ventura Basin and the Santa Ynez Mountains.
Analysis of the wavenumber filtered gravity data has allowed boundaries for regions of similary gravity anomalies to be determined. No new information has been added to the data set. However, filtering has allowed trends that had otherwise been obscured to become visible. Now to understand the tectonics of the region better, these gravity anomaly can be compared to the geology.
