Santa Cruz Mountains and San Francisco Bay Peninsula Morphometry



George Hilley and Ramon Arrowsmith



Table of Contents

Introduction
Preliminary Results



Introduction

We analyzed the morphometry of the Southern San Francisco Bay Area in order to 1) identify areas potentially undergoing high active uplift, 2) the location of faults that may pose seismic risk to the Santa Clara Valley, and 3) identify study areas for detailed work in the Peninsula area. We aquired 23 USGS 7.5 minute Digital Elevation Models (DEMs) as a topography base for our analysis. The quadrangles used are listed in Table 1. Three dimensional visualization of the topography in the area was used to identify lineaments in the topography. In addition, a Geographic Information System (GIS) containing the geology of the Southern San Francisco Bay Area (courtesy of C. Wentworth) was overlain onto the topography in order to see the relative influence of lithologic contacts and active uplift on determining the morphology of the Southern Bay Area.

Several morphometric parameters were computed in order to determine the degree of incision into the Santa Cruz Mountains. We hypothesize that the bulk of the relief in the Santa Cruz Mountains is formed by uplift along thrust faults that strike sub-paralell to the San Andreas Fault. Therefore, there is an intimate link between uplift rates, material redistribution rates (due to geomorphic processes), and the morphology of the Santa Cruz Mountains. By quantifying features of the Santa Cruz mountains, we hope to infer tectonic uplift rates and constrain geomorphic process rates. We will bridge the gap between the morphology of the landscape and these rates through the use of a process-based, two-dimensional coupled tectonic and geomorphic numerical model. While a morphometric analysis uncalibrated by model simulations cannot provide us with quantitative rates for these processes, it can help us gain intuition as to the relative distribution of uplift in the Santa Cruz Mountains.


Preliminary Results

I. Three-dimensional visualization

We created three-dimensional images of the Santa Cruz Mountains in order to identify topographic lineaments and study the general morphology of this area. All images were produced on a Silicon Graphics Workstation Power Indigo2 R10000 running ERMapper 5.5. These images were rendered using shading and reflectance algorithms. The rendered images were exported as JPEG graphics files.

Presented in Figure 1 is an overview of the landscapes of the San Francisco Peninsula. A cursory inspection of this oblique topographic image shows the influence of the San Andreas Fault and associated secondary structures (e.g. the Monte Vista, Berrocal, Sargent Fault Zones) on the landscape. The clear linear trend running through the topography is the San Andreas Fault. Labeled on the map are Mt. Loma Prieta (the site of the 1989 Loma Prieta Earthquake) and Black Mountain (a focus of deformation during the 1906 San Francisco Earthquake). The Santa Cruz Mountains in this area are likely produced by uplift accomodated along thrust faults east of the San Andreas Fault (Burgmann et al, 1994).



Figure 1: Three dimensional perspective view of the Southern San Francisco Bay Area. Noted on the image are Black Mountain (large deformation accomodated in this block during the 1906 San Francisco Earthquake) and Mt. Loma Prieta (area of the 1989 Loma Prieta Earthquake). No vertical exageration in this image.


Figure 2 shows us a perspective view looking down strike of the San Andreas Fault from Mt. Loma Prieta. Clearly visible in this image is the uplifted area east of the San Andreas Fault (left side of fault in figure) that is being uplifted along the Monte Vista, Berrocal, Shannon, and Sargent thrust faults. These faults have not produced significant seismic events in historic time; however, they may pose a large seismic hazard to the Bay Area. These faults, collectively referred to as the Southern Santa Clara Valley Thrust Zone (SSCVTZ) are a focus of this research. Also visible in this image are several topographic welts, including Black Mountain. These topographic welts may represent blocks that are being rotated by movement along the San Andreas Fault and the Southern Santa Clara Valley Thrust Zone.



Figure 2: Prespective view of the San Andreas Fault looking toward San Francisco from Mt. Loma Prieta. Note the Black Mountain block and the uplifted area surrounding the San Andreas Fault.


Figure 3 is a perspective view looking down the strike of the San Andreas Fault toward San Francisco. The vantage point is approximately centered at Black Mountain. In this figure, we see a reduction in relief as we move farther away from the restraining bend in the San Andreas Fault (near Mt. Loma Prieta). The segment of the fault we are looking at contains Crystal Springs Resevoir. There is no vertical exageration in any of these figures.



Figure 3: Perspective view of the San Andreas Fault looking toward San Francisco from Black Mountain. Notice the decreasing relief in this area as we move farther away from the restraining bend in this section of the San Andreas Fault (the restraining bend includes and continues to the south of Mt. Loma Prieta)


II. Development of Morphometric Analysis Tools

One of the major problems in using a morphometric analysis to quantify features about the landscape is the inability to reproduce many morphometric parameters. For example, the topographic residual gives a measure of relief within the drainage basins in a landscape. It is calculated by subtracting two derived surfaces, the envelope and the subenvelope surfaces. The envelope surface is calculated by taking elevations from the ridgelines in a landscape and interpolating a surface from these points. Likewise, the subenvelope surface is calculated by selecting elevations from the stream channel bottoms in a landscape and interpolating a surface between those points. By subtracting these two surfaces, the relief within drainage basins is quantified. However, the end distribution of the residual values is dependent on which points are selected for the envelope and subenvelope surfaces. Therefore, the residual surface is plauged with interpretation and hence, non-reproducability.

We developed a standard algorithm for computing the envelope, subenvelope, and residual surfaces from Digital Elevation Models. The calculations are performed by a computer and only two numbers need to be input to uniquely define the envelope, subenvelope, and residual surface. These techniques represent an effort to standardize the computation of morphometric parameters, making them more useful for quantitative analyses. Our computations are performed with the aid of the ARC/INFO GIS software. We will be providing our macros for computing morphometric parameters in order to standardize their calculations. The general method for computing the envelope, subenvelope, and residual surfaces is shown schematically in Figure 4.



Figure 4: Schematic flowchart of our algorithm for producing envelope, subenvelope, and residual plots from Digital Elevation Models. Our algorithm has been successfully implemented in ARC/INFO.


III. Morphometry of the Loma Prieta Area and Cupertino Area

We tested our morphometric techniques on the Loma Prieta area and the Cupertino area. The 7.5 minute DEMs used in the Loma Prieta area are the Los Gatos Quadrangle, the Loma Prieta Quadrangle, the Laurel Quadrangle, and the Santa Teresa Hills Quadrangle. The 7.5 minute DEM used in the Cupertino area is the Cupertino Quadrangle. In addition, Digital Orthophoto Quadragles are available for the Cupertino area and were used there to aid in our geomorphic interpretations.

The relative magnitudes of the residual surface is shown in Figure 5. High values of the residual are found northeast of the San Andreas Fault in this area. Fission track data show that the block northeast of the San Andreas fault may be undergoing uplift as large as 1 mm/yr. The spatial distribution of the high uplift rates inferred from fission track data correlate well with the spatial distribution of the residual magnitudes. The area in Figure 5 encompasses four 7.5 minute quadrangles.

We hypothesize that the uplift in the Loma Prieta area is being accomodated by movement along the Southern Santa Clara Valley Thrust Zone faults. In the area of Loma Prieta, the Sargent, Shannon, and Berrocal faults are potential candidates for accomodating this uplift. We will use morphometric studies and model simulations to determine the history of the slip along these fault zones and the current slip rates on these faults.



Figure 5: Values of the topographic residual in the area of Mt. Loma Prieta. High values are red, low values are blue. Notice high values of the residual east of the San Andreas Fault, near Mt. Loma Prieta. Fission track data shows a long-term rock uplift rate of approximately 1 mm/yr in this area. The spatial distribution of uplift and the topographic residual correlate well in this area.


The Santa Clara Valley harbors the majority of the world's high tech industry. In order to assess the risk to this strategically important area, we conducted a detailed morphometry of the Cupertino Quadrangle. This quadrangle is located in the heart of the high tech industry. In addition, the Cupertino Quadrangle has three sets of faults running through it- the San Andreas Fault, and two of the faults of the Southern Santa Clara Valley Thrust Zone (the Monte Vista and Berrocal Thrusts). We used morphometry to analyze the spatial distribution of uplift as indicated by the residual calculation.

Our residual calculations in the Cupertino Quadrangle are based on the following values for the residual algorithm presented: channelization threshold was set to 70, and we let the ARC/INFO function BASIN (GRID function) delineate our drainage basin boundaries. The results of our morphometric analysis are presented in Figure 6. While the residual correlates with the position of the Monte Vista and Berrocal Faults in this area, the diffuse distribution of the residual magnitudes between centers of local high residual complicate interpretation. In order to generalize the residual surface to show areas of concentrated residual magnitudes, we performed a nearest neighbor analysis in which the value of the "Generalized Residual" at any point is equal to the average of the magnitudes of areas lying within 250 meters of the point under consideration. This calculation brings out the general trends in the residual magnitudes and helps to filter geomorphic noise out of the data. The results of this "Generalized Residual" are shown in Figure 7.



Figure 6: The topographic residual surface of the Cupertino 7.5 minute USGS quadrangle. The calculations were performed using the algorithm described above with channelization occuring at flow accumulations exceeding 70. Notice the high residuals near the San Andreas Fault and near the Berrocal Fault. Also notice the diffuse magnitudes of the residual between these loci of high magnitude residuals.




Figure 7: The "Generalized Residual" for the Cupertino 7.5 minute USGS quadrangle. This plot is derived from the residual surface plotted in Figure 6. In order to remove geomorphic noise in the data and highlight trends in the residual, we performed a nearest neighbor analysis in which the value of the generalized residual at any point is equal to the average of the residual values of the surrounding 250 meters. Notice that this plot shows a locus of high residuals along the Berrocal Fault.


IV. Morphometric Analysis of the Southern San Francisco Bay Area, California

We calculated the topographic residual for the entire Southern San Francisco Bay Area in order to identify areas that may be undergoing active uplift ue to thrust faulting. We aquired the DEMs listed in Table 1 and calculated the envelope, subenvelope, and residual surfaces based on these data. The critical channelization flow accumulation was set to 70, and the critical basin flow accumulation value was set to 60. The generalized topographic residual for the Southern Bay Area was computed using a 15 km search radius, and the large-scale topographic residual was computed using a 1.5 km search radius.

Figure 8 shows the generalized topographic residual surface for the area investigated. The red lines in the image are mapped faults in the area. The zone of faulting trending approximately northwest-southeast in the figure is the San Andreas Fault Zone. The generalized residual surface serves to highlight some general areas of high residual in the area investigated. From this generalized residual surface, we identified three areas with high values of the topographic residual. These areas are located near Mt. Loma Prieta, Black Mountain, and San Mateo. The locations detailed maps of the residual for these areas are indexed in Figure 9. In general, high values of the generalized topographic residual correlate with the location of active faults; however, the details of the topographic residual in these areas is not as clear as the general trend. At this time, one author believes (GEH) that the details in the topographic residual are a function of 1) complex fault geometries, both in map view and at depth, 2) complex average slip distributions along these faults, resulting in a complicated uplift distribution in areas surrounding these faults, 3) disequalibrium in geomorphic processes (ungraded river channels, partial relaxation of surrounding hillslopes to graded channels, importance of landsliding), 4) accuracy of 7.5 minute DEMs, 5) noise due to gridding algorithms of surfaces.


Figure 8: Generalized Residual Map of the Southern San Francisco Bay Area, California. Channels are defined by flow accumulations exceeding 70 on the positive topographic surface. Basin boundaries are defined by flow accumulations exceeding 60 on the negative topographic surface. The topographic residual was generalized with a nearest neighbor radial search with a search radius of 15 km.




Figure 9: Residual Map of the Southern San Francisco Bay Area, California showing the location of detailed maps presented in Figure 10, Figure 11, andFigure 12. Channels are defined by flow accumulations exceeding 70 on the positive topographic surface. Basin boundaries are defined by flow accumulations exceeding 60 on the negative topographic surface. The topographic residual was generalized with a nearest neighbor radial search with a search radius of 1.5 km.


The residual surface was calculated for three areas that displayed high residual values on the Generalized Residual Map of the Southern Bay Area (Figure 8). The first of these areas is the Sierra Azul block, located at the beginning of the restraining bend near Santa Cruz in the San Andreas Fault. The residual surface for this area is shown in Figure 10. Fission track data suggest that the area has undergone rapid exhumation (on the order of 0.8mm/yr) over the last 4.6 million years (Burgmann et. al, 1994). Uplifted marine terraces near Santa Cruz and correlation of geologic units contrain the surface uplift in the area suggesting 3 km of unroofing. The combination of morphometric analyses and fission track data provide a means of calibrating the residual magnitudes to uplift rates.

In the Loma Prieta area, uplift is likely accomodated along the Sargent, Shannon, and Berrocal thrust faults (part of the SSCVTZ). While the fission track data provide a means of imaging long-term uplift in this area, a calibrated morphometric analysis may yield details of the uplift distribution in this area. This distribution could be used to infer at-depth fault geometries and slip rates.



Figure 10: Residual Map of the Sierra Azul block, Southern San Francisco Bay Area, California. Channels are defined by flow accumulations exceeding 70 on the positive topographic surface. Basin boundaries are defined by flow accumulations exceeding 60 on the negative topographic surface. The topographic residual was generalized with a nearest neighbor radial search with a search radius of 1.5 km. Mt. Loma Prieta is situated near the epicenter of the 1989 Loma Prieta earthquake which resulted in extensive damage in the Bay Area.




Another area of high residual was the Black Mountain area (Figure 11). We computed a detailed topographic residual map of this area in order to characterize the residual distribution. In this area, the Monte Vista and Berrocal Fault are the primary thrust faults in the area. Black Mountain was an area that underwent large deformation during the 1906 San Francisco earthquake. Note in this residual map the low values of the topographic residual in the Steven's Creek embayment of the Santa Cruz mountains. Uplifted terraces have been well documented in this area, demonstrating recent and continual uplift of this area. The lack of correlation between the topographic residual and field evidence for Quaternary uplift may result from the gridding algorithms used in determining the envelope and subenvelope surfaces.



Figure 11: Residual Map of the Black Mountain area, Southern San Francisco Bay Area, California. Residual values are generally low in the area of the Cupertino embayment. The lack of correlation between field evidence in this area (recently uplifted alluvial terraces) and the magnitude of the topographic residual may result from gridding algorithms of the envelope and subenvelope surface. Channels are defined by flow accumulations exceeding 70 on the positive topographic surface. Basin boundaries are defined by flow accumulations exceeding 60 on the negative topographic surface. The topographic residual was generalized with a nearest neighbor radial search with a search radius of 1.5 km.



The last area we investigated was the Half Moon Bay/San Mateo area of the Bay Area. This area shows high residual values. Figure 12 is a map of this area. The inferred uplift in this area may be a result of complex faulting in this area and/or lithologic influences on the residual values. This area is near Montara Mountain which contains a granite more resistant to weathering than the surrounding material.



Figure 12: Residual Map of the San Mateo area, Southern San Francisco Bay Area, California.Channels are defined by flow accumulations exceeding 70 on the positive topographic surface. Basin boundaries are defined by flow accumulations exceeding 60 on the negative topographic surface. The topographic residual was generalized with a nearest neighbor radial search with a search radius of 1.5 km.

Table 1: 7.5 Minute USGS Digital Elevation Models used in morphometric analysis.
Ano NuevoMindego Hill
Big BasinMontara Mountain
Castle Rock RidgeMorgan Hill
CupertinoMount Madonna
DavenportMount Madonna West
FeltonPalo Alto
Franklin PointPigeon Point
Half Moon BaySan Gregorio
La HondaSan Mateo
LaurelSan Francisco South
Los GatosSanta Teresa Hills
Loma PrietaWoodside




Figure 13: Index Map of the Quadrangles used in calculating the morphometric indecies discussed. All data were downloaded from the Bay Area Regional Database (BARD; http://bard.wr.usgs.gov/). The data used were 7.5 minute Digital Elevation models with a horizontal spatial resolution of 30 meters and a vertical accuracy of 3 meters.