WAVENUMBER FILTERING OF GRAVITY DATA AND ITS
APPLICATION TO INTERPRETING STRUCTURE IN THE WESTERN
TRANSVERSE RANGES OF SOUTHERN CALIFORNIA
by
Tim Fogarty
____________
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTERS OF SCIENCE
(Geological Sciences)
May 1985
I wish to acknowledge my committee, Drs. Tom Henyey, Greg Davis and Steve Lund. I also wish to thank Dr. Warren Thomas for help preparing the final draft of this thesis.
All computer work, including word processing and drafting of figures, was performed on USC's Department of Geology's VAX-11/750. The color contour map was created on Union International Oil's VAX-11/780 using a Grinnell Systems graphic television display system.
An easy and rapid method of filtering potential field data is available with the Fast Fourier Transform algorithm. Instead of convolving data with a filter in the space domain, simple multiplication can be performed in the wavenumber domain. The derivation and application of the filtering method is described in detail for the following type of filters: upward/downward continuation, vertical and horizontal derivatives, band-pass and strike-pass.
Wavenumber filtering is possible because of the Fast Fourier Transform, but using this algorithm without understanding its techniques can result in errors such as leakage and Gibb's phenomenon. Why these errors occur and methods to limit them are discussed. It is shown that the best method to limit errors due to leakage and Gibb's phenomenon is to extend the data set, and filling the extended region with a reflection of the data set. Source code for computer programs to perform wavenumber filtering is listed in Appendix A.
To show the application of wavenumber filtering, the method has been applied to gravity data from a region of southern California. Appendix B contains contour maps of the data filtered by various types of Band-pass, Nth Derivative, Upward and Downward Continuation and Strike-pass filters. Filtering the gravity data allows structure to become apparent that otherwise would be hidden. The filtered gravity maps show many anomalies of various size, shape and orientations. Most features filter out easily, indicating that they are shallow features. Anomalies due to the San Gabriel and San Bernardino Mountains are removed after little filtering, supporting the view that they have no roots. The Mojave Desert is a relatively structureless feature; most anomalies in the province can be related to shallow sedimentary basins. Many of the anomalies of southern California are shown to have orientations parallel to the San Andreas, San Jacinto and Elsinore faults. In the Transverse Ranges, although the province is defined as a region of east-west mountain ranges, only anomalies in the Western Transverse Ranges have a true east-west orientation. The gravity anomalies of the San Gabriel Mountains are more aligned with the San Andreas fault and the anomalies associated with the San Bernardino mountains have no profound consistent orientation. In the Western Transverse Ranges, the filtered gravity maps indicate that the Santa Monica Mountains either have a deep root or are a shallow feature of high density. A gravity low along the Santa Clara River continues into the Santa Barbara Channel just south of the city of Santa Barbara, suggesting that the Ventura Basin in the east is continuous with the Santa Barbara basin in the west.
Analysis of the filtered gravity maps allows boundaries of possible tectonic features to be drawn. The San Bernardino and Little San Bernardino mountains are shown to be one with the Mojave block. The region between the Elsinore and San Jacinto faults appears to be a southern extension of the San Gabriel block. The Santa Monica Mountains is shown t continue to the west to the northern Channel Islands, with only a slight offset between the two. It is proposed that the Santa Monica Mountains, the Northern Channel Islands, and the southern half of the Ventura and Santa Barbara Basins make up a single terrane. This terrane, referred to as the Santa Monica terrane, extends from Pasadena to San Miguel Island, and from the Malibu - Santa Monica - Raymond Hill fault on the south to approximately the Oakridge fault on the north.
Two-dimensional gravity modeling has been performed along selected profiles across the Western Transverse Ranges and the California Continental Borderland. Modeling across the Santa Monica terrane suggest that this terrane is made up of a high density mafic or ultramafic body with a thin sedimentary cover, and a northern sedimentary wedge. Similar models of high density ridges flanked by deep sedimentary basins can be developed for the Palos Verdes Peninsula, the San Clemente ridge, the Santa Rosa Rigde and perhaps the Santa Catalina Ridge in the California Continental Borderland. It is proposed that each ridge in the Califorina Continental Borderlands is a separate terrane.
Using paleomagnetic data showing northward motion of 10 to 15 degrees, and (for the Santa Monica terrane) rotations of 90 to 120 degrees, a tectonic model is proposed. In this model, slivers of cratonic material (terranes) have been broken off the North American plate, attached to the Pacific plate, and carried north-northwest to their present locations since the Miocene. The Pacific plate acted as a sort of treadmill. The Santa Monica terrane differs from other terranes in the California Continental Borderland in that when it came in contact with the North American plate, it rotated 90 to 120 degrees clockwise, and collided with the sedimentary wedge of the North American continent. This collision caused deformation, forming the Western Transverse Ranges, including the Santa Ynez Mountains, the Ventura and Santa Barbara Basins, the Santa Monica Mountains and the northern Channel Islands. The Ventura Basin is not a basin formed due to of subsidence or extension, but from to the collision of two offshore sedimentary wedges of different size and thickness. In this basin, the Santa Clara Trough represents the northern sedimentary wedge, while the Oxnard shelf represents the southern sedimentary wedge. The Los Angeles basin to the south of the Santa Monica terrane could have been formed in the wake of the rotating plate.