Abstract
Tomographic inversions for velocity variations in western Washington indicate a high correlation with surface geology and geophysical measurements, including gravity observations. By assuming a simple linear relationship between density and velocity (Birch's law) it is possible to calculate the gravity field predicted from the velocity perturbations obtained by local tomographic inversion. While the predicted gravity matches observations in parts of the model, the overall correlation is not satisfactory. In this paper we suggest a method of constraining the tomographic inversion to fit the gravity observations simultaneously with the seismic travel time data. The method is shown to work well with synthetic data in 3 dimensions where the assumption of Birch's law holds strictly. If the sources of the gravity anomalies are assumed to be spatially localized, integration can be carried out over a relatively small volume below the observation points and sparse matrix techniques can be applied. We have applied the constrained inversion method to western Washington using 4,387 shallow earthquakes, to depths of 40.0 km, (36,865 raypaths) convering a 150×250 km region and found that the gravitational constraints may be satisfied with minor effect on the degree of misfit to the seismic data.
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References
Aki, K., Christoffersson, A., andHusebye, E. S. (1977),Determination of the Three-dimensional Seismic Structure of the Lithosphere, J. Geophys. Res.82, 277–296.
Birch, F. (1961),The Velocity of Compressional Waves in Rocks to 10 Kilobars, 2, J. Geophys. Res.66, 2199–2224.
Bonini, W. E., Hughes, D. W., andDanes, Z. F. (1974),Complete Bouguer Gravity Anomaly Map of Washington, Washington Division of Geology and Earth Resources, Scale approximately 1:500,000.
Backus, G., andGilbert, G. (1968),The Resolving Power of Gross Earth Data, Geophys. J. R. astr. Soc.266, 169–205.
Chiu, S. K. L., Kanasewich, E. R., andPhadke, S. (1986),Three-dimensional Determination of Structure and Velocity by Seismic Tomography, Geophys.51 (8), 1559–1571.
Chou, C. W., andBooker, J. R. (1979),A Backus-Gilbert Approach to Inversion of Travel-time Data for Three-dimensional Velocity Structure, Geophys. J. R. astr. Soc.59, 325–344.
Crosson, R. S. (1976),Crustal Structure Modelling of Earthquake Data. 1. Simultaneous Least-squares Estimation of Hypocenter and Velocity Parameters, J. Geophys. Res.71 (17), 3036–3046.
Dines, K. A., andLytle, R. J. (1979),Computerized Geophysical Tomography, Proc. IEEE67, 1065–1073.
Evans, J. R., andZucca, J. J. (1988),Active High-resolution Seismic Tomography of Compressional Wave Velocity and Attenuation Structure at Medicine Lake Volcano, Northern California Cascade Range, J. Geophys. Res.93, 15016–15036.
Gower, H. D., Yount, J. C., andCrosson, R. S. (1985),Seismotectonic Map of the Puget Sound Region, Washington, Map I-1613, U.S. Geol. Survey.
Hearn, T. M., andClayton, R. W. (1986),Lateral Velocity Variations in Southern California. 1. Results for the Upper Crust from Pg Waves, Bull. Seismol. Soc. Am.76 (2), 495–427.
Herman, G. T.,Image Reconstructions from Projections (Academic Press, New York 1980).
Ho-Liu, P., Kanamori, H., andClayton, R. W. (1988),Applications of Attenuation Tomography to Imperial Valley and Cos-Indian Wells Region, Southern California, J. Geophys. Res.93, 10501–10520.
Humphreys, E., Clayton, R. W., andHager, B. H. (1984),A Tomographic Image of Mantle Structure Beneath Southern California, Geophys. Res. Lett.11 (7), 625–627.
Inoue, H., Fukao, Y., Tanabe, K., andOgata, Y. (1990),Whole Mantle P-wave Travel Time Tomography, Phys. Earth and Planet. Int.59, 294–328.
Ivansson, S. (1986),Seismic Borehole Tomography—Theory and Computational Methods, Proc. IEEE74, 2.
Jupp, D. L. B., andVozoff, K. (1975),Stable Iterative Methods for the Inversion of Geophysical Data, Geophys. J. R. astr. Soc.42, 957–976.
Kissling, E., Ellsworth, W. L., andCockerham, R. S. (1984),Three-dimensional Structure of the Long Valley Caldera, California, Region by Geotomography, Proc. of Workshop XIX, Active Tectonic and Magmatic Processes beneath Long Valley Caldera, Eastern California, 1, U.S. Geol. Surv. Open File Report, 84-939, 188–220.
Lees, J. M.,Seismic Tomography in Western Washington (University of Washington, Ph.D. Thesis 1989).
Lees, J. M., andCrosson, R. S.,Bayesian ART versus conjugate gradient methods in tomographic seismic imaging: An application at Mount St. Helens, Washington, InSpatial Statistics and Imaging: Proceedings of the 1988 AMS-IMS-SIAM Summer Research Conference (ed. Posollo, A.) (in press 1991).
Lees, J. M., andCrosson, R. S. (1989),Tomographic Inversion for Three-dimensional Velocity Structure at Mount St. Helens Using Earthquake Data, J. Geophys. Res.94 (B5), 5716–5728.
Lees, J. M., andCrosson, R. S. (1990),Tomographic Imaging of Local Earthquake Delay Times for Three-dimensional Velocity Variation in Western Washington, J. Geophys. Res.95 (B4), 4763–4776.
Lines, L. R., Schultz, A. K., andTreitel, S. (1988),Cooperative Inversion of Geophysical Data, Geophysics 53 (1), 8–20.
Meissner, R.,The Continental Crust: A Geophysical Approach (Academic Press, Orlando 1986).
Menke, W.,Geophysical Data Analysis: Discrete Inverse Theory (Academic Press, Orlando 1984).
Nakanishi, I. (1985),Three-dimensional Structure Beneath the Hokkaido-Tohoku Region as Derived from a Tomographic Inversion of P-arrival Times, J. Phys. Earth33, 241–256.
Neumann-Denzau, G., andBehrens, J. (1984),Inversion of Seismic Data Using Tomographical Reconstruction Techniques for Investigations of Laterally Inhomogeneous Media, Geophys. J. R. astr. Soc.79, 305–315.
O'Sullivan, F. (1986),A Statistical Perspective on Ill-posed Inverse Problems, Stat. Sci.1 (4), 502–527.
Oppenheimer, D. H., andHerkenhoff, K. E. (1981),Velocity Density Properties of the Lithosphere from Three-dimensional Modeling at the Geysers-Clear Lake Region, California, J. Geophys. Res.86, 6057–6065.
Paige, C. C., andSaunders, M. A. (1982),LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares, Trans. Math. Software8, 43–71.
Pavlis, G. L. (1986),Geotomography Using Refraction Fan Shots, J. Geophys. Res.91, 6522–6534.
Rodi, W. L., Jordan, T. H., Masso, J. F., andSavino, J. M. (1980),Determination of the Three-dimensional Structure of the Eastern Washington from the Joint Inversion of Gravity and Earthquake Travel Time Data, Final Tech. Rep. SSS-R-80-4516, Systems, Science and Software, La Jolla, California.
Savino, J. M., Rodi, W. L., Goff, R. C., Jordan, T. H., Alexander, J. H., andLambert, D. G. (1977),Inversion of Combined Geophysical Data for Determination of Structure Beneath the Imperial Valley Geothermal Region., Final Tech. Rep. SSS-R-78-3412 to the Department of Energy, Systems, Science and Software, La Jolla, California.
Spakman, W., andNolet, G.,Imaging algorithms, accuracy and resolution in delay time tomography, InMathematical Geophysics (ed. Vlaar, N. J.) (D. Reidel Publishing Co. 1988) pp. 155–187.
Stacey, F. D.,Physics of the Earth (John Wiley & Sons, Inc., New York 1977).
Stanley, W. D., Finn, C., andPlesha, J. L. (1987),Tectonics and Conductivity Structures in the Southern Washington Cascades, J. Geophys. Res.92, 10,179–10,193.
Walck, M. C. (1988),Three-dimensional V p /V s Variations for the Coso REgion, California, J. Geophys. Res.93, 2047–2052.
Walck, M. C., andClayton, R. W. (1987),P Wave Velocity Variations for the Coso Region, California, Derived from Local Earthquake Travel Times, J. Geophys. Res.92, 393–405.
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Lees, J.M., VanDecar, J.C. Seismic tomography constrained by bouguer gravity anomalies: Applications in western Washington. PAGEOPH 135, 31–52 (1991). https://doi.org/10.1007/BF00877007
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DOI: https://doi.org/10.1007/BF00877007