Two-Dimensional Seismic Refraction Tomography

Summary An iterative tomographic inversion scheme is presented for determination of 2-D velocity structure from seismic refraction first-arrival traveltimes. the method is suited to refraction profiles where source/receiver spacings are denser than for conventional profiles. the inversion method is based on an iterative solution of the linearized problem, and allows for determination of continuous velocity variations as welt as geometry of subhorizontal interfaces. In each iteration, two-point ray tracing is performed using a shooting method to construct the linear system. the velocity field is defined using triangular cells within which the velocity gradient is constant, allowing analytic calculation of ray paths. Two different inversion techniques are considered, based on distinct linearized formulations of the forward problem. Inversion using a linearized traveltime-velocity Jacobian produced better results than a slowness formulation more akin to common series expansion-techniques. Resolution examples reveal horizontal smearing due to ray geometry, drop-off in resolution with depth, as well as the effect of source-receiver geometry and velocity structure on resolution. Inversion examples indicate that a global norm produces solutions closer to the true model than solutions calculated using a smallest perturbation approach, when a good starting model is available. Streak effects caused by inhomogeneous ray coverage and the removal of these effects are demonstrated.

[1]  G. Pavlis.  Geotomography using refraction fan shots , 1986 .

[2]  Constantine A. Balanis,et al.  A stable geotomography technique for refractive media , 1984, IEEE Transactions on Geoscience and Remote Sensing.

[3]  Vlastislav Červený,et al.  Ray method in seismology , 1977 .

[4]  B. Cassell,et al.  A method for calculating synthetic seismograms in laterally varying media , 1982 .

[5]  D. Oldenburg.  Funnel functions in linear and nonlinear appraisal , 1983 .

[6]  A. C. Kak,et al.  Digital ray tracing in two‐dimensional refractive fields , 1982 .

[7]  Y. Censor.  Row-Action Methods for Huge and Sparse Systems and Their Applications , 1981 .

[8]  S. Ivansson,et al.  Seismic borehole tomography—Measurement system and field studies , 1986, Proceedings of the IEEE.

[9]  P. Firbas.  Tomography from seismic profiles , 1987 .

[10]  George A. McMechan,et al.  Seismic tomography in boreholes , 1983 .

[11]  R. Clayton,et al.  Lateral velocity variations in southern California. I. Results for the upper crust from Pg waves , 1986 .

[12]  John E. Peterson,et al.  Applications of algebraic reconstruction techniques to crosshole seismic data , 1985 .

[13]  B. Julian.  Ray Tracing in Arbitrarily Heterogeneous Media , 1970 .

[14]  S. Ivansson,et al.  Seismic borehole tomography—Theory and computational methods , 1986, Proceedings of the IEEE.

[15]  A.M. Smith,et al.  Numerical Ray Tracing in Media Involving Continuous and Discrete Refractive Boundaries , 1980 .

[16]  C. H. Chapman,et al.  Body-wave seismograms in inhomogeneous media using Maslov asymptotic theory , 1982 .

[17]  Robert W. Clayton,et al.  Tomographic reconstruction of velocity anomalies , 1984 .

[18]  Keiiti Aki,et al.  Determination of the three‐dimensional seismic structure of the lithosphere , 1977 .

[19]  G. F. West,et al.  Crosshole seismology and seismic imaging in crystalline rocks , 1983 .

[20]  E. Bessonova,et al.  The Tau Method for Inversion of Travel Times-I. Deep Seismic Sounding Data , 1974 .

[21]  H. A. van der Vorst,et al.  Numerical solution of large, sparse linear algebraic systems arising from tomographic problems , 1987 .

[22]  I. Lerche,et al.  Tracing of rays through heterogeneous media; an accurate and efficient procedure , 1985 .

[23]  D. L. Anderson,et al.  Travel times, apparent velocities and amplitudes of body waves , 1968 .

[24]  P. Bois,et al.  Well-to-well seismic measurements , 1972 .

[25]  R. Jeffrey Lytle,et al.  Iterative Ray Tracing between Boreholes for Underground Image Reconstruction , 1980, IEEE Transactions on Geoscience and Remote Sensing.

[26]  Freeman Gilbert,et al.  The Effect of Small, Aspherical Perturbations on Travel Times and a Re-examination of the Corrections for Ellipticity , 1976 .

[27]  G. Backus,et al.  Constructing P-velocity models to fit restricted sets of travel-time data , 1969 .

[28]  E. Kanasewich,et al.  Least-squares inversion of spatial seismic refraction data , 1985 .

[29]  R. Parker,et al.  Occam's inversion; a practical algorithm for generating smooth models from electromagnetic sounding data , 1987 .

[30]  David Gubbins,et al.  Three-dimensional seismic ray tracing , 1977 .

[31]  W. Menke.  Geophysical data analysis : discrete inverse theory , 1984 .

[32]  R. Clayton,et al.  Inversion of refraction data by wave field continuation , 1981 .

[33]  R. T. Cutler,et al.  Tomographic determination of velocity and depth in laterally varying media , 1985 .

[34]  Y. Censor.  Finite series-expansion reconstruction methods , 1983, Proceedings of the IEEE.

[35]  R. Clayton,et al.  Analysis of the Resolution Between Ambiguous Velocity And Reflector Position For Traveltime Tomography , 1986 .

[36]  Michael A. Saunders,et al.  LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares , 1982, TOMS.

[37]  Victor Pereyra,et al.  Solving two-point seismic-ray tracing problems in a heterogeneous medium. Part 1. A general adaptive finite difference method , 1980 .

[38]  Donald W. Marquaridt.  Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation , 1970 .

[39]  J. Gillis,et al.  Linear Differential Operators , 1963 .

[40]  Sven Ivansson,et al.  Tomographic velocity estimation in the presence of low velocity zones , 1984 .

[41]  William Menke,et al.  The resolving power of cross‐borehole tomography , 1984 .

[42]  I. Nakanishi.  THREE-DIMENSIONAL STRUCTURE BENEATH THE HOKKAIDO-TOHOKU REGION AS DERIVED FROM A TOMOGRAPHIC INVERSION OF P-ARRIVAL TIMES , 1985 .

[43]  R. Clayton,et al.  A tomographic image of mantle structure beneath Southern California , 1984 .

[44]  Guust Nolet,et al.  Solving or resolving inadequate and noisy tomographic systems , 1985 .

[45]  R. Wiggins,et al.  The general linear inverse problem - Implication of surface waves and free oscillations for earth structure. , 1972 .