TY - JOUR
AU - White, D., J.
AB - 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 well 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. inversion, tomography, traveltimes, seismic refraction References Aki K. Christoffersson A. Husebye E. , 1977 Determination of the three—dimensional seismic structure of the lithosphere , J. geophys. Res. , 82 , 277 – 296 . Google Scholar Crossref Search ADS WorldCat Andersen A. H. Kak A. C. , 1982 . Digital ray tracing in two—dimensional refractive fields , J. acoust. Soc. Am. , 72 , 1593 – 1606 . Google Scholar Crossref Search ADS WorldCat Backus G. Gilbert F. , 1969 . Constructing p—velocity models to fit restricted sets of traveltime data , Bull. seism. Soc. Am. , 59 , 1407 – 1414 . OpenURL Placeholder Text WorldCat Bessonova E. N. Fishman V. M. Ryaboyi V. Z. Sitikova G. A. , 1974 . the tau method for the inversion of travel times—I. Deep seismic sounding , Geophys. J. R. astr. Soc. , 36 , 377 – 398 . Google Scholar Crossref Search ADS WorldCat Bishop T. N. Bube K. P. Cutler R. T. Langan R. T. Love P. L. Resnick J. R. Shuey R. T. Spindler D. A. Wyld H. W. , 1985 . Tomographic determination of velocity and depth in laterally varying media , Geophysics , 50 , 903 – 923 . Google Scholar Crossref Search ADS WorldCat Bois P. La Porte M. Lavergne M. Thomas G. , 1972 . Well—To—Well Seismic Measurements , Geophysics , 37 , 471 – 480 . Google Scholar Crossref Search ADS WorldCat Bregman N. , 1986 . Tomographic inversion of crosshole seismic data , PhD thesis , Department of Physics , University of Toronto. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Cassell B. R. , 1982 . A method for calculating synthetic seismograms in laterally varying media , Geophys. J. R. astr. Soc. , 69 , 339 – 354 . Google Scholar Crossref Search ADS WorldCat Censor Y. , 1981 . Row—action methods for huge and sparse systems and their applications , SIAM Rev. , 23 , 444 – 466 . Google Scholar Crossref Search ADS WorldCat Censor Y. , 1983 . Finite series—expansion reconstruction methods , Proc. IEEE , 71 , 409 – 419 . Google Scholar Crossref Search ADS WorldCat Cerveny V. I. Molotkov A. Psencik I. , 1977 . Ray Method in Seismology , University of Karlova , Prague, Czechoslovakia. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Chander R. , 1975 . On tracing seismic rays with specified end points , J. Geophys. , 41 , 173 – 177 . OpenURL Placeholder Text WorldCat Chapman C. H. Drummond R. , 1982 . Body—wave seismograms in inhomogenous media using Maslov asymptotic theory , Bull. seism. Soc. Am. , 72 , S277 – S317 . OpenURL Placeholder Text WorldCat Chapman C. H. , 1987 . the Radon transform and seismic tomography , in Seismic Tomography , ed. Nolet G., pp. 25 – 47 , Reidel , Dordrecht. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Clayton R. W. Mcmechan G. A. , 1981 . Inversion of refraction data by wave field continuation , Geophysics , 46 , 860 – 868 . Google Scholar Crossref Search ADS WorldCat Constable S. C. Parker R. L. Constable C. G. , 1987 . Occam's inversion: a practical algorithm for generating smooth models from electromagnetic sounding data , Geophysics , 52 , 289 – 300 . Google Scholar Crossref Search ADS WorldCat Dziewonski A. M. Gilbert F. , 1976 . the effect of small, aspherical perturbations on travel times and a re—examination of the corrections for eliipticity , Geophys. J. R. astr. Soc. , 44 , 7 – 17 . Google Scholar Crossref Search ADS WorldCat Ewing J. I. , 1963 . Elementary theory of seismic refraction and reflection measurements , in The Sea, 3 , ed. Hill M. N., pp. 1 – 19 , Interscience , New York. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Fawcett J. A. Clayton R. W. , 1984 . Tomographic reconstruction of velocity anomalies , Bull. seism. Soc. Am. , 74 , 2201 – 2219 . OpenURL Placeholder Text WorldCat Firbas P. , 1987 . Tomography from seismic profiles , in Seismic Tomography , ed. Nolet G., pp. 189 – 202 . Reidel , Dordrecht. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Gustavsson M. Ivansson S. Moreń P. Jögen P. , 1986 . Seismic borehole tomography—measurement system and field studies , Proc. IEEE , 74 , 339 – 346 . Google Scholar Crossref Search ADS WorldCat Hearn T.M. Clayton R. W. , 1986 , Lateral velocity variations in southern California. I. Results for the upper crust from P8 waves , Bull, seism. Soc. Am. , 76 , 495 – 509 . OpenURL Placeholder Text WorldCat Humphreys E. Clayton R. W. Hager B. H. , 1984 . A tomographic image of mantle structure beneath southern California , Geophys. Res Lett. , 11 , 625 – 627 . Google Scholar Crossref Search ADS WorldCat Ivansson S. , 1985 A study of methods for tomographic velocity estimation in the presence of low—velocity zones , Geophysics , 50 , 969 – 988 . Google Scholar Crossref Search ADS WorldCat Ivansson S. , 1986 . Seismic borehole tomography—theory and computational methods , Proc. IEEE , 74 , 328 – 338 . Google Scholar Crossref Search ADS WorldCat Julian B. R. , 1970 . Ray tracing in arbitrarily heterogeneous media , Technical Note 1970-45 . Lincoln Laboratory, Massachusetts Institute of Technology . Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Julian B. R. Anderson D. L. , 1968 . Travel times, apparent velocities and amplitudes of body waves . Bull. seism. Soc. Am. 58 , 339 – 366 . OpenURL Placeholder Text WorldCat Julian B. R. Gubbins D. , 1977 . Three—dimensional seismic ray tracing . J. Geophys. , 43 , 95 – 113 . OpenURL Placeholder Text WorldCat Kanasewich E. R. Chiu S. K. , 1985 . Least—squares inversion of spatial seismic refraction data , Bull. seism. Soc. Am. , 75 , 865 – 880 . OpenURL Placeholder Text WorldCat Lanczos C. , 1961 . Linear Differential Operators , Van Nostrand , London. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Langan R. T. Lerche I. Cutler R. T. , 1985 . Tracing of rays through heterogeneous media: an accurate and efficient procedure , Geophysics , 50 , 1456 – 1465 . Google Scholar Crossref Search ADS WorldCat Lytle R. J. Dines K. A. , 1980 . Iterative ray tracing between boreholes for underground image reconstruction , IEEE Trans. Geosci. remote Sensing , GE—18 , 234 – 240 . Google Scholar Crossref Search ADS WorldCat Mcmechan G. A. , 1983 Seismic tomography in boreholes , Geophys. J. R. astr. Soc. , 74 , 601 – 612 . Google Scholar Crossref Search ADS WorldCat Marks L. W. , 1980 . Computational topics in ray seismology , PhD thesis , Department of Physics, University of Alberta . Marquardt D. W. , 1970 . Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation , Technometrics , 12 , 591 – 612 . Google Scholar Crossref Search ADS WorldCat Menke W. , 1984 . the resolving power of cross—borehole tomography , Geophys. Res. Lett. , 11 , 105 – 108 . Google Scholar Crossref Search ADS WorldCat Menke W. , 1984 . Geophysical Data Analysis: Discrete Inverse Theory , Academic Press , Orlando. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Nakanishi I. , 1985 . Three—dimensional structure beneath the Hokkaido—Tohoku region as derived from a tomographic inversion of p—arrival times , J. Phys. Earth , 33 , 241 – 256 . Google Scholar Crossref Search ADS WorldCat Nolet G. , 1985 . Solving or resolving inadequate and noisy tomographic systems , J. Comp. Phys. , 61 , 463 – 482 . Google Scholar Crossref Search ADS WorldCat Oldenburg D. W. , 1983 . Funnel functions in linear and nonlinear appraisal , J. geophys. Res. , 88 , 7387 – 7398 . Google Scholar Crossref Search ADS WorldCat Paige C. C. Saunders M. A. , 1982 . LSQR: an algorithm for sparse linear equations and sparse least squares , ACM Trans. Math Softw. , 8 , 43 – 71 . Google Scholar Crossref Search ADS WorldCat Pavlis G. L. , 1986 . Geotomography using refraction fan shots . J. geophys. Res. , 91 , 6522 – 6534 . Google Scholar Crossref Search ADS WorldCat Pereyra V. Lee W. H. K. Keller H. B. , 1980 . Solving two—point seismic—ray tracing problems in a heterogeneous medium . Bull. seism. Soc. Am. , 70 , 79 – 99 . OpenURL Placeholder Text WorldCat Peterson J. E. Paulesson B. N. P. Mcevilly T. V. , 1985 . Applications of algebraic reconstruction techniques to crosshole seismic data , Geophysics , 56 , 1566 – 1580 . Google Scholar Crossref Search ADS WorldCat Radcliff R. D. Balanis C. A. Hill H. W. Jr , 1984 . A stable geotomography technique for refractive media , IEEE Trans. Geosci. Remote Sensing , GE—22 , 698 – 703 . Google Scholar Crossref Search ADS WorldCat Smith A. M. Goldberg M. Liu E. S. K. , 1980 . Numerical ray tracing in media involving continuous and discrete refractive boundaries . Ultrasonic Imaging , 2 , 291 – 301 . Google Scholar Crossref Search ADS PubMed WorldCat Stork C. Clayton R. W. , 1986 . Analysis of the resolution between ambiguous velocity and reflector position for traveltime tomography .SEG Expanded Abstracts, 56th Annual International SEG Meeting. Telford W. M. Geldart L. P. Sheriff R. E. Keys D. A. , 1976 . Applied Geophysics , Cambridge University Press , Cambridge. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Van Der Sluis A. Van Der Vorst H. A. , 1987 . Numerical solution of large, sparse linear algebraic systems arising from tomographic problems , in Seismic Tomography , ed. Nolet G., pp. 49 – 83 . Reidel , Dordrecht. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Whittall K. P. Clowes R. M. , 1979 . A simple, efficient method for the calculation of travel times and ray paths in laterally inhomogeneous media . J. Can. Soc. exp. Geophys. , 15 , 21 – 29 . OpenURL Placeholder Text WorldCat Wiggins R. A. , 1972 . the general linear inverse problem: implication of surface waves and free oscillations for earth structure . Rev. Phys. Space Phys. , 10 , 251 – 285 . OpenURL Placeholder Text WorldCat Will M. , 1976 . Calculation ot travel—times and ray paths for lateral inhomogeneous media , in Explosion Seismology in Central Europe: Dates and Results , eds Giese P. Prodehi C. Stein A., pp. 168 – 177 , Springer—Verlag , Berlin. Google Scholar Google Preview OpenURL Placeholder Text WorldCat COPAC Wong J. Hurley P. West G. F. , 1983 . Crosshole seismology and seismic imaging in crystalline rocks , Geophys. Res. Lett. , 10 , 686 – 689 . Google Scholar Crossref Search ADS WorldCat This content is only available as a PDF. Author notes * On leave from the Pacific Geoscience Centre, Sidney, Canada.
TI - Two-Dimensional Seismic Refraction Tomography
JF - Geophysical Journal International
DO - 10.1111/j.1365-246X.1989.tb00498.x
DA - 1989-05-01
UR - https://www.deepdyve.com/lp/oxford-university-press/two-dimensional-seismic-refraction-tomography-2mjPSqoJy7
SP - 223
EP - 245
VL - 97
IS - 2
DP - DeepDyve
ER -