Global Extrema in Traveltime Tomography

Conference · Wed Jun 26 04:00:00 EDT 1991

OSTI ID:5459719

Berryman, James G. ^[1]

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1. Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

In acoustics of inhomogeneous media, Fermat's principle of least time has often been used in bending methods of ray tracing to determine ray paths for purposes of forward modeling. Fermat's principle plays an equally important role in traveltime inversion, i.e., when attempting to estimate the wave velocities in a medium through which the wave has traveled in a measured time from known source to receiver. Since measured first-arrival traveltimes are necessarily the minimum traveltimes through the medium whose sound velocity profile is to be reconstructed, Fermat's principle allows us to assign all possible wave-speed profiles to one of two classes: a model is either infeasible or feasible depending on whether or not there are any paths from source to receiver that has less traveltime than that measured. The feasible set is convex and furthermore an exact solution to the inversion problem (if any) must lie on the boundary between the feasible and infeasible sets. Thus, Fermat's principle permits the convexification of the nonlinear traveltime inversion problem, so the only extrema are global extrema.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division (CSGB)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5459719
• Report Number(s): UCRL-JC-107927; CONF-9106262--3; ON: DE91017666
• Country of Publication: United States
• Language: English

Related Subjects

440700* -- Geophysical & Meteorological Instrumentation-- (1990-)
47 OTHER INSTRUMENTATION
58 GEOSCIENCES
580000 -- Geosciences
97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
DIAGNOSTIC TECHNIQUES
EARTHQUAKES
FERMAT PRINCIPLE
LEAST SQUARE FIT
MATHEMATICAL LOGIC
MAXIMUM-LIKELIHOOD FIT
NONLINEAR PROGRAMMING
NUMERICAL SOLUTION
PARALLEL PROCESSING
PROGRAMMING
SEISMIC EVENTS
SEISMIC WAVES
TOMOGRAPHY
WAVE PROPAGATION