Tomographic determination of three‐dimensional seismic velocity structure using well logs, vertical seismic profiles, and surface seismic data

Abstract

A tomographic technique (traveltime inversion) has been developed to obtain a two‐ or three‐dimensional velocity structure of the subsurface from well logs, vertical seismic profiles (VSP), and surface seismic measurements. The earth was modeled by continuous curved interfaces (polynomial or sinusoidal series), separating regions of constant velocity or transversely isotropic velocity. Ray tracing for each seismic source‐receiver pair was performed by solving a system of nonlinear equations which satisfy the generalized Snell’s law. Surface‐to‐borehole and surface‐to‐surface rays were included. A damped least‐squares formulation provided the updating of the earth model by minimizing the difference between the traveltimes picked from the real data and calculated traveltimes. Synthetic results indicated the following conclusions. For noise‐free cases, the inversion converged closely from the initial guess to the true model for either surface or VSP data. Adding random noise to the observations and performing the inversion indicated that (1) using surface data alone allows reconstruction of the broad velocity structure but with some inaccuracy; (2) using VSP data alone gives a very accurate but laterally limited velocity structure; and (3) the integration of both data sets produces a more laterally extensive, accurate image of the subsurface. Finally, a field example illustrates the viability of the method to construct a velocity structure from real data.

Convex constrained optimization for the seismic reflection tomography problem

“…Our presentation of the discretized model is based on the paper by Castillo et al (2000) (see also Lines and Treitel, 1984;Chiu and Stewart, 1987;Stork and Clayton, 1991). The function f ð pÞ : R m YR n is given by f ð pÞ ¼ ð f 1 ð pÞ; f 2 ð pÞ; N ; f n ð pÞÞ and…”

3D raytracing through homogeneous anisotropic media with smooth interfaces

“…The algorithm is an extension to the anisotropic case of previous works for isotropic media (KELLER;PEROZZI, 1983;DOCHERTY;BLEISTEIN, 1984).…”

“…The algorithm has the same perfomance described by Docherty and Bleistein (1984) for isotropic models when computing qP raypaths. The computation of qS 1 and qS 2 raypaths presents difficulties at the singular regions where the slowness surfaces for these waves intersects one another and regions where they are not convex.…”

“…The algorithm can be a forward problem routine for a traveltime inversion scheme which produces estimatives of the elastic constants structure for subsurface, most like the works of Whitmore and Lines (1986), Chiu and Stewart (1987) and Guiziou and Haas (1988), without the limitations of the elliptical anisotropy assumption. Other possible applications include VSP-CDP mapping and the computation of wavefront attributes,slowness vector and wavefront curvature, along the raypath.…”

Development and Calibration of New 3-D Vector VSP Imaging Technology: Vinton Salt Dome, LA

“…Since the vertical VSP velocity must be slower than the sonic velocity, the lateral VSP velocity must be much faster than the sonic velocity in order for the VSP velocity to be 2.75% faster than the sonic velocity. We plan to investigate more on the level of anisotropy, following previous works by (Chiu and Stewart, 1987;Mao and Stuart, 1997;Grech, et al, 2002;. ) evaluated phase screen migration of VSP geometries.…”