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Proceedings Paper

Three-dimensional depth migration by using finite-difference formulation of the linearly transformed wave equation
Author(s): Daniel L. Mujica R.
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Paper Abstract

In this paper, I present a derivation of a 3D one-pass post-stack depth migration algorithm which is based on the use of the linearly transformed wave equation (LITWEQ). This 3D migration operator is able to properly migrate steeply dipping events in a 3D heterogeneous media. Additionally, I propose an explicit finite-difference scheme formulation for LITWEQ 3D, which is eighth order in space and second order in time. This formulation leads to dispersion free seismograms at Nyquist with higher degree of accuracy than those derived from conventional schemes of second order in time and space. The Von Neumann stability analysis shows that the finite-difference scheme is conditionally stable, then, a proper discretization of the medium is required. Examples with synthetic models show how the wavefield is properly extrapolated by the finite-difference formulation of LITWEQ 3D. The impulse response of the 3D migration fits very well that calculated analytically for a homogeneous medium. Impulse responses are also checked in an heterogeneous medium composed of two materials separated by a 90 degrees corner interface. Finally, a LITWEQ 3D migration is performed on a 3D model which is built in a linearly varying velocity in all three spatial coordinates.

Paper Details

Date Published: 23 September 1994
PDF: 9 pages
Proc. SPIE 2301, Mathematical Methods in Geophysical Imaging II, (23 September 1994); doi: 10.1117/12.187489
Show Author Affiliations
Daniel L. Mujica R., INTEVEP S.A. (Venezuela)

Published in SPIE Proceedings Vol. 2301:
Mathematical Methods in Geophysical Imaging II
Siamak Hassanzadeh, Editor(s)

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