Three-dimensional depth migration by using finite-difference formulation of the linearly transformed wave equation

Daniel L. Mujica R.

doi:10.1117/12.187489

23 September 1994 Three-dimensional depth migration by using finite-difference formulation of the linearly transformed wave equation

Daniel L. Mujica R.

Author Affiliations +

Proceedings Volume 2301, Mathematical Methods in Geophysical Imaging II; (1994) https://doi.org/10.1117/12.187489
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

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.

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Daniel L. Mujica R. "Three-dimensional depth migration by using finite-difference formulation of the linearly transformed wave equation", Proc. SPIE 2301, Mathematical Methods in Geophysical Imaging II, (23 September 1994); https://doi.org/10.1117/12.187489

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KEYWORDS

3D modeling

Interfaces

3D acquisition

Diffraction

3D image processing

Wave propagation

Chemical mechanical planarization

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