Seismic Modeling in the Implicit Mode*

Abstract

A B S T R A C TMUFTI, I.R. 1985, Seismic Modeling in the Implicit Mode, Geophysical Prospecting 33, Finite-difference seismic models are often saddled with huge memory requirements for data manipulation, a prohibitive amount of CPU time and even approximate results. At least part of these costs may be due to the fact that most of the work reported on this subject is devoted to the development of explicit models which suffer from severe limitations of stability and necessitate extremely fine time sampling of the wavefield.A new method of seismic modeling which works in the implicit mode and is unconditionally stable is put forward. It is based on the self-adjoint version of the acoustic wave equation. The evaluation of the wavefield is done by using a highly efficient splitting algorithm which does not require transposing the field data at the various time steps. Moreover, it can accommodate anisotropic media as well as three-dimensional structures. Computational efficiency is achieved by introducing an unconventional procedure which yields the sum of the values of the wavefield corresponding to a new time step and a previous time step. The new value can be obtained from this sum by a simple subtraction. I 2 1 c J J t I

Mixed-grid and staggered-grid finite-difference methods for frequency-domain acoustic wave modelling

“…In the time domain, acceleration averaging leads to an implicit formulation of the time integration, which has only been considered by few authors (e.g. Mufti 1985) in seismology. The main drawback is the induced matrix inversion, which may limit the size of the domain to be considered.…”

Delay Boundary Conditions for Elastic Wave Modeling

“…This study make numerical modeling of a wave filed on inner nodes of a model using the explicit difference method [20] . The elastic wave field is excited by a point source in a homogeneous medium and the delay boundary is used to the calculation.…”

The stable‐beam seismic modelling method1

“…T he comp I e xity pr ob I ern One of the main reasons for using ray-tracing methods rather than, say, finitedifference modelling methods (Alterman and Karal 1968;Claerbout 1970;Boore t972;Kelly et al 1976;Stephens 1983;Mofti 1985) is that they are generally considered to be much faster. However, this is not true for complex models.…”