Application of Finite Difference Methods to Exploration Seismology

Radiation boundary conditions for acoustic and elastic wave calculations

“…Because of the restrictions imposed by present day computers, many of the calculations in scientific computing require the use of artificial computational boundaries. This problem has stimulated considerable interest recently in the computational literature (see the bibliography in [4], [5] and [9]). Important areas of application which use artificial boundaries are seismology utilizing both scalar and elastic waves (see [l] and [5]), local and global numerical weather prediction (see [3] and [9]), and a wide variety of problems in transonic fluid dynamics.…”

“…For simplicity we concentrate on a class of problems typical in exploration seismology using the acoustic or elastic wave equations. These calculations (see [ 5 ] ) usually involve a rectangular region given by Figure 0.1, where x = O is the surface of the earth with its layer structure below and the boundary x = 0 is a physical boundary while the remaining three sides of the rectangle are computational artificial boundaries. One is interested in computing a solution which is a response to a known forcing function on the surface x = 0, where this solution satisfies the variable coefficient acoustic or elastic wave equation with the appropriate physical boundary conditions at x = 0.…”

Absorbing boundary conditions for numerical simulation of waves

“…The operator we study has the form and the approximations analogous to those in [4] The costs of publication of this article were defrayed in part by the payment of page charges from funds made available to support the research which is the subject of the article. This article must therefore be hereby marked "advertisement" in accordance with 18 U. S. C. §1734 solely to indicate this fact.…”