Modelling complex media: an introduction to the phase-screen method

Abstract

Traditional ray-tracing methods for seismic modelling become prohibitively difficult to implement for complex media, and are inappropriate to systems where diffraction by sub-wavelength scatterers dominates the seismic response. Direct simulation methods, such as finite-differences, can handle complexity well but are severely restricted by their computational and storage requirements, especially in 3D. The phase-screen method, used for modelling scalar waves in a variety of contexts, promises to overcome both these limitations and was generalized recently to complex-screen or generalized screen method [Wu, R.-S., 1994. Wide-angle elastic wave one-way propagation in heterogeneous media and an elastic wave complex-screen method. J. Geophys. Res. 99 (B1) 751–766; Wild, A.J., Hudson, J.A., 1998. A geometrical approach to the elastic complex-screen. J. Geophys. Res. 103, 707–726] to handle elastic waves. As a “full-wavefield” method, it implicitly accommodates diffracted and converted phases and it is more computationally efficient than 3D finite-difference modelling, because the wavefield is represented at any instant by a 2D plane of values, which are mapped progressively through the 3D volume. In this paper, the basic principles of the phase-screen concept are presented together with an example of the scattered wavefield from a spherical body. The result shows that for a spherical anomaly set in a homogeneous background the reflection from the base has the same apparent polarity as the reflection from the top. This is contrary from what is expected and appears to be a property of spherical bodies. This surprising result is verified by comparison with results from a 3D finite difference code.