Reflection and transmission operator for irregular interfaces derived from the indirect boundary element method

Abstract

SUMMARY A method is presented to turn into reality the idea of the reflection and transmission operators in the space–frequency domain for infinitely spread irregular interface in terms of the indirect boundary element method (abbreviated to I-BEM), and to apply them to the wavefield in irregularly stratified media. This method is a hybrid between the strategy of the reflection and transmission matrices method (abbreviated to R /T-MM) developed in seismology and that of I-BEM developing in the engineering community. The I-BEM is one of the ways to disassemble the wavefield into up and down going waves in layers sandwiched between irregular interfaces. Green’s function matrices of I-BEM play the role of the wave function of R /T-MM, and the imaginary forces distributed along both faces of interfaces that of the coefficients vectors. The usage of the reference solution, that is the wavefield in the corresponding horizontally stratified media, gives us a good approximation to handle infinitely spread interfaces. This method of calculation can stack the effect of reflection and transmission at irregular interfaces on the wavefield as the wave goes by. Therefore, for example, the waves coming directly from the seismic source can be extracted from latter phases. The test case for a 2-D homogeneous basin shows the incident wave and reflected waves that bounce up and down in the basin. It is expected that the formulation shown here can make consideration of the wavefield in complex velocity structures and the search for appropriate and efficient approximations easier.