ON THE EQUIVALENCE BETWEEN STRATIFIED MEDIA AND OSCILLATORS

Abstract

A new method of modelling scattered seismic pulses is developed, based on the deformation that suffers an initial pulse due to scattering and on a reinterpretation of the product of convolution of a Green function with a source time function. In this new interpretation, the convolution product is equivalent to the solution of an ordinary differential equation, in which the source term corresponds to the solution of the homogeneous differential equation. The medium response (identified with the Green function) corresponds to the inhomogeneous term of the differential equation. Numerical solutions show the equivalence between the proposed method and the classical one based on convolution. This method can easily be generalized to any kind of complex medium and source time function.