Multi-Source, Multi-Receiver Synthetic Seismograms For Laterally Heterogeneous Media Using F-K Domain Propagators

A practical method for computing coupled wavenumber ‘super-propagators’ has been developed. By allowing for a depth of penetration for each wavenumber the inherent numerical instability of the classical propagator method for seismic waves is avoided. Adjustments to the definitions of various quantities are made to allow for wavenumbers not being considered beyond their depths of penetration in the wavefield simulations. Even so, the form of the basic equations for coupled wavenumbers in laterally heterogeneous media is maintained. the 2-D acoustic-wave case is presented. Allowance is made for surface topography by introducing conformal transformations that map the Earth into a flat half-space. At various levels in the flat half-space upgoing and downgoing elements have to be either converted into or extracted from the stress-displacement vectors comprising the wavefield. to do this the eigenvectors of the laterally uniform part of the coefficient matrix for the medium are used. Though computational convenience is the real reason for this choice, it is established to be of the appropriate form for propagation invariants to lead to symmetry properties of transmission and reflection operators. Efficient algorithms have been developed to construct numerical solutions. These include a novel hybrid scheme for updating the propagator from one level to another, which employs a high-precision, standard procedure to calculate variations in the wavefield associated with the laterally uniform part of the coefficient matrix, together with an algorithm requiring few computations which allows for the lateral heterogeneity terms. Many sources, each with multiple receivers, can be considered in the same calculation. an example involving stratified media is presented which illustrates how much distortion in the input model is acceptable before the approach ceases to be viable.