In many cases, comparison of real data with synthetic seismograms provides additional constraints on the velocity‐depth profiles obtained with simple inversion techniques. Obtaining a satisfactory match between the real and computed data usually requires several trials with different models but can be performed rapidly if the theoretical seismograms are themselves easily interpretable, i.e., if the major contributions which make up the synthetic traces can be identified and separated. In horizontally stratified media, modeling is further simplified and is faster if the simulation techniques are implemented in the domain of the intercept time τ and the ray parameter p. The generalized reflection and transmission matrix method is well suited for these purposes and may be used to generate synthetic seismograms in both the t-x and τ-p planes. Computation of plane‐wave seismograms is straightforward and merely corresponds to an inverse Fourier transform of the overall reflectivity matrix for each ray parameter. The construction of point‐source seismograms can be carried out in several ways. In this paper, I combine the generalized reflection and transmission matrix method with a discrete wavenumber integration of the reflectivity function, extending previous work to include fluid‐solid interfaces. The introduction of scaling parameters also simplifies the reflectivity matrices. Simple numerical experiments demonstrate that the relations between the earth model and the corresponding seismic response are simpler in the τ-p domain than in the t-x domain. In particular, calculation of the PP, SP, and SS contributions to the complete seismic response shows that shear and converted waves may have a clearer expression in the τ-p plane than in the t-x plane and can in some cases provide discrimination between several earth models. Finally, the main features of a real marine seismic profile are well reproduced by synthetic sections in both the t-x and τ-p domains.
An Early Study on Imaging 3D Objects Hidden Behind Highly Scattering Media: a Round-Trip Optical Transmission Matrix Method
