Three-dimensional seismic modeling with source-receiver offset

Previously, wave theory solutions involving the Kirchhoff integral for the calculation of diffractions have assumed a zero source-receiver offset. However, seismic data is normally recorded from non-zero sourcereceiver offsets. Therefore, to better represent the physical seismic model a mathematical solution of the pressure response for a non-zero source-receiver offset, which is applicable to any three-dimensional subsurface model, has been found. The non-zero offset solution has been determined by first transforming the Kirchhoff surface integral into a line integral around the diffracting dege and then simplifying the line integral by expressing it as a convolution. By expressing the non-zero offset solution in this manner, it is easy to see that the known zero-offset solution is a special case. From numerical comparisons between the non-zero and zero-offset models, we found that the major factor governing the diffraction amplitudes for the non-zero offset is the location of the source-receiver midpoint. In essence, except for large offsets which produce slight variations in the diffractions, the zero-offset mathematical model represents a good approximation of the non-zero offset model.