Frequency-domain seismic data transformation from point source to line source for 2D viscoelastic anisotropic media

Abstract

We have developed a simple yet effective transform function to convert 3D point-source seismic data to equivalent 2D line-source data, which is required when applying efficient 2D migration and full-waveform inversion to field data collected along a line. By numerically comparing the 3D and corresponding 2D Green’s tensors in various media, the phase shift approximately 45° and the offset amplitude compensation factor, as well as small fluctuations of the amplitude ratios, are observed in all nonzero components of the wave-equation solutions. Based on these observations, we derive a transform function consisting of (1) a simple filter for compensating amplitude and phase shift and (2) stretching scalars for scaling amplitude differences for different components. We use the 3D and 2D analytical wave solutions in various homogeneous media to demonstrate the accuracy of our transform function, and then apply it to a heterogeneous viscoelastic anisotropic model and a modified Marmousi model. All of these results indicate that our transform function is applicable for the conversion of point-source data to equivalent line-source data for imaging 2D subsurface structure.