Double-source frequency-wavenumber transform for accurate extraction of 2-D media dispersion

Extracting the dispersion energy image is one of the key steps of surface wave analysis, which is considered an effective and important way to obtain the vertical velocity structure. The quality of the dispersion energy image directly affects the accuracy of selected dispersion curves and the subsequent inversion. However, if we can theoretically obtain an accurate 2-D dispersion energy diagram, we will skip the step of extracting the dispersion curves. Here, we present the double-source frequency-wavenumber (DSFK) transform to extract theoretical 2-D dispersion energy images from multichannel data. Unlike 1-D dispersion energy images, which are based on the assumption of a horizontally layered medium structure, 2-D dispersion energy images also reflect information about the irregular interfaces of media. We adopt a geometry in which two reciprocal sources are on both ends of a receiver array. Then, the multichannel data obtained by this geometry are transformed into the frequency domain, and a 2-D dispersion energy image that corresponds to the 2-D structure is obtained by the DSFK transform. By producing a variety of synthetic data and processing active source data from the Salton Seismic Imaging Project, we confirm the accuracy and applicability of the DSFK transform. As demonstrated by the results, the DSFK transform can obtain the theoretical 2-D dispersion energy distribution and shows significant potential in the field of seismic tomography.