Abstract:
Diffracted waves are seismic responses caused by local heterogeneities of underground strata, which carry high resolution heterogeneous information. The key to identify and track the heterogeneous body (or region) by diffractions is to accurately image them. A post stacked diffraction migration imaging method based on path integral has been developed. Firstly, a migration filter in f k domain is constructed by combining the path integral theory with the analytical solution of the isotropic zero migration velocity continuation partial differential equation. Then, the filtering characteristics are varied according to the integral interval (velocity). Finally, the post stacked diffraction imaging is achieved after using an amplitude and phase control in the f k domain to highlight the top of the diffraction arc and weaken the steep wings of the diffraction event. In addition, a Gaussian weighting factor is introduced into the filter to suppress the tail line interferences and improve the imaging quality, and a selection principle of imaging control parameters is also discussed. The results show that this imaging process is equivalent to a continuous summation of all constant velocity continuation sections in a given velocity range. It accumulates stable contribution to boost the energy of the diffraction arc apex, and simultaneously offsets the wings of the event by continuous phase shifting. However, the migration components caused by interval endpoints cannot be offset in this way, which may lead to residual events under and over migrated in the imaging results. To suppress the tail lines and converge the diffraction event, a Gaussian factor can be introduced into the filter. The Gaussian weight can enhance the contribution near the accurate velocity and diminish the migration components caused by wrong velocities. Moreover, for the Gaussian method, the endpoint values on both sides of the velocity interval correspond respectively to the under and over migration components in the imaging section. The size of the velocity range is directly proportional to the energy of the migrated event apex. The focusing degree of diffraction points is determined by the velocity bias and standard deviation. Two theoretical diffraction models verified the effectiveness of this method. The processed results of real seismic data sets show that this method does not need to build an imaging velocity model in advance, and it can effectively improve the imaging quality under the premise of complete extraction of diffracted waves.