Diffraction imaging using the two-way imaging condition

Abstract

Diffraction imaging can increase the spatial resolution of seismic images beyond conventional means to provide interpreters with high-resolution structural and stratigraphic sections. The reflection image of a specular reflector only exists in either the positive- or negative-dip structure image; however, the image of a diffractor appears in the both positive- and negative-dip images. By applying a sample-by-sample multiplication imaging condition to the opposite dip images, the diffraction energy is retained while the reflection energy is significantly attenuated. The two dip images are generated by separating the source and receiver wavefields into different propagation directions. Two challenges are faced when we use the left-downgoing source and receiver wavefields to calculate the positive-dip structure image and the right-downgoing source and receiver wavefields to generate the negative-dip structure image. First, we need to compute the up- and downgoing wavefields by the Hilbert transform with respect to time and depth for the source and receiver wavefields. This operation requires two additional forward modeling calculations with the Hilbert-transformed source and receiver wavefields. Second, the information provided by the upgoing wave is missing if we only use the downgoing wave to generate two opposite dip structure images. To overcome the limitations of the one-way imaging condition, we use the two-way imaging condition of positive- and negative-dip structure images. Impulse response analysis demonstrates that the two-way imaging condition has the ability to image the positive- and negative-dip structure images separately. Without up and downgoing wavefield separation, the upgoing source and receiver wavefields can generate the same structure dip as using the downgoing source and receiver wavefields. Results indicate that using the two-way imaging condition can provide broader illumination and enhance the diffraction image because of the additional contribution from the upgoing wavefield. In addition, it saves almost half the computation cost compared to using the one-way imaging condition.