Chapter 3 - Seismic wave modeling and high-resolution imaging

Abstract

High-resolution imaging is becoming increasingly important in the oil and gas industry, as the need to exploit smaller hydrocarbon traps within complex structures is growing. The main purpose of diffraction imaging is to obtain a subsurface representation of structural features with the highest possible sharpness and resolution. Diffraction imaging offers superresolution information, which consists of image details that are beyond the classical Rayleigh limit of half a seismic wavelength, since diffraction waves have shorter wavelengths than seismic waves. Superresolution imagery greatly aids interpreters by allowing for the instant identification of small events such as fracture zones, pinch-outs, channel edges, small-scale faults, reflector unconformities, salt flanks, karst, caves, and fluid fronts (all of which are referred to as “small scattering objects”). The primary goal of this chapter was to develop and apply diffraction theory in order to better understand diffraction phenomena. Using input seismic variables such as velocity, frequency, depth, and migration aperture, an algorithm is developed to observe the behavior of diffraction hyperbolas. Analysis reveals that diffraction hyperbolas are affected not only by velocity but also by depth and frequency. An advanced wave-modeling algorithm based on low-rank approximation is developed, resulting in high-resolution imaging and an improved modeling environment. The wave-modeling and imaging algorithm is implemented on two velocity models: the Marmousi model and the Sigsbee model. These are then contrasted with traditional wave modeling. In comparison to conventional modeling, the results show that advanced wave modeling provides dispersion-free and noise-free data. The third section of this chapter focuses on the issues associated with diffraction imaging, as diffraction is suppressed during processing, either intentionally or unintentionally. To avoid this, careful image preprocessing is recommended, and two algorithms to preserve these diffractions are developed. Dip frequency filtering (DFF) is a quick and reliable method for preserving diffraction. To suppress data reflection, this algorithm works in the frequency domain by defining a slope filter with respect to dt/dx. Because this algorithm requires an accurate local data slope, plane-wave destruction (PWD) filtering techniques are slightly slower than DFF but more efficient. The plane-wave differential equation is used in the design of PWD, which is purely deterministic and linear. A local window is not required to generate a smoothly varying estimate of the slope, and nonstationary signals are handled gracefully in the local slope estimation. The final results show an improvement in resolution, which can be confirmed by the frequency spectrum, which shows that (0–10Hz) frequencies are improved as well as higher frequency data (from 20 to 50Hz) is preserved after the newly developed algorithms.