Spatial resolution of acoustic imaging with the Born approximation

Abstract

The practical limits on resolution of images produced by processing seismic data with a Born approximation depend on the spectrum of the source pulse, the incompleteness of the recording geometry, and the fidelity with which one can model the reference medium. These factors together prevent one from recovering a point image from data produced by a point diffractor in the subsurface. A simple imaging formula quantifies the effect of the source pulse, showing that spatial wavelet extent in an imaged volume is related to the product of the local velocity and the period of the propagating pulse. A general 3-D scheme for estimating the effect on resolution of the recording geometry is applied to various recording geometries in a homogeneous 3-D medium to show the importance of increasing the aperture of recording. A study of layered versus homogeneous media on the image resolution, lateral and horizontal, with 2-D models shows that layering, with a monotonic velocity increase, actually improves the lateral image resolution attainable with surface seismic data. A salt‐dome 2-D model shows how imperfect knowledge of either the velocities or structure (or both) can severely smear the acoustic image. Errors on the order of 5–10 percent in velocity of the layers of the reference model will greatly affect the clarity of depth images. Errors on the order of a wavelength in the position of interfaces will similarly affect the image. The addition of wells to the data acquisition plan for the salt model markedly improves the lateral resolution of the image.