Measuring velocity from zero-offset data by image focusing analysis

Introduction

In Biondi (2009) I presented a method to extract quantitative velocity information by analyzing the focusing and defocusing of seismic images. This method is based on the image-focusing semblance functional that simultaneously measures image coherency along the structural-dip axes and the aperture-angle axes. I also discussed the ambiguity between reflector curvature and velocity, and how reflector curvature may bias velocity estimates from image focusing. The method I presented has two important characteristics. First, it explicitly takes into account the relation between reflector curvature and velocity. Second, it provides velocity information from image focusing that is consistent with the velocity information that we routinely extract from migrated images by analyzing their coherency along the data offset or the reflection-aperture angle axes.

In this paper, I apply the new method to velocity estimation from zero-offset data. Zero-offset data represent the extreme case where there is no velocity information coming from data redundancy with offset. In this case, velocity-estimation methods can only rely on velocity information contained in the focusing of the image. Therefore, the ambiguity between reflector curvature and migration velocity can severely limit velocity resolution.

Tests on simple synthetic data sets illustrate the curvature-velocity ambiguity, but also demonstrate that velocity resolution increases as the range of reflector curvature broadens. These results are corroborated by the application of the method to zero-offset data acquired by a shallow-seismic survey in the New York harbor. I iteratively update interval velocity in a sedimentary layer just below the water bottom. At each iteration, I estimate the value of residual-migration parameter that corresponds to the best focused image by evaluating the image-focusing semblance and picking its maximum. This value is then used to perform a conventional vertical interval-velocity update. The process converged after two iterations to an estimate of the sediment velocity that is consistent with available geologic information and improves the focusing of the migrated image.

Measuring velocity from zero-offset data by image focusing analysis