On the Estimation of Local Slopes

Current algorithms for the estimation of Common Reflection Surface (CRS) parameters are based on one- or multi-parameter coherency analysis (semblance) schemes applied to the data. Such procedures, besides computationally expensive, leads to significant uncertainties on the searched parameters. Conventional semblance methods can be avoided for a number imaging tasks if local slopes can be directly extracted from prestack data, for example, by filtering schemes. Although the idea is not at all new, recent literature shows its revival for various purposes, such as velocity analysis, tau-p imaging, migration to zero offset and time migration. Here, we discuss several different ways of extracting the desired slope information from the data. We propose a simple, straightforward correction to linear plane-wave destructors. The correction is based on the observation that additionally to the local slope, also its inverse can be extracted from the data in a fully analogous way. Combining the information of both extractions yields a simple but powerful correction to the local slopes. In our numerical examples, the naive application of simple linear plane-wave destructors with our simple, straightforward correction produced results of high quality, even in an example with a rather high noise level and interfering events.