Coding and decoding: Seismic data modeling, acquisition and processing

Abstract

We present a method for coding and decoding seismic data acquired, based on the concept of multishooting. In this concept, waves generated simultaneously from several locations at the surface of the earth, near the sea surface, at the sea floor, or inside a borehole propagate in the subsurface before being recorded at sensor locations as mixtures of various signals. The coding and decoding method for seismic data described here works with both instantaneous mixtures and convolutive mixtures. Furthermore, the mixtures can be undedetemined [i.e., the number of mixtures (K) is smaller than the number of seismic sources (I) associated with a multi‐shot] or determined [i.e., the number of mixtures is equal to or greater than the number of sources). When mixtures are determined, we can reorganize our seismic data as zero‐mean random variables and use the independent component analysis (ICA) or, alternatively, the principal component analysis (PCA) to decode. We can also alternatively take advantage of the sparsity of seismic data in our decoding process. When mixtures are underdetermined and the number of mixtures is at least two, we utilize higher‐order statistics to overcome the underdeterminacy. Alternatively, we can use the constraint that seismic data are sparse to overcome the underdeterminacy. When mixtures are underdetermined and limited to single mixtures, we use a priori knowledge about seismic acquisition to computationally generate additional mixtures from the actual recorded mixtures. Then we organize our data as zero‐mean random variables and use ICA or PCA to decode the data. The a priori knowledge includes source encoding, seismic acquisition geometries, and reference data collected for the purpose of aiding the decoding processing. The coding and decoding processes described can be used to acquire and process real seismic data in the field or in laboratories, and to model and process synthetic data.