MODEL‐BASED TRANSFORMATIONS OF COMMON MIDPOINT GATHERS¹

A method for transforming Normal Moveout corrected CMP‐gathers is proposed. The method is based upon the availability of a model of the CMP‐gather. However, the transformation can be performed with any degree of accuracy in the model. Ideally the employed model should be a synthesis of all available a priori information about the particular data set.

Mathematically the transformation is performed as follows. The CMP‐gather is considered to be a matrix. This matrix is first decomposed into a set of submatrices of the same dimensions. Each submatrix consists of non‐zero elements or samples with the same relative amount of noise. By reducing each of these submatrices to a vector (a trace) we get a new set of traces. This set then represents the transformed CMP‐gather.

The purpose of the transformation is to organize the CMP data in a form which makes it easier both to analyse the noise distribution and to take the necessary steps to improve the signal‐to‐noise ratio at the stacking stage. In principle the method incorporates the exploitation of multichannel recordings with the use of models. Several examples of transformed gathers and their applications to the improvement of real seismic data are shown.