Method for combining seismic data sets
A method is disclosed for combining seismic data sets. This method has application in merging data sets of different vintages, merging data sets collected using different acquisition technologies, and merging data sets acquired using different types of sensors, for example merging hydrophone and geophone measurements in ocean bottom seismic data. In one embodiment, a desired data trace is to be determined from a set of measured data traces, and the following steps are applied: (a) model filters are constructed which express the deterministic relationship between the desired data trace and each available measured trace that depends on the desired data trace; (b) the noise properties associated with each measured data trace are determined; (c) a sufficient statistic for the desired data trace is formed by application of an appropriate filter to each measured trace and summing the filter outputs; (d) the sufficient statistic is further processed by a single-input single-output estimator to construct an estimate of the desired data trace from the sufficient statistic.
1. A method for combining at least two seismic data sets into a single desired data set to generate a subsurface image, comprising:
(a) selecting a corresponding of measured data element from each of the at least two seismic data sets, wherein each seismic data sets comprises a plurality of measured data elements;
(b) for each selected measured data element, determining a complex-valued model filter which, if applied to a single corresponding data element from the desired data set, would produce an output which, when added to a noise signal that may be different for each measured data element, equals the selected measured data element, wherein a covariance matrix R characterizes the noise signals for the selected measured data elements including any dependence between the noise signals in different selected measured data elements, and wherein a vector M has as its components the model filters for the selected measured data elements;
(c) estimating the desired data element by using a computer to apply a complex-valued filter vector G=(M H R −1 M) −1 M H R −1 to the selected measured data elements, wherein the i th element of vector G is applied to an i th measured data element, and superscript H indicates Hermitian transpose;
(d) repeating (a)-(c) for a plurality of different corresponding measured data elements; and
(e) using the estimated desired data elements of the single desired data set to generate a subsurface image.
2. The method of claim 1 , wherein G, M, and R are specified in one of: frequency domain and frequency wavenumber domain.
3. The method of claim 1 , wherein the at least two seismic data sets are differentiated by at least one of: being acquired at different times; being acquired using different acquisition technologies, being acquired using different sensors, and being acquired using different source-receiver pairs.
4. The method of claim 3 , wherein the covariance matrix R specifies non-zero correlations between the noises in the measured data elements.