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Optimal selection of locations for sensors in a seismic survey has been a long-standing issue for geophysicists. If we could sample the earth at two points per wavelength or better in all dimensions according to Nyquist sampling theory, design would not be an issue. The reality of limited access and funding requires us to make do with orders of magnitude fewer sampling points than Nyquist theory would dictate. The field of Compressive Sensing (CS) provides a new theory for non-uniform sampling that allows for using significantly fewer sensors than current practice in seismic exploration. We describe the application of CS concepts to seismic survey design. We refer to our method as Non-Uniform Optimal Sampling, or NUOS. This method differs from earlier work on the application of CS to seismic acquisition in that an optimization loop is used to determine the locations of sources and receivers for a non-uniform design, rather than relying solely on decimation, jittering, or randomization. Optimization can also be applied to the problem of simultaneous shooting. As an extension of the NUOS methodology, we design shooting patterns for simultaneous source surveys by creating non-uniform patterns for each source that have minimal cross-coherence with each other. We have used a combination of computer modeling and targeted field trials to develop and validate CS designs for seismic acquisition. Full 3D finite difference modeling is used to provide data for computer analysis of CS designs in conjunction with conventional survey design systems. Field trials show that we are able to obtain significant improvements in bandwidth and data quaility with NUOS designs for source and receiver locations. NUOS designs for simultaneous shooting further reduce acquisition shooting time by factors of 2 or more, depending on the number of simultaneous sources employed. We illustrate the application of CS designs to ocean bottom recording using examples from offshore Malaysia and the North Sea. Application of Compressive Sensing theory to seismic data acquisition will result in significant improvements in data quality and acquisition efficiency, leading to more effective use of seismic data for exploration and production. |
