Multisource encoding and decoding using the signal apparition technique

Signal apparition is a method for encoding sources in simultaneous multisource seismic acquisition and decoding the multisource response of the earth into its single-source responses. For M sources, encoding is performed by applying periodic sequences of period M to each of the sources along source lines. Decoding is achieved in the wavenumber domain for each frequency by solving an M × M linear system of equations. The system's matrix is the product of a Fourier matrix and an encoding matrix, the latter containing the information of the codes. The solution of the system is unique when the encoding matrix is invertible. When the encoding sequences consist of time delays applied to sources' firing times, the determinant of the encoding matrix becomes a polynomial. A unique solution to decoding then exists if the roots of the polynomial avoid the unit circle. Periodic time-shift sequences for two, three, four, and six sources are discussed. A model example of simultaneous four-source data acquisition illustrates the performance of the encoding/decoding technique for the spatially nonaliased case.