Separation of Signal and Noise by Signature Deconvolution

The paper proposes a method for signature deconvolution that also separates signal from noise and provides a measure of the quality of the estimated source signature. Classical signature deconvolution designs an inverse filter for the estimated source signature and convolves this filter with the measured data to obtain an estimate of the earth impulse response. There is no measure of the quality of the result. This paper formulates recovery of the earth impulse response as the calculation of a Wiener filter in which the estimated source signature is the input and the measured seismogram is the output. There is thus a separate Wiener filter calculation for each trace. Convolution of this filter with the estimated source signature is the component of the measured data that is correlated with the estimated signature. Subtraction of this correlated component from the measured data yields the uncorrelated component: the estimated noise. If the estimated source signature contains errors, the estimated earth impulse response is incomplete, and the estimated noise contains signal, recognizable as trace-to-trace correlation. The method can be applied to many types of geophysical data, including transient and electromagnetic data; it is illustrated with an example of marine transient electromagnetic data.