Two unequal shots in the same hole: Statistical versus deterministic deconvolution

Determination of the source time function and earth impulse response for explosive source seismic reflection data is traditionally performed using predictive deconvolution, which assumes the reflection seismogram is the convolution of a minimum-phase wavelet with a white, random, stationary sequence of impulses. We compare this statistical method with a new deterministic method that uses two unequal shots close together in the same hole and assumes a seismogram is the convolution of a source time function with a Green’s function, plus noise. The seismograms from the two shots share essentially the same Green’s function to any receiver because the shots are close together. The Green’s function is estimated by deconvolving the two seismograms at a given receiver for the corresponding source time functions, which are modeled independently; source parameters are obtained by trial and error by minimizing the difference between the two estimates of the Green’s function. We test these competing theories using seismic reflection data acquired with two charges fired separately in the same hole into a receiver spread of 1178 bunched geophone groups at 10 m intervals: a 1 kg charge at 42 m depth and a 2 kg charge at 40 m depth. The criterion for a comparison of the theories is the similarity of the recovered impulse responses at any receiver. Each method recovers a wavelet, or source time function, for each shot and two estimates of the impulse response, or Green’s function, at each receiver. Green’s functions recovered from the two shots using the deterministic method are almost identical and are measurably more similar than the impulse responses recovered using predictive deconvolution. That is, the deterministic method is better. The resolution of explosive source seismic reflection data can now be significantly improved with the new method and minimal additional field effort of loading one extra charge per shot hole.