Seismic time‐invariant convolutional model

A layered‐earth seismic model is subdivided into two subsystems. The upper subsystem can have any sequence of reflection coefficients but the lower subsystem has a sequence of reflection coefficients which are small in magnitude and have the characteristics of random white noise. It is shown that if an arbitrary wavelet is the input to the lower lithologic section, the same wavelet convolved with the white sequence of reflection coefficients will be the reflected output. That is, a white sedimentary system passes a wavelet in reflection as a linear time‐invariant filter with impulse response given by the reflection coefficients. Thus, the small white lithologic section acts as an ideal reflecting window, producing perfect primary reflections with no multiple reflections and no transmission losses. The upper subsystem produces a minimum‐delay multiple‐reflection waveform. The seismic wavelet is the convolution of the source wavelet, the absorption effect, this multiple‐reflection waveform, and the instrume...