Reflection response for normal incidence probing of vertically nonhomogeneous media

A time domain synthetic reflection seismogram is detailed and, as a limiting condition on this model, the analytic reflection impulse response for a one-dimensional lossless acoustic medium with piecewise continuous acoustic impedance is obtained. This analytic impulse response solution, in the structure of a sum of terms by order of reflection, provides insight to some of the poorly understood aspects of acoustic reflections from stratified and smoothly varying media as may be encountered in shallow marine sediments and elsewhere. It offers as well an approach for the inverse problem of extracting acoustic impedance profiles from reflection response data, though other effects (such as wavefront spreading, dispersive and absorptive attenuation, and wavelet broadening attendant with pulse propagation through a medium) need to be accommodated.