INTERPRETATION OF SYNTHETIC SEISMOGRAMS

Abstract

A linear filter model of the complicated seismic process can be formulated by assuming that (1) the layering of the earth is described by the continuous velocity log, (2) the shot pulse is time‐invariant and propagates as a plane wave with normal incidence, and (3) all multiples, ghosts, and other noise are negligible. Then, the model earth with discrete layers can be considered a filter whose impulse response is the set of reflection coefficients. The set of reflection coefficients becomes the reflectivity function when the model earth has a continuously varying velocity. By definition, the reflectivity function is the derivative of the logarithm of velocity, where both are functions of two‐way travel time. The input to this filter is the time‐invariant shot pulse. The output is a synthetic seismogram that contains the reflectivity function filtered by the shot pulse; in other words, it consists of primary reflections only. Since the filter is linear, the input and the filter may be interchanged, the reflectivity function becoming the input and the shot pulse becoming the filter. A non‐mathematical discussion of the reflections from simple, ideal velocity layering shows that: (1) The reflection from a step velocity function is the shot pulse itself. (2) Thin beds produce a differentiated shot pulse. (3) Beds which approximate a square pulse in velocity produce a pair of shot pulses, with the second delayed in time and reversed in phase with respect to the first. The composite reflection has its greatest amplitude when the layer thickness (in two‐way travel time) is one‐half the basic period of the shot pulse. This situation is called “tuning.” The strongest reflections on field records result when the shot pulse is tuned to the velocity layering. (4) Ramp‐transition zones (linear increase in the logarithm of velocity) produce integrated shot pulses at the changes in slope of the velocity function. A correspondence can be established between the velocity function and the synthetic seismogram by shifting the velocity function later in time. The shift is required because of “filter delay.” The amount of filter delay is related to the impulse response waveform, which, in the case of the synthetic seismogram, is given by the reflection from a step velocity function.