The effect of subsurface sampling on one‐dimensional synthetic seismograms

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Abstract
In generating one‐dimensional (1-D) synthetic seismograms from sonic and density logs, the actual subsurface is replaced by a sequence of beds so constructed that the time required to traverse each bed is the same. Since Wuenschel (1960) devised the method, geophysicists have assumed that as long as the beds were thin, i.e., subsurface time sampling was fine enough to avoid aliasing in the source waveform, the synthetic seismograms would be independent of the sampling rate. We have found this assumption to be unjustified. Even when the subsurface is sampled more than twice per period at the maximum source frequency, the traces generated by a synthetic seismogram program may change as the sampling changes. For the wells that were analyzed, the reflections were delayed by an increasing amount as the sampling became finer. The delay appeared to approach a constant value; but for the most cyclic of the logs, even a 0.5-msec sample interval apparently was not small enough. However, when instead of computing the velocity for a sample interval by simply summing transit times we turned to a method suggested by Sherwood (1962), the total reflection time delay became less dependent on the sampling rate. Attenuation over the seismic band increased as the sampling became finer, regardless of the method used to obtain velocity from transit times. Although the time delays found in this study are greatly reduced when the method of computing velocity from sonic log transit times is modified from that of simply summing sample values, it is not clear that this more complicated procedure is free of problems due to correction of sonic log integrated times to check‐shots times. Part of the difficulty in tying check‐shot traveltimes to seismic reflection times may originate in the phenomena discussed here.

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