Abstract

This paper discusses two ways of compressing seismic data prior to long-distance transmission for display. A Walsh transform technique and an analogous time-domain method eliminate redundant seismic information allowing data sets to be compressed with little visual degradation. The basic approach consists of using an average 3-bit code to describe data in such a way as to minimize information loss; the method also uses the Walsh transform to achieve further compaction through sequency bandlimiting. A second technique is entirely a time-domain operation and does not use transforms. The Walsh method, however, produces larger compression ratios than the time technique before serious image degradation occurs. Both schemes have six basic parts: bandlimiting, quantization, encoding, decoding, interpolation, and band-pass filtering; they differ only in band limiting and interpolation. Band limiting sequencies in the Walsh domain is very similar to, but not the same as, alias filtering and resampling in time. Reducing Walsh bandwidths by some power of two has a time-domain implementation consisting of an averaging procedure with subsequent resampling, while the inverse Walsh transform step can be viewed as a means of interpolating in the time domain.The convergence properties of three Rademacher derived transforms--Hadamard, Paley, and Walsh--are studied with regard to exploration seismic data. Hadamard energy has been found to be uniformly distributed over its entire spectrum, whereas Walsh and Paley transforms concentrate about 80 percent of the total energy into a major lobe occupying about 15 percent of the total bandwidth (2 msec sampling). Smaller minor lobes containing the remaining 20 percent are discarded while bandlimiting. The major lobe energy suffices for many seismic applications such as VA/VD plot displays. Optimum quantization and encoding of major lobe energy results in an overall 28:1 compression factor for 12 bit data sampled every 2 msec. Analogous time domain compression, on the other hand, only achieves a 16:1 reduction because of the power of two restriction imposed by the resampling and averaging process.

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