REFLECTED AND TRANSMITTED FILTER FUNCTIONS FOR SIMPLE SUBSURFACE GEOMETRIES

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Abstract
A zone of sands embedded in shale acts as a filter, both in reflecting energy back to the surface and in transmitting energy to reflectors below them. For a single layer of sand, the reflection filter is periodic—reflecting no energy at some frequencies and more than either of the two individual interfaces at other frequencies. Separating the sand zone into two parts by inserting a thin layer of shale results in reflection filters which differ greatly from one another. The particular filter curve generated depends upon the location of the shale layer. A sand zone filters reflections from interfaces below the zone in a manner complementary to the reflection filter. Where the most energy is reflected, the least is transmitted; conversely, where the least energy is reflected, the most is transmitted. The models considered in this report could easily give rise to high‐amplitude reflections; but, unless the amplitudes were very high, there would be little filtering of deeper reflections. However, for very high‐amplitude reflections and narrow‐band data, little energy would be transmitted and a shadow zone would result. For very high‐amplitude shallow reflections and broad‐band data, a low‐frequency shallow reflection would cause high‐frequency deep reflections; a high‐frequency shallow reflection would cause low‐frequency deep reflections.

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