REFLECTED AND TRANSMITTED FILTER FUNCTIONS FOR SIMPLE SUBSURFACE GEOMETRIES

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 wouldmore » cause low-frequency deep reflections. (17 figures)« less