Kansas Geological Survey, Subsurface Geology 12, p. 51-52
Ralph W. Knapp
Kansas Geological Survey
Resolution is directly related to the bandwidth of a signal, and detection of thin beds is directly related to the wavelength of the signal. High-frequency data generally are also broader band and are also shorter wavelength. In other words, improving the high-frequency content of a signal improves the resolution and thin-bed-detection capabilities of a seismic signal dramatically. Typical bed thicknesses of cyclothems in Kansas are generally less than 10 m (33 ft) and often about 2 m (7 ft). Given an average velocity of about 3,200 m (10,560 ft)/sec, this suggests that frequencies of at least 400 Hz are needed to resolve the beds as thin as 2 m (7 ft). This is based on the resolution of thin beds being one-quarter wavelength. This generalization is related to the rock type of the bed; low-velocity shales (~2,000 m [6,600 ft]/s) require only about 250 Hz and high-velocity limestones (~4,000 m [13,200 ft]/s) require about 500 Hz for the same resolution. Furthermore, tuning will occur in a thin bed such that the instantaneous frequency of a reflection response will depend on the thickness and interval velocity of the bed.
With standard exploration reflection seismology, the frequency band is generally less than 100 Hz. As a consequence, the seismic response is greatly generalized. For instance, the Kansas City-Lansing groups are commonly seen as a strong ringy (tuned to 50-60 Hz) reflection. The low-frequency content of the signal is not only unable to resolve the individual beds of the groups, it is only able to return the reflection response of the two groups combined.
It is found that when the reflection signal content includes frequencies as high as 500 Hz or greater that the reflection response will include all but the thinnest of the individual beds. Instantaneous frequency response will depend on the bed thickness and the velocity of the bed, and the amplitude of the reflection will depend on the frequency (high frequencies having lower amplitudes), the bed thickness, cyclic repetition (constructive interference), and die strength of the reflector. In other words, a limestone of 2-m (7-ft) thickness will respond with a small amplitude reflection of about 500-Hz signal. A series of alternating shales and limestones will respond with a relatively large amplitude reflection and a frequency appropriate for the tuning character of the cycles.
The reflection character of the eastern Kansas cyclothems for signals as high as 500 Hz is generally that of thin beds because bed thicknesses are usually less than 10 m (33 ft). For thick-bed response there is an isolated reflector for both the top and the bottom of the bed. For thin-bed response the top and the bottom reflectors interfere, resulting in a single response for the bed as a whole. Consequently, individual reflectors in the eastern Kansas cyclothems generally represent beds rather than interfaces. With the simple application of a phase-shift filter, it is possible to process the data such that positive reflectors (peaks) represent thin-bed limestones and negative reflectors (troughs) represent thin-bed shales and sandstones. This simplification may make classical interpreters shudder because it is one of the first generalizations that they are taught to avoid; however, in the case of cyclothems it is valid for much of the section.
When high-resolution, high-detail data are obtained, Kansas cyclothems are revealed to not be the typical layercake that most geophysicists and even many geologists think. The section (see fig. 1) is of sufficient detail that inspection of it is reminiscent of looking at an outcrop from the distance of a few tens of meters. It is found that lateral sampling (trace interval of the section) of less than 1 m (3.3 ft) is necessary to see the lateral changes that are taking place in the section. Beds are found to change character in the distance of only a few meters. Most of the lateral changes are occurring in sandstones and shales, but even limestones can change character within a few tens of meters. These changes include presence of sand channels and sandstone-bedding structure, small faults, thickness variation, and facies changes.
Figure 1--Seismic section of the Pennsylvanian beneath Lawrence, Kansas, with a velocity log (arrow) and formation identification, 1-m (3.3-ft) trace interval.
Kansas Geological Survey
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Web version May 11, 2010. Original publication date 1989.