Absorption loss and transmission loss
Science, by its very nature, must work with idealized situations because the real situation is much too difficult to handle. The difference between the idealized situation (i.e., a model) and the real situation (i.e., the actuality) is called the specification error. A major objective of science is to keep coming up with increasingly realistic models that reduce the specification error.
Much of seismology addresses idealized rocks that are perfectly elastic. Real rocks are always inelastic to some extent. When a seismic wave travels through the real earth, kinetic energy is lost forever because heat is produced. This type of energy loss is called intrinsic absorption. In dry rocks, the loss per unit distance is approximately proportional to frequency.
Thus, a seismic wavelet broadens as it travels (Ziolkowski and Fokkema, 1986). A wavelet at a given distance away from a source is visibly smoother and of longer duration than is a wavelet closer to the source. For example, in the Pierre Shale in Colorado, a tenfold loss of amplitude occurs between 10 Hz and 70 Hz, and frequencies above 100 Hz are lost substantially. Many rocks are less attenuating than the Pierre Shale. However, for any rock, inelasticity sets a limit on achievable seismic resolution.
Another type of kinetic energy loss is transmission loss. For example, the amplitude of a primary pulse must be multiplied by each sedimentary layer’s transmission coefficient in the direct path down to a reflecting horizon as well as by each layer’s transmission coefficient in the direct path back to the surface. Such losses give rise to extrinsic absorption, in contrast to the intrinsic absorption described above. Each of these two-way transmission coefficients is less than one, so the net effect is that the transmission losses can reduce the amplitude of a primary event greatly. For example, when an incident wave encounters an interface, transmission loss occurs because only some of the kinetic energy is transmitted through the interface. The rest of the kinetic energy is reflected away from the interface. In extrinsic absorption, kinetic energy is not lost but merely is transferred away from the path of interest. Such transferred kinetic energy shows up somewhere else.
Multiples also suffer losses each time the pulse is reflected from an interface. Multiples from weakly reflecting horizons are severely attenuated, so multiples from strongly reflecting horizons are usually the ones that are troublesome (Taner, 1980; Rosenberger et al., 1999).
- Ziolkowski, A., and J. T. Fokkema, 1986, The progressive attenuation of high-frequency energy in seismic reflection data: Geophysical Prospecting, 34, 981–1001.
- Taner, T., 1980, Long period sea-floor multiples and their suppression: Geophysical Prospecting, 28, 30–48.
- Rosenberger, A., H. Meyer, and B. Buttkus, 1999, A multichannel approach to long-period multiple prediction and attenuation: Geophysical Prospecting, 47, 903–921.
|The wave equation
Also in this chapter
- The seismic reflection method
- Seismic interpretation
- The wave equation
- Wave velocity
- Velocity analysis
- Seismic tomography
- Appendix C: Exercises