BAsins.html

Seismic Wave Resonance in Sedimentary Basins

This project concerns the theoretical determination of the ground motion induced by earthquakes at sites located on the surface of a sediment-filled valley or sedimentary basin. The objective is the theoretical determination of the eigenmodes (eigenfrequencies and eigenfunctions) of elastic waves in sedimentary basins of arbitrary shape, with emphasis on the study of how irregularities in the basament's topography influence the ground motion at the earth's surface. The phenomenon can be described in general terms as follows: In a typical sediment-filled valley or sedimentary basin the interface sediment/bedrock or basament's surface, may locally be flat, convex (topographic high), or concave (topographic low, or sub-basin) as shown in Figures 1 and 2 below. Such smooth, concave sections of the basement can induce highly periodic, long-lasting, amplified resonant motions at the earth's surface by trapping incoming seismic waves both vertically and laterally; in contrast, convex sections of the basament disrupt constructive interference and act as strong wave scatterers which tend to reduce the amplitude of the ground motions directly above them. The highly periodic, sustained motion that results from the resonance of the basin or local sub-basin implies that urban zones overlying topographic lows of the basament may be at higher seismic risk than those overlying topographic highs, since any buildings or engineered structures with natural frequencies of oscillation close to those of the resonant basin, or sub-basin, may themselves resonate with the sustained ground motion. This coincidental match of oscillation frequencies, known as "double resonance" is potentially very destructive, and in most cases leads to the total collapse of the building; as seems to have happened to buildings in Mexico city in 1985 (Rosenblueth, 1986), and perhaps to a section of the I-880 overpass in West Oakland, California, in 1989 ( Hough et.al., 1990). In contrast, with all other factors being the same, urban zones overlying topographic highs of the basement may be relatively at a much lower seismic risk.

Figure 1. The fundamental eigenmode of pure SH motion in a sedimentary basin of ellipsoidal shape is a rotation motion around the vertical axis, as shown in the two frames above and below (Figure 2). See Rial, J., N. Saltzman & H. Ling in American Scientist, 1992; see also Bolt (1993) Earthquakes and Geologic Discovery, Scientific American Library.

Figure2.

This study aims to produce the quantitative criteria that tie the basement topography to the resulting frequencies and amplitudes of ground motions. This will help identify high (as well as low) seismic risk areas from the point of view of wave propagation influence. The proposal that there exists such a close relationship between basement topography and seismic risk was put forward by Rial,1989; Rial et.al., 1991; 1992; Rial and Ling, 1993, Ling and Rial, 1994; and predicts that areas which suffer high structural damage should be found to overlie concave sections of the basement (Figure 3). Provided no unusually large seismic velocity gradients, special sensitivity to liquefaction nor other exceptional circumstances exist, this implies that wave propagation effects introduced by the shape of the sediment/rock interface are the determinant factors in the distribution of earthquake-induced damage. Numerical results to be discussed later support these ideas. There are also increasingly frequent instances in which field data point to the underlying geological structure as causative of (potentially damaging) anomalies in ground motion shaking. For instance, the distribution of damage resulting from the Northridge 1994 earthquake in southern California is the basis for claims that sedimentary basins, such as the San Fernando valley, have "demonstrated a tendency to distribute, focus and amplify the earthquake energy to a much larger degree than previously expected", and that the basin induced "amplified shaking and focusing of energy that was a direct cause of a substantial amount of building damage" (NEHRP-NSF official RFP 94-50, 1994; p.2). Thus, to understand the physical reasons for such focusing and amplification becomes an essential part of seismic risk assesment. It is important to emphasize that we are mostly interested in the response in which the effect of basin's geometry and basement topography are maximized by a high rock/sediment impedance contrast, efficient lateral wave trapping and normally attenuating, uniform or nearly uniform sediments, i.e., circumstances under which focusing, amplification and resonance are likely to occur. Even with these restrictions many sedimentary basins in important urban areas of the world and the US qualify, including San Francisco, Los Angeles, Seattle, etc. In southern California, basin resonance acquires an even more important significance because of the presence of buried active faults directly under the cities. Since a sedimentary basin is thoroughly and uniformly "illuminated" when earthquakes occur directly underneath, the chances of exciting a large number of the resonant modes of the basin ( and sub-basins ) are highest, and consequently the risk of double resonance is effectively increased. Fortunately, given a basement topography, resonances and caustics are the most predictable features of the resultant seismic wave field. In practice, knowing the basament's topography will help to produce maps of public use which delimit zones with high resonant potential in a given region. It is however inconvenient that the degree of detail required for microzonation at such scale is not yet available for the majority of seismically-at-risk basins. Important efforts are however under way to provide investigators with detailed subsurface images through both passive and active seismic experiments, especially in the Los Angeles area. The situation begs the question; since there are so many details of the basins that are unknown, is it possible to use the seismic data themselves to identify a potentially resonant basement structure from the data? The answer may be yes; at least in some cases.

References

Rial, J.A. (1989): Seismic wave resonances in 3D sedimentary basins, Geophys. Jour. Int, 99,81-90.

Rial, J.A., N.G. Saltzman and H. Ling (1991): Computation of normal modes of three-dimensional resonators by semiclassical and variational methods: seismological implications, Wave Motion, 14, 377-398.

Rial, J.A., N. Saltzman and H. Ling (1992): Earthquake-induced resonance in sedimentary basins, American Scientist , Nov-Dec 1992, pp 566-578.

Rial, J.A. and H. Ling(1992): Theoretical estimation of the eigenfrequencies of 2-D resonant sedimentary basins: numerical computations and analytic approximations to the elastic problem, Bull. Seism. Soc. Am., 82,6, 2350-2367.

Ling, H. and J.A. Rial (1994): Asymptotic analysis of SH-wave modes in geologic resonators (sedimentary basins) of non-separable geometry, Wave Motion, 19, 245-270.

Ling, H. (1994): Asymptotic-numeric methods to problems of seismic wave resonances and diffraction, PhD thesis, University of North Carolina, Chapel Hill.

Saltzman, N.(1995): Elastic resonance in three dimensional sedimentary basin models and seismic risk PhD thesis, University of North Carolina, Chapel Hill.

Research Activities and Projects

Computer Simulations of Wave Phenomena
Shear-wave Splitting in Fractured Reservoirs
Signal Analysis of Geologic and Climatologic Time Series
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J.A. Rial, jar@wave.gphys.unc.edu

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