Enhanced Backscattering of Seismic Waves from Irregular Interfaces

by
Craig Schultz

Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on {Date} in partial fulfillment of the requirements for the degree of {Degree}

ABSTRACT

In this thesis I study the general scattering of seismic waves from highly irregular, 2--D elastic interfaces and show that the "enhanced backscattering" or "retroreflectance" of seismic waves, which has been previously identified in optics, exists. Theoretically, using the Somigliana identity and the extinction theorem, exact integral expressions are obtained for the scattered seismic displacement produced when a P, SV, or SH wave of general form is incident on a highly irregular, 2--D elastic interface. The scattered pressure over a fluid--solid boundary is also obtained by coupling Green's second integral theorem with the Somigliana identity. The final coupled pair of inhomogeneous integral equations are solved numerically and, unlike most numerical approaches, the curvature of the interface is included in the formulation. Comparisons between this Somigliana approach and the discrete wavenumber (DWN) approach show that the Somigliana approach is accurate up to the 45º slopes tested. Comparisons with finite--difference and DWN algorithms also show that the Somigliana algorithm is more computationally efficient for the statistical analyses carried out in this thesis.

Utilizing the Somigliana approach, the final scattered energy is expressed in terms of a deterministic reflection coefficient. Averaging over hundreds of realizations of scattering from an irregular interface with given statistical properties a mean reflection coefficient is determined, therefore describing the average amplitude distribution for waves propagating away from the interface. The total, coherent, and incoherent contribution to this mean reflection coefficient are determined. This statistical analysis shows that for interfaces with a large impedance contrast and large slopes, an enhancement of energy scattered towards the source, otherwise known as `retroreflectance' or `enhanced backscattering', is observed in the incoherent component. The retroreflective properties of the interface are characterized by varying the height and length of irregularities with respect to the incident wavelength and varying the incident angle and impedance contrast at the interface. In general, the width of the retroreflective peak was found to increase as the ratio between the incident wavelength and the mean free path of the interface is increased, thus tying the retroreflective properties directly to the interface statistics. The retroreflective peak height also decreases dramatically with a decrease in impedance contrast and an increase in the incident angle. Finally, the absence of retroreflectance for specific conversions in the P--SV case gives strong support to the optical hypothesis of `time--reversed paths'.

Experimentally, using our in--house ultrasonic water tank, acoustic energy scattered from a fluid--solid boundary is studied in detail. A glass etching process which utilizes numerically generated photoresist templates allows for the fabrication of a 3--D glass surface which is characterized by approximately Gaussian statistics. We find that our 2--D numerical reflection coefficients can give insight into the experimentally observed 3--D scattering. The 2--D numerical results predict the presence of enhanced backscattering and the experimental results strongly support the existence of this coherent scattering phenomenon. In terms of the diffuse reflection coefficient, the numerical results predict the asymmetry and general trend of the observed amplitude distributions. Strikingly, however, as the incident angle is increased, backscattering from the numerical 2--D interface appears to decrease more slowly than for the 3--D interface, suggesting an inherent difference between 2--D and 3--D scattering mechanisms.

Seismic retroreflectance and general scattering can also give insight into the crustal scattering problem. Scattering, from both an irregular Moho discontinuity and a high impedance intracrustal boundary, is shown to be consistent with a preliminary analysis of P coda energy observed at NORESS, FINESA, ARCESS, and NYNEX arrays. General backscattering and retroreflectance of energy from irregular topography and intracrustal interfaces may also provide a mechanism whereby various phases can be retropropagated laterally in the crust. Preliminary evidence for retropropagation is discussed. We find that further investigation into the role that irregular interfaces play (including free surface topography) in the generation of P coda and S coda at regional distances is well warranted.

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Updated: June, 1999

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