THE INTERFACE PROBLEM IN MODEL SEISMOLOGY

Many seismic problems involve interfaces. Seismic modeling provides a means of passing from the mathematical formulation to the solution of such problems when suitable analytical techniques are not available. Accurate interface formulations are necessary if modeling is to be as effective as possible in this role. Application of improved techniques has provided more accurate and detailed results than possible in the original work (Toksöz and Schwab, 1964) on model interface formulations. The present investigation was limited to butt‐joined, two‐dimensional models constructed with metallic sheets and epoxy bonding agents. Experimental results were first compared with those predicted by the simplest of “welded‐contact” theories—that which totally ignores the bonding layer. For a layer thickness of 0.007 cm, fair agreement was noted for frequencies below 125 kHz. New theoretical results were then predicted by taking the finite thickness and elastic properties of the bonding layer into consideration. The metal‐epoxy interfaces were assumed “welded‐contacts.” Irrespective of whether the formulation specified a perfectly elastic or an anelastic bonding material, the correlation between predicted and experimental results was quite poor. The disparity was much greater, over the entire frequency range, than that obtained from the formulation which totally ignored the bonding layer. All the welded‐contact interface formulations tested in this investigation were found unsatisfactory for highly accurate work. Based on the technique used to test the welded‐contact assumption, a mathematically accurate description of the interface was developed.

ACCURACY IN MODEL SEISMOLOGY

The most common technique currently used in model seismology makes use of a fixed source of elastic waves and a single receiver. This receiver is moved from position to position on a model in order to determine the relative spatial response to the source excitation. Inaccuracies occur due to the difficulty in obtaining the same receiver‐model coupling at each position. This coupling problem can be solved through the use of two source positions, the simultaneous use of two receivers, and the application of a general symmetry condition to the source‐receiver, and model geometries. Basic relations are established for this method. Independently of whether displacement, velocity, or acceleration detectors are used as receivers, these relations yield relative amplitude and phase spectra of the displacement at two different points on the model. These basic relations, and thus the validity of the method, are established by experiment. When a receiver is coupled to a model, the incident pulse is scattered as it passes the receiver position. This effect is negligible when bimorph receivers are used with two‐dimensional, steel‐sheet models. Edge receivers, used in conjunction with the same type models, produce significant, frequency‐dependent scatter. Quantitative results for this latter type of receiver‐model combination are obtained by experiment. These results show the amplitude‐spectrum of the displacement pulse to be attenuated by as much as 41 percent. Over the entire frequency range treated, the attenuation is never less than 4 percent. If it is necessary to use scattering receiver‐model combinations, the technique described for obtaining improved accuracy can be modified to correct for this effect.