Download Advances in Geophysics, Vol. 43 by Barry Saltzman, Renata Dmowska PDF

By Barry Saltzman, Renata Dmowska

This sequence presents a venue for longer studies of present advances in geophysics. Written at a degree available to graduate scholars, the articles serve to expand wisdom of assorted fields and will be important in classes and seminars.

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5 """..... 8 frequency (Hz) FIG. 10. Coupling coefficients for CFPF and PFCF. The dashed and the thin lines indicate the coefficients defined by Eq. (85). For the sake of simplicity, in the following figures the models CONTINENT and PAMIR (Levshin, 1985) will be called model C and model P, while the fundamental mode and the higher modes are indicated, respectively, as F, 1, 2, etc. Therefore, the fundamental mode of model C is named CF, the first higher mode of model P is named P 1, and so on. Each coupling coefficient is associated with a four-character acronym: the first two characters identify the incoming mode, the last two identify the outgoing mode.

The next step in obtaining a numerical solution is the discretization of the surface integral, approximating the surface S with N elements of area AS i, for which the source density functions are assumed constant. Supposing that P and P' are lying, at the same point Q, on the two sides of the interface, Eqs. (58) and (59) become N V ( Q j ) - - V~176 N s, G(Qj, Q)dQ (60) The continuity condition across the interface of displacements V (Q j) = V'(Qj), and of stresses T(Qj) = T'(Qj), leads to a system of 2N equations with 2N unknowns represented by the source density functions.

In Fig. 16 we show the intracoupling energies for the first four higher modes and for topographic steps of 1 or 5 km. The minima in the coupling value become wider and deeper as the height of the topographic step increases. 2. Coupling Coefficient for Rayleigh Modes For Rayleigh modes the formulation is similar to the one discussed in Sect. 1, and the basic definitions (75-80) and (85-88) are identical; the stress-displacement vectors in medium I and medium II and their scalar product can be written as AI = (111) (Uxi, O, Uzi , (Yxxl, O, O'zxi) (112) A l l "~ (UxlI, O, UzlI, O'xxll , O, O'zxlI ) (AI,A11) = ~ [u~id'~,l + u:id':x,l - u~It~1 - uz11~z~t]dz.

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