P P and Crustal Structure by Franc

INTRODUCTION The effect of the crust on the reflected compressional wave P P has been studied extensively by Gutenberg and Richter (1935), Mei (1943), Byerly et al (1949), and Papazachos (1964). Most of the quantitative work in these studies has involved determination of the amplitude ratio P P / P or the variation in the angle of incidence. Although Gutenberg and Richter attempted to investigate the differences in crustal structure beneath the Atlantic and Pacific Oceans using the amplitude ratio P P / P , others (Byerly et al, 1949; Ben Menahem et al, 1965) have indicated that the fluctuation of this ratio could result from the radiation pattern of the source rather than the crustal structure at the point of reflection. In any event, a great deal of information is lost in any investigation using only the maximum amplitudes of the pulse. In order to provide a more sensitive measure of the crustal effect at the receiver, frequency dependent reflection coefficients have been computed for several typical oceanic and continental crustal models for frequencies less than 0.45 cps. Using these coefficients and the transmission coefficients for a central U. S. crustal structure, waveforms are synthesized and compared to seismograms from the Banda Sea earthquake of March 21, 1964. The synthesized wave forms exhibit many of the properties found on the actual seismograms. METHOD OF COh~[PUTATION In order to obtain some measure of the effect of crustal layering on reflected waves such as PP, it is convenient to consider a crustal model composed of plane parallel layers. If the incident wave is represented as a plane wave, then the frequency response of a model of this type, both in transmission and reflection, may be determined by the IIaskell-Thomson matrix method (Haskell, 1953, 1960, 1962; 733 734 ] B U L L E T I N O F T t t E S E I S M O L O G I C A L S O C I E T Y O F A M E R I C A Thomson, 1950). The theory has been discussed in the works of Haskell and Thomson above, and in papers by Dorman (1962) and Harkrider (1964b). Although the discussions of layered systems involving liquid layers are quite general in the works of Dorman and Harkrider, the techniques considered are oriented toward surface waves. Since there are some aspects of the matrix formulation which are of particular interest when a model of an oceanic structure is considered, a brief development of the theory for a layered system consisting of liquid layers overlying solid layers will be presented here. In a system of n layers (Figure 1) let the upper r ( r < n ) layers be liquid and the remaining layers be solid. The horizontal motion at the fluid-solid interface is decoupled and the tangential stress vanishes. Then the relations among the horizontal particle velocity at the liquid-solid interface, the vertical particle velocity at the free surface and the dilatations and rotations in the half-space may be expressed as where: (1) (2) (3) (4) A ' _ _ A /' n n