ABSTRACT

Exact solutions to Lamb's problem exhibit a pulse that is related to a complex root of the Rayleigh function. We use the symbol

P
to denote the pulse. For normal values of σ (Poisson's ratio)
P
arrives at nearly the same time as P, but when σ is near 0.5,
P
is more distinct and arrives between P and S. The wave
P
has a prograde orbit and is, in this respect, the dual to the Rayleigh pulse. In this paper the symbol
S
is defined and is used to denote the Rayleigh pulse.

The idea that a pulse can be associated with an extraneous root of the Rayleigh function has been extended to Cagniard's problem, the solid-solid interface problem. In this problem it has long been thought that interface pulses (Stoneley pulses) could exist only for certain values of the elastic parameters and densities. Exact solutions to this problem show that Stoneley-like pulses occur for almost all solid pairs. The symbol

S
is used to denote these pulses. The
P
wave also occurs in this problem. As one of the solids becomes a fluid, it seems that its
P
becomes the fluid-solid Stoneley pulse if the P velocity in the fluid is less than the S velocity in the solid.

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