When expressed in the form of characteristic differential equations, the laws governing propagation of linear one-dimensional waves through heterogeneous media show that the only properties of significance are the sound speed c and the acoustic impedance ρc, either of which may vary spatially. The former occurs in the differential equations governing the (curved) characteristics, while the latter appears in the differential equations governing the evolution of particle velocity and stress along the characteristics. The present study employs an inherently stable finite difference representation of the characteristic equations, in which the spatial grid is obtained by evaluating the intersections in space-time of constant time lines with comparable increments of the characteristic variables. The numerical procedure is used to follow the propagation of a single-lobe sine pulse in cases where only ρ or c fluctuates spatially about a mean value while the other property is constant, and compares those results to the case were both material properties vary. Nonconstancy of c is shown to cause temporal shifts in waveforms, while spatial variation of ρc causes attenuation and distortion of the waveform.

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