UNIFORMLY VALID BODY-WAVE RAY THEORY

We present a uniformly valid ray theory for body-wave propagation in l aterally heterogeneous earth models. This is accomplished by implement ing Maslov theory, which is a 3-D analogue of the widely used WKBJ sei smogram method for spherically symmetric earth models. Away from caust ics, complete seismic waveforms can be calculated by solving a system of 14 coupled first-order ordinary differential equations: four equati ons determine the ray geometry, eight additional equations determine t he amplitude, and two further equations determine traveltime and atten uation. In the vicinity of a caustic, neighbouring rays cross, and asy mptotic ray theory breaks down. Rather than considering the contributi on to the wavefield of one single ray, our strategy is to express the wavefield in the vicinity of a caustic as a summation over neighbourin g, non-Fermat rays based upon Maslov theory. Away from caustics, Maslo v theory reduces to asymptotic ray theory. We present examples of the ray geometry in the 3-D model SKS12WM13, and demonstrate that small-sc ale triplications in the traveltime curve associated with large-scale heterogeneities in the lowermost mantle are ubiquitous. The theory is applicable to direct, turning and reflected waves, may to a limited ex tent be advanced to include head waves, but does not describe waves th at are diffracted into the deep shadow. The determination of the geome tric ray that connects a given source and receiver is based upon a 'sh ooting' method. Initial guesses for the take-off angles are determined based upon perturbation theory, which substantially reduces the numbe r of iterations required to hit a receiver. Perturbation theory also p rovides predictions for arrival angles and amplitude anomalies. These predictions incorporate the effects of long-wavelength topography on i nternal boundaries and the free surface, and may be used as a basis fo r tomographic inversions. Generally, predictions based upon perturbati on theory agree very well with exact 3-D ray tracing. Just as travelti me measurements provide constraints on velocity, arrival angles constr ain velocity gradients, and amplitude anomalies put constraints on sec ond derivatives in velocity. In SKS12WM13, traveltime anomalies can be as much as +/-10 s, arrival-angle anomalies can be larger than +/-5 d egrees, and 3-D amplitudes can differ by more than 100 per cent from P REM amplitudes.