The early 1990s saw many interesting contributions to the field of seismic wave propagation from a variety of US researchers, even as many wave-propagation specialists shifted their research focus away from new methods for seismogram synthesis toward data acquisition and inversion. In part, this shift was a natural consequence of the explosive growth in the amount and availability of high-quality digital seismic data, ready to be processed with interpretation tools developed in previous decades. As a result, observational seismology has recently made dramatic contributions toward imaging global geodynamics, revealing the great variety of crustal structures, and laying the foundation for a collaborative global network of broadband seismometers to monitor earthquakes and other seismic events. However, recent observational studies have brought to light new problems in wave propagation theory, and have made some older problems more difficult to ignore.
In this review, ``wave propagation studies'' are defined as investigations of the seismic forward problem, of how wave energy travels from source to receiver in an elastic, or slightly anelastic, medium. This definition includes work on raytracing algorithms, and is biased toward earthquake studies by virtue of the author's nominal expertise. Seismic wave propagation is sufficiently youthful as a field for US researchers to publish papers that clarify fundamental questions, such as the classification of a new body wave [ Kanamori, 1993]; the imbalance of P (compressional) and S (shear) wave interaction in random media [ Aki, 1992]; a symmetry argument that excludes outer core fluid flow as an explanation for the anomalous splitting of free oscillation overtones [ Gilbert, 1994], and a seismic analog for an unusual wave effect in adiabatic quantum mechanics [ Tromp and Dahlen, 1993a]. However, most efforts by researchers have involved improvements in techniques for calculating differential seismograms for use in inverse problems, or studies of wave propagation in complex media. This research sometimes must sacrifice elegance in order to incorporate realistic seismic velocity structure. Even so, the intellectual gap between ``brute force'' solutions in complex media and analytic solutions in simple media has often been bridged in innovative ways.