A linear inversion procedure is introduced that images weak velocity anomalies using amplitudes of transmitted seismic waves. Using projection operators from geometrical ray theory, an image of an anomaly is constructed from amplitudes recorded at arrays of receivers using arrays of sources. The image is related to the velocity anomaly by a second-order partial-differential equation that is inverted using 2-D discrete Fourier transforms.
As an example of the inversion procedure, magnitude residuals for European stations recording Shagan River explosions are used to image the deep lithospheric anomaly beneath the Shagan River test site described in Part 1. This formal inversion analysis confirms the existence of a small-scale lateral heterogeneity located 50 km west-northwest of the test site at a probable depth between 80 and 100 km and indicates that it is consistent with a deterministic 1.5% peak-to-peak (or 0.5% rms) velocity anomaly with a scale length of about 3 km. 3-D dynamic raytracing is then used to verify that the inferred laterally varying structure produces amplitude fluctuations consistent with observations.