WAVEPATH EIKONAL TRAVEL-TIME INVERSION - THEORY

We present a general formula for the back projection of traveltime residuals in traveltime tomography. For special choices of an arbitrary weighting factor this formula reduces to the asymptotic back-projection term in ray-tracing tomography (RT), the Woodward-Rocca method, wavepath eikonal traveltime inversion (WET), and wave-equation traveltime inversion (WT). This unification provides for an understanding of the differences and similarities among these traveltime tomography methods. The special case of the WET formula leads to a computationally efficient inversion scheme in the space-time domain that is, in principle, almost as effective as WT inversion yet is an order of magnitude faster. It also leads to an analytic formula for the fast computation of wavepaths. Unlike ray-tracing tomography, WET partially accounts for band-limited source and shadow effects in the data. Several numerical tests of the WET method are used to illustrate its properties.