WAVEPATH EIKONAL TRAVEL-TIME INVERSION - THEORY

We present a general formula for the back projection of traveltime res iduals in traveltime tomography. For special choices of an arbitrary w eighting factor this formula reduces to the asymptotic back-projection term in ray-tracing tomography (RT), the Woodward-Rocca method, wavep ath eikonal traveltime inversion (WET), and wave-equation traveltime i nversion (WT). This unification provides for an understanding of the d ifferences and similarities among these traveltime tomography methods. The special case of the WET formula leads to a computationally effici ent inversion scheme in the space-time domain that is, in principle, a lmost as effective as WT inversion yet is an order of magnitude faster . It also leads to an analytic formula for the fast computation of wav epaths. Unlike ray-tracing tomography, WET partially accounts for band -limited source and shadow effects in the data. Several numerical test s of the WET method are used to illustrate its properties.