Vertical seismic profile (VSP) direct arrivals provide an insitu measurement of traveltime with depth into the earth. In this note, we describe a weighted, damped least-squares inversion of VSP traveltimes for a smooth velocity/depth function that inherently reveals the resolution of the data. Smooth velocity/depth profiles of this type are suitable for migration or as a starting models for waveform inversion or tomography. The application of this inversion is particularly simple, requiring only the value of the damping parameter to be determined, and this value is determined from residual statistics.

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