Introduction

Reflection tomography Clapp (2001); Stork and Clayton (1991); Stork (1992) is one of the most effective and widely used velocity estimation methods. However, reflection tomography has velocity-depth ambiguity problem (we do not know how much a traveltime error is due to a velocity error and how much is due to a reflector misposition) because of insufficient source-receiver offset and lateral velocity changes Bickel (1990); Lines (1993); Ross (1994); Tieman (1994).

From borehole data, we can obtain the correct reflection positions around the borehole. The normal shift between the correct reflection positions and the apparent reflection positions can be linearly mapped to the traveltime perturbation along the normal ray van Trier (1990). However, from borehole data, we can only obtain the correct position for only a few reflection points along the borehole. In this paper, we assume all the reflection points within a local area around the borehole have the same normal shift. The normal ray traveltime perturbation for all these reflection points are then backpropagated simultaneously with the reflection traveltime perturbation. We applied this scheme on a synthetic model and obtained a better inversion result than using reflection tomography without this control. We further discuss how to improve this method for more complex datasets.