## 1 Introduction

[2] Waveform tomography is a method for building seismic velocity models through multiple applications of nonlinear inversion of seismic waveform (phase and amplitude) data. An initial stage of inversion is carried out via a conventional ray-tracing tomography approach, typically using an iterative nonlinear inversion framework that seeks to improve a simple starting model by inversion of picked first-arrival travel time data. The model resulting from travel time inversion is then iteratively updated by full-waveform inversion of the seismic data set to better predict the data waveforms. The successful application of the combination of travel time inversion and full-waveform inversion is predicated on the assumption that the model from the initial tomography stage is representative of a low wavenumber version of the ultimate result.

[3] We implement a 2.5D method for the full-waveform inversion stage. It reproduces results equivalent to those of a 3D method with a specially constrained model. This leads to significant computational benefits, in terms of reduced processing time compared to a 3D work flow. The use of a 2.5D method allows for improved accuracy when modeling 3D geometric spreading effects that cannot be reproduced in a 2D work flow. By constructing the equivalent 3D wavefield in the receiver plane, the method accounts for a crooked-line acquisition geometry that would make 2D processing unfeasible. Waveform tomography in 2.5D is thus particularly applicable to most crustal reflection data, which are generally acquired in 2D geometry along existing crooked roads. Waveform tomography cannot be applied to such data without some allowance for the crooked-line acquisition geometry, such as an approximate geometric correction by travel time statics [*Smithyman and Clowes*, 2012], a modification of the encoded source and receiver locations in 2D to account partially for 3D offset (not considered here), the approach discussed in this paper, or application of full 3D waveform tomography.

[4] The first part of this paper provides a discussion of the 2.5D full-waveform inversion method, including special focus on the extension of the method to account for 3D geometry effects, which we believe represents a new development. We then provide a real-data case study to contrast this approach with a more typical 2D approach based on reprocessing of previous work. Our examples are derived from a data set acquired in south-central British Columbia, Canada.