A seismic-reflection survey was carried out on Vancouver Island as part of Lithoprobe – Phase I to study the crustal structure and tectonics of this convergent margin. Four seismic profiles, which provided structural and velocity information using standard common-depth-point stacking, were shot. The lines were crooked; hence, this approach does not give one full confidence in the results obtained. However, because of the crookedness of the lines, the reflection points were located in three-dimensional space; therefore, it was possible to obtain the three-dimensional structure of the subsurface.Since the traveltime is a nonlinear function of model parameters, an iterative, damped least-squares technique is used to obtain three-dimensional structure and velocity with gradients. The ray tracing is performed for each shot–receiver pair by solving a system of nonlinear equations. In constant-velocity media the raypath is a straight line, whereas in media with velocity varying linearly with depth the raypath follows the arc of a circle. The interfaces are defined by polynomial surfaces where the raypaths satisfy Snell's law.The method was tested for a synthetic model: it was fast and effective. Then the method was applied to a small portion of line 1 to obtain velocity gradients and three-dimensional structures of the décollement and subduction zones. For reflector C on line 1 at an approximate depth of 15 km the velocity at the top of the horizon is found to be 6.8 km/s, with a gradient of 0.034 km/s per km. The dip and strike are 3 °and N18°E, respectively. For reflector E on line 1 at an approximate depth of 28 km the velocity at the top of the horizon is found to be 7.8 km/s. The dip and strike are 8.9 °and N65°E, respectively. To obtain more precise results, efforts should be made to record at wider angles of incidence.

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