Smooth inversion of travel-time tomography of crosshole data by global optimization

Crosshole seismic travel-time tomography is often applied to image the velocity structure of an inter-well medium and involves in finding a velocity model that minimizes the error energy between the measured and the theoretical travel times. Travel-time tomography is a non-linear inverse problem because the ray paths depend on the unknown velocity field. Linearized techniques are usually employed to reconstruct the velocity field in an iterative manner. A limitation, inherent to deterministic methods, is the strong relation between the starting model and local minima entrapment. Global optimization methods such as particle swarm optimization (PSO) can be applied to such problems. Regardless of the starting model, global optimization ideally finds the region of the solution space containing global minima without calculating derivatives. In this paper, the regularized PSO approach to seismic travel-time tomography is described, and is tested on synthetic as well as real seismic data, and is also compared with a local optimization method that is Levenberg-Marquart (LM) algorithm. The results show that the proposed method estimates the velocity model better than LM, especially in the absence of good prior information.