A 2D seismic time-lapse inversion approach can image the evolution of seismic velocities over time and space. The forward modeling is based on solving the eikonal equation using a second-order fast-marching method. Wave paths are represented by Fresnel volumes rather than by conventional rays. This approach accounts for complex velocity models and has the advantage of considering the effects of wave frequency on velocity resolution. The aim of time-lapse inversion is to find changes in velocities of each cell in the model as a function of time. Each model along the time axis is called a reference space model. This approach can be simplified into an inverse problem that seeks the optimum of several reference space models taken together, using the approximation that the change in seismic velocity varies linearly in time between two subsequent reference models. The method is demonstrated on a synthetic example that includes regularization in time in the cost function and reduces inversion artifacts associated with noise in the data by comparison with independent inversions at each time.

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