Time vs frequency for 3D wavefield tomography

Unlike the situation in two-dimensions, where direct factorisation of the matrix equations makes frequency-domain methods much faster than explicit solution in the time-domain, the computational resources required for practical wavefield tomography in 3D can be rather similar in the two domains. We have developed and optimised schemes that undertake wavefield tomography using explicit time stepping in the time domain and that iteratively solve the matrix equations of the implicit problem in the frequency domain.<br>We have applied these two methods systematically to the same suite of problems. In the frequency domain, the principal advantages are that the initial tomographic updates for lowest frequencies are often seen more quickly, and spatial resolution can be better at the highest frequencies. In the time domain, one of the principal advantages is that it is possible to mute and/or weight the field data in time, and consequently the method can be made to work more effectively with difficult datasets. In practice, both approaches are useful, and both should be available within a comprehensive suite of inversion tools.