Conclusions and Future Work

The algorithm presented in this paper offers a fast and efficient method for $\ell_1$ regularized inversion problems. By using $\ell_1$ regularization the result is often more consistent geologically because the sharp boundaries are preserved. Even though this method reduces the number of conjugate gradients steps, it could be slow since it must use matrix multiplication. This can be overcome, however, if we implement the matrix multiplication in a parallel fashion as presented by Lomask and Clapp (2006).

Further work involves applying the smoothness along the midpoint-axis and adding hard equality and inequality constraints to the inversion, limiting the range of velocities acceptable in different parts of the model. This would ensure that bad data did not put an impossible velocity in a particular area, such as an ultra-low velocity at great depths. It would also allow for other forms of data, especially ground truth through well logs, to be easily incorporated into the inversion.