Conclusion

L-BFGS-B is an algorithm that solves non-linear problems by imposing some constraints on the model. This program incorporates concepts from trust region methods plus BFGS matrices and line searches. Per iteration, this program requires roughly O(N) computations, N being the size of the model space. Used with single precision arithmetic and no bounds, this program is not quite twice as slow as conjugate gradient. Therefore, L-BFGS-B can be used for solving many non-linear geophysical problems.

As an illustration, the bound constrained optimization code was employed to estimate local dips from seismic data. These examples show that the bounds were effectively working and that this method was converging toward acceptable solutions. In addition, this technique clearly improves on the existing method without bounds by discarding non-physical dip values at locations where aliasing is present. Flattening Lomask (2003) could greatly benefit from this improvement.

In geophysics, the number of applications for this type of solver could be quite large. An obvious choice is velocity estimation. For instance, Dix inversion might benefit from the possibility of constraining the estimated interval velocities to a reasonable range.