L1-norm is better than L2-norm at dealing with noisy data and yielding
blocky models, features crucial in many geophysical applications.
In this report, we develop a hybrid-norm solver proposed by
Claerbout (2009) to perform L1 regressions. The solver is tested
on a 1-D field RMS velocity inversion, a 2-D regularized Kirchhoff
migration inversion and a 2-D velocity analysis problem. The results
of the inversions show that this solver can yield
``blocky'' models, and has the advantage of straightforward
parametrization.
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