Information from smiles: mono-plane-annihilator weighted regression

 

Jon F. Claerbout

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ABSTRACT

An interpreter looking at a migrated section containing two dips in the same place knows that something is wrong. To minimize the presence of multiple dipping events in the same place, we can design a rejection filter to remove the best fitting local plane. This is called a LOMOPLAN (LOcal MOno PLane ANnihilator). The output of a LOMOPLAN contains only other dips so minimizing that output should enable us to improve estimation of model parameters and missing data. Although the LOMOPLAN concept applies to models, not data, experience shows that processing field data with a LOMOPLAN quickly identifies data quality problems. A LOMOPLAN for adequately sampled 3-D data is $(\partial_x + p_x \partial_\tau, \, \partial_y + p_y \partial_\tau)$ which has two outputs, both of which should be minimized.