Short Note Trace balancing with PEF plane annihilators

Land seismic data often shows large variations in energy from one trace to the next. Localized noise bursts or changes in signal to noise ratio in a shot gather, for instance where the receiver spread nears a road or machinery, are not uncommon problems. Also, geophones may be poorly coupled in an area, because of surface conditions or simply having been kicked loose. Claerbout (1994) points out in addition that local wavefields add amplitudes rather than energy. This means that wave interference can result in anomalously high or low trace energy where waves add or extinguish. Typically, traces are scaled to have equal energies or equal mean absolute values. In situations such as those above this is not a perfect solution. In the case of noisebursts or machinery, reflection events may be given variable amplitudes depending on the amount of noise in individual traces when they should be constant along many traces. Or where events have extinguished, the resulting drop in initial trace power will result in noise being scaled up. Claerbout (1994) suggests that using a prediction error filter to destroy plane waves is perhaps a better way to estimate scales. In other words, scale traces based on the amplitudes along events rather than by total trace power or amplitude. When the proper filter is known, power in the output from locally planar data is minimized when the magnitude along events of a given dip is easily predictable, i.e. constant or smoothly increasing or decreasing. Unfortunately, the scale anomalies we seek to solve for make the data less predictable, and the correct filter cannot be estimated from the input. I use a nonlinear technique to simultaneously solve for the scale factors and the filter. The inversion is unstable and conjugate gradient solutions typically diverge, but in general this occurs after a good solution has been reached. Below I describe first the formulation of the problem, and afterwards the patches that enable the program to output good results despite divergence.