Smoothing seismic tomograms with alpha-trimmed means

Due to ill-conditioning and the presence of noise in the data, tomographic inversion by traditional techniques usually requires some sort of smoothing, either to filter out small-scale variations in the solution which are beyond the resolution of the data or to produce smooth background models during the iterative inversion procedure. We shall describe the use of α-trimmed means for smoothing computed tomograms. The α-trimmed means range continuously from the median to the mean. They are all efficient computationally and can be tailored to smooth the tomogram without destroying sharp geological features, such as faults and reflecting layers, and without introducing artifacts. Further, the median and trimmed means close to it are statistically robust in the sense that they reject bursts of noise whereas the mean simply averages the noise into the solution and can therefore be adversely affected by outliers in the data. All of these filters can be applied directly to the computed tomogram after solution, or during the solution phase as a means to stabilize the inversion.