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In general, smoothing filters regularize functions by reducing differences between adjacent values. Thesmoothing filters, therefore, can regularize inverse solutions and produce more accurate subsurface structure when weapply it to full waveform inversion. If we apply a smoothing filter with a constant coefficient to subsurface image orvelocity model, it will make layer interfaces and fault structures vague because it does not consider any information ofgeologic structures and variations of velocity. In this study, we develop a selective smoothing regularization technique,which adapts smoothing coefficients according to inversion iteration, to solve the weakness of smoothing regularizationwith a constant coefficient. First, we determine appropriate frequencies and analyze the corresponding wavenumbercoverage. Then, we define effective maximum wavenumber as 99 percentile of wavenumber spectrum in order to choosesmoothing coefficients which can effectively limit the wavenumber coverage. By adapting the chosen smoothingcoefficients according to the iteration, we can implement multi-scale full waveform inversion while inverting multifrequencycomponents simultaneously. Through the successful inversion example on a salt model with high-contrastvelocity structures, we can note that our method effectively regularizes the inverse solution. We also verify that ourscheme is applicable to field data through the numerical example to the synthetic data containing random noise.

Application of Effective Regularization to Gradient-based Seismic Full Waveform Inversion using Selective Smoothing Coefficients