## Variable norm deconvolution |

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additive noise assumed autocorrelation averaging bubble oscillations cepstrums chapter Claerbout computationally computed convergence crosscorrelations current estimate deconvolution method deconvolved density derived described determined displayed in Figure Doctor of Philosophy double exponential estimated distribution estimated reflectivity series exponential gain family of distributions frequency domain gain constant Gaussian family given by Equation gradient Hessian matrix initial inputs inverse filter inverse spectrum kurtosis length Levinson recursion minimizing minimum phase multichannel Newton-type method Newton's method noise level noise ratio non-Gaussianness non-linear objective function observed seismogram optimum outputs parsimony plotted prediction error filtering probability distributions problem procedure proposed random sample recorded reflection amplitudes reflection seismology results obtained Rms error scale scale invariant seismic data shape parameter signal to noise solution solved source waveform spherical divergence spiky synthetic techniques TEST STATISTIC trace VARIABLE NORM DECONVOLUTION Variable Norm Ratio variance vector Wiggins-type algorithm yields zero