The use of a suitable norm in the solution of geophysical inverse problems plays an important role in the performance of all inversion algorithms. We examine nonlinear optimization using different measures of error fer a genetic algorithm (GA) as applied to the problem of 1-D seismic waveform inversion. Geometric and harmonic measures of error are defined for arbitrary power. Harmonic measures of error energy (h2) and absolute deviation (h1) are investigated and the h1 measure is found superior. A norm that linearly varies in each generation from h1 to h2 is also investigated but the results are not any better than the h1 case. A fractional harmonic norm (h1/2) is evaluated and found superior to error energy and absolute deviation. This measure of error de-emphasizes differences between the observed data and the synthetic data. This effect improves the diversity of the population and prevents and reduces the influence of model parameters that would unduly bias the objective function as the optimization procedure converges.


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