A new algorithm is proposed for the automatic picking of seismic first arrivals that detects the presence of a signal by analyzing the variation in fractal dimension along the trace. The "divider-method" is found to be the most suitable method for calculating the fractal dimension. A change in dimension is found to occur close to the transition from noise to signal plus noise, that is the first arrival. The nature of this change varies from trace to trace, but a detectable change is always found to occur. The algorithm has been tested on real data sets with varying S/N ratios and the results compared to those obtained using previously published algorithms. With an appropriate tuning of its parameters, the fractal-based algorithm proved more accurate than all these other algorithms, especially in the presence of significant noise. The fractal method proved able to tolerate noise up to 80% of the average signal amplitude. However, the fractal-based algorithm is considerably slower than the other methods and hence is intended for use only on data sets with low S/N ratios. CALCULATION OF FRACTAL DIMENSION Since its original introduction by Mandelbrot (1967) the concept of fractals and fractal dimension has found widespread applications in many fields including the earth sciences. For the definition and an extensive description of the concepts behind fractals the reader is
The use of genetic algorithms in geophysical inverse problems is a relatively recent development and offers many advantages in dealing with the nonlinearity inherent in such applications. However, in their application to specific problems, as with all algorithms, problems of implementation arise. After extensive numerical tests, we implemented a genetic algorithm to efficiently invert several sets of synthetic seismic refraction data. In particular, we aimed at overcoming one of the main problems in the application of genetic algorithms to geophysical problems: i.e., high dimensionality. The addition of a pseudo-subspace method to the genetic algorithm, whereby the complexity and dimensionality of a problem is progressively increased during the inversion, improves the convergence of the process. The method allows the region of the solution space containing the global minimum to be quickly found. The use of local optimization methods at the last stage of the search further improves the quality of the inversion. The genetic algorithm has been tested on a field data set to determine the structure and base of the weathered layer (regolith) overlaying a basement of granite and greenstones in an Archaean terrain of Western Australia.
Existing surface wave modelling methods fail to correctly interpret some velocity structures that are critical from a geotechnical perspective, for example those with large velocity contrasts and reversals. An inversion scheme based on the observation of an 'effective' phase velocity has proven more successful than conventional methods in such situations. Our new approach incorporates dominant higher modes into the dispersion curve inversion by using a forward calculation with full-waveform P-SV reflectivity synthetic shot gathers to reproduce all wavefields. We then extract the theoretical surface wave dispersion from the plane-wave transformed synthetic gathers, removing the need for mode identification. The measured field dispersion is then inverted, using the forward modelling scheme and a linearised optimisation, to a flat-layered, shear velocity model.With the new method, velocity reversals are better modelled than with conventional inversion methods. In general, low velocity layers directly under a surface caprock are inverted with more accuracy than those masked by buried high velocity layers. Limitations of surface wave inversion which remain include the need to assume layer thicknesses, and the rapid loss of resolution with depth.
We present a genetic algorithm that simultaneously generates a large number of different solutions to various potential field inverse problems. It is shown that in simple cases a satisfactory description of the ambiguity domain inherent in potential field problems can be efficiently obtained by a simple analysis of the ensemble of solutions. From this analysis we can also obtain information about the expected bounds on the unknown parameters as well as a measure of the reliability of the final solution that cannot be recovered with local optimization methods. We discuss how the algorithm can be modified to address large dimensional problems. This can be achieved by the use of a ‘pseudo‐subspace method’, whereby problems of high dimensionality can be globally optimized by progressively increasing the complexity and dimensionality of the problem as well as by subdividing the overall calculation domain into a number of small subdomains. The effectiveness and flexibility of the method is shown on a range of different potential field inverse problems, both in 2D and 3D, on synthetic and field data.
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