A fractal‐based algorithm for detecting first arrivals on seismic traces

Abstract

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

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