Fractals in Geophysics

AFPT algorithm amplitude aperture approximately area fraction autocorrelation average bathymetry brown noise Cantor dust cell characteristic displacement contact area continuum percolation correlation curve data set defined density derived diameter earthquakes equation error estimate example fault maps fault system filter flow path fluid flow Fourier fractal analysis fractal dimension fractal distribution fractal geometry fractal model fractal set fracture fragmentation frequency function geological Geophys geophysics gouge interpolation interval linear logarithm MANDELBROT multifractal multifractal measures natural nonstationary obtained parameters particles pattern percolation theory percolation threshold Phys planform plot pluton power law power spectrum predicted profiles properties random reflection sequence region renormalization rock Rock Fracture sample San Andreas Fault Sawtooth Range scale invariance SCHOLZ sea-floor Section seismic self-affine self-similar shown in Figure signal slope spectral exponent spectral intercept statistical stress surface synthetic techniques threshold topography turbulence values variable velocity wavelength white noise