A Study on the Generalized Multifractal Dimension and the Spectrum in Seabottom Topography

The scaling behavior of random fractals and multifractals is investigated numerically on the seabottom depth in the seabottom topography. In the self-affine structure the critical length for the crossover can be found from the value of standard deviations for the seabottom depth. The generalized dimension and the spectrum in the multifractal structure are discussed numerically, as it is assumed that the seabottom depth is located on a two-dimensional square lattice. For this case, the fractal dimension D$_0$ is respectively calculated as 1.312476, 1.366726, and 1.372243 in our three regions, and our result is compared with other numerical calculations.