Fractal behavior and detectibility limits of geophysical surveys

Abstract

The detectibility limits of a large‐scale geophysical measuring network (such as arrays of seismometers for seismic hazard assessment, arrays of air guns and vibrators in seismic profiling, and station spacing in gravity, magnetic, magnetotelluric, and other geophysical surveys for exploration of oil, minerals, and groundwater) depends on the fractal dimension of the network and the anomaly (Lovejoy et al., 1986; Korvin, 1992). The geophysical anomaly resulting from the fractal nature of sources (Turcotte, 1992) [such as length of fault (Okubo and Aki, 1987; Robertson et al., 1995), velocity inhomogeneities (Sato, 1988), nonrandom distribution of density (Thorarinsson and Magnusson, 1990) and susceptibility (Pilkington and Todoeschuck, 1993; Pilkington et al., 1994; Maus and Dimri, 1994, 1995, 1996), reflectivity (Todoeschuck et al., 1990; Dimri, 1992), etc.] cannot be accurately measured unless its fractal dimension does not exceed the difference of the 2-D Euclidean and fractal dimension of the network (Lovejoy et al., 1986; Korvin, 1992).