Linearized least‐squares method for interpretation of potential‐field data from sources of simple geometry

Abstract

We present a new method for interpreting isolated potential‐field (gravity and magnetic) anomaly data. A linear equation, involving a symmetric anomalous field and its horizontal gradient, is derived to provide both the depth and nature of the buried sources. In many currently available methods, either higher order derivatives or postprocessing is necessary to extract both pieces of information; therefore, data must be of very high quality. In contrast, for gravity work with our method, only a first‐order horizontal derivative is needed and the traditional data quality is sufficient. Our proposed method is similar to the Euler technique; it uses a shape factor instead of a structural index to characterize the buried sources. The method is tested using theoretical anomaly data with and without random noise. In all cases, the method adequately estimates the location and the approximate shape of the source. The practical utility of the method is demonstrated using gravity and magnetic field examples from the United States and Zimbabwe.

A very fast simulated annealing method for inversion of magnetic anomaly over semi-infinite vertical rod-type structure

“…Analyses of magnetic data are generally performed with the help of different interpretation techniques. The interpretation methods include curves matching (Gay 1963(Gay , 1965McGrath 1970), Fourier transform (Bhattacharyya 1965), Hilbert transforms (Mohan et al 1982), monograms (Prakasa Rao et al 1986), least squares minimization (McGrath and Hood 1973;Silva 1989), characteristic points and distance approaches (Grant and West 1965;Abdelrahman 1994), correlation factors between successive least-squares residual anomalies (Abdelrahman and Sharafeldin 1996), Henkel transform (Singh et al 2000), linearized least squares (Salem et al 2004), normalized local wave number (Salem and Smith 2005), analytic signal derivatives (Salem 2005), Euler deconvolution (Salem and Ravat 2003), Fair function minimization (Tlas and Asfahani 2011a), deconvolution technique (Tlas and Asfahani 2011b), secondhorizontal derivatives (Abdelrahman and Essa 2015), Simplex algorithm (Tlas and Asfahani 2015). Also, simulated annealing (Gokturkler and Balkaya 2012), very fast simulated annealing (Sharma and Biswas 2013a;Sharma 2014a, b, 2015;Biswas 2015), Particle swarm optimization (Singh and Biswas 2016) have been effectively used to solve similar nonlinear inversion problems of geometrically simple bodies.…”

A New Method for Depth and Shape Determinations from Magnetic Data

“…ABDELRAHMAN and HASSANEIN (2000) developed a parametric-curves method (window-curves method) to determine simultaneously the shape and the depth of a buried structure from a residual magnetic anomaly profile. SALEM et al (2004) presented a method for interpreting a residual magnetic anomaly where a linear equation involving a symmetric anomalous field and its horizontal gradient is derived to provide the depth and the shape of the buried structures. ABDELRAHMAN et al (2013) described a procedure for automated determination of the best-fit model parameters including the depth and shape of the buried structure from magnetic data.…”

Subsurface structural mapping of Gebel El-Zeit area, Gulf of Suez, Egypt using aeromagnetic data

“…Such noise may come from various sources such as the measurement uncertainty, the removal of the background fields and the computation errors of gradients. Noise reducing techniques such as upward continuation and low pass filters can be implemented to reduce the effect of noise and enhance signal to noise ratio of the observed data (Salem et al, 2004). In this study, we have applied upward continuation with a distance of 0.5 km as a smoothing filter.…”