Automatic interpretation techniques for potential fields data

The homogeneity of potential fields serves as the theoretical basis of most of the semiautomatic and automatic methods used in processing large magnetic and gravity datasets – for example, Euler deconvolution, the wavelet transform, and the similarity transform methods. Comparing three automatic methods that could be applied to magnetic and gravity surveys has helped determine the best methodology for interpreting a vertical component magnetic data grid from the Bolyarovo-Voden anomalous zone in Bulgaria. The three methods compared were magnetic and gravity sounding based on the differential similarity transform (MaGSoundDST), magnetic and gravity sounding based on the finite difference similarity transform (MaGSoundFDST), and Euler deconvolution based on the differential similarity transform (DST Euler) algorithm.

Comparing three automatic methods for interpretation of magnetic and gravity data grids helped determine the best methodology for interpreting a vertical component data grid from the Bolyarovo-Voden anomalous zone in Bulgaria. (Figures courtesy of the University of Edinburgh and the European Association of Geoscientists and Engineers)

MaGSoundDST
MaGSoundDST uses the property of the difference similarity transform (DST) function of a magnetic or a gravity anomaly to become zero or linear in the presence of a constant or linear background, respectively, at all observation points when the central point of similarity (CPS) of the transform coincides with a source’s singular point. It uses a measured anomaly and calculated or measured first-order derivatives of this field. The procedure involves calculating a 3-D function under the observation surface which evaluates the linearity of the DST function for different integer or non-integer structural indices using a moving window and “sounding” the subsurface along a vertical line under each window center for different structural indices. Then the method combines all the 3-D results into a map to obtain optimum source depth estimates below each horizontal location. The horizontal positions of the function’s local minima map determine the horizontal positions of simple sources.

MaGSoundFDST
MaGSoundFDST is based on the property of the finite difference similarity transform (FDST) function of a magnetic or gravity anomaly to become zero or linear in the presence of a constant or linear background, respectively, at all observation points when the CPS of the transform coincides with a source’s field singular point. It uses measured anomalous and upward continued field data.

MaGSoundFDST is similar to MaGSoundDST in the sense that they both sound the subsurface for simple magnetic and gravity sources using the theory that a 3-D sounding function has a minimum at the point where a source exists. In the MaGSoundFDST case, this function is the estimator of linearity of the FDST function. The estimators of linearity of FDST and DST are calculated in a similar way as the normalized residual dispersion after linear regression of the FDST and the DST, respectively. MaGSoundFDST also combines the 3-D functions for different values into three maps, defining the horizontal location, depth, and structural index of the sources using the same focusing principle as MaGSoundDST. Though discrete locations of the subsurface are probed, MaGSoundFDST extrapolates the source locations as in MaGSoundDST to intermediate points using a refinement procedure. The difference between MaGSoundFDST and MaGSoundDST lies in the definition and respective calculation of the FDST and DST functions.

The magnitude magnetic anomaly on a logarithmic scale is shown.

DST Euler
DST Euler is an interpretation method to estimate simple source coordinates and structural indices in the presence of a linear background. It solves the Euler homogeneous equation by using the property of the DST of a simple homogeneous source to vanish when the CPS coincides with the source and when the correct structural index is used. It is a window-based method and produces numerous solutions per simple source. A two-stage clustering technique, which allows a single estimate per source to be assigned, facilitates the interpretation of the results.

MaGSoundDST uses the property of the DST function of a magnetic or a gravity anomaly to become zero or linear in the presence of constant or linear background, respectively, at all observation points when the CPS of the transform coincides with a source’s singular point. The estimated sources are marked by red circles, squares, pentagrams, and hexagrams.

Bolyarovo-Voden magnetic anomaly
The three methods were applied to a vertical component data grid from the Bolyarovo-Voden magnetic anomalous zone using, in the MaGSoundDST and MaGSoundFDST cases, a CPS set with a 3-D grid spacing of 0.15 by 0.15 by 0.069 miles (0.25 by 0.25 by 0.1 km) and a fixed window of 19 by 19 points (2.7 by 2.7 miles or 4.5 by 4.5 km). The lower space was probed to a depth of 2.4 miles (4 km) with an upward continuation height of 0.069 miles in the MaGSoundFDST case.

DST Euler, MaGSoundDST, and MaGSoundFDST solve for horizontal position, depth, and structural index of simple sources. They are independent of the magnetization vector direction and do not require reduction to the pole in the magnetic data case. A linear background does not influence the results from the three procedures – an improvement over standard Euler deconvolution, which only accounts for a constant background in the measured anomalies.

For this experiment, MaGSoundFDST performed best in detecting the deeper central parts of sources that almost crop out on the surface.

The stability to random noise is similar, with MaGSoundFDST slightly more stable than DST Euler and MaGSoundDST, which use first-order derivatives of the field. The three procedures work in window mode but differ in the presentation of the results. The DST Euler method obtains many solutions per source, which requires a subsequent application of clustering techniques to assign one solution per source. MaGSoundDST and MaGSoundFDST give a single solution per source, which makes the results easier to interpret. In terms of calculation speed, DST Euler is the fastest, followed by MaGSoundDST and MaGSoundFDST. MaGSoundDST and MaGSoundFDST can be used adaptively, increasing with the depth of the probe point window, thus making the procedures fully automatic and requiring no input parameters other than the data.

For this experiment, MaGSoundFDST performed best in detecting the deeper central parts of sources that almost crop out on the surface. The structural index of a magnetic field or gravity field caused by the same source can vary depending on from how high the source is “seen” (i.e., the field observation height). Standing directly over the source, only its top is seen (structural index N=0). Going up, a point down is seen closer to the upper surface (N=2). Going further up, the central point of a body would look isometric. Thus, the depths obtained corresponding to different structural indices in the case of the three methods will correspond to different parts of the real geological body causing the anomaly.

Horizontal locations of the solution clusters from DST Euler, an interpretation method to estimate simple source coordinates and structural indices in the presence of a linear background, are shown.

The sources of the Bolyarovo-Voden magnetic anomaly have tops close to the surface, and measurements of the vertical component field are a result of a ground survey. Therefore, MaGSoundFDST, which used FDST (the difference between an analytically continued field at a height of 0.069 miles and the similarly transformed anomalous field at the same height), proved most suitable to see the deepest point possible from a method based on the assumption of a one-point homogeneous source. For example, a source with index 6 detected by MaGSoundFDST – which has N=3 and a depth of 0.9 miles (1.4 km) – indicates its center point. The same source is detected by MaGSoundDST through the solution with index 4 and a depth of 0.4 miles (0.7 km). DST Euler detected the same source with two solutions with indices one and four, N between 0.9±1 and 0.5±0.5, and depths between 0.2±0.2 and 0.1±0.1 miles (0.4±0.3 and 0.2±0.1 km).

DST Euler and MaGSound DST both use the field and its derivatives at ground level; the difference is that DST Euler is more of an averaging method and its output corresponds to clusters of solutions. Despite the differences, the result N=0.9+1=1.9 and corresponding depth 0.2+0.2=0.4 miles (0.4+0.3=0.7 km) (taking the upper bounds from the standard deviations) for the solution index 1 for DST Euler is similar to the solution index 4 of MaGSoundDST.

A 2.5-D model highlights the profile A-B found in the vertical component data results.

Acknowledgements
This work was funded by UK Natural Environmental Research Council grant NER/0/S/2003/00674. This article was originally a presentation at the 2010 meeting of the European Association of Geoscientists and Engineers and has been revised with permission from the authors.