automatic interpretation techniques for potential fields data

By Daniela Gerovska and Kathryn Whaler, University of Edinburgh, and Marcos J.Araúzo-Bravo, Max Planck Institute for Molecular Biomedicine

August 1, 2010

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

Automatic interpretation techniques for potential fieldsdataThree methods were studied to interpret a magnetic anomaly in Bulgaria.

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.

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

Automatic interpretation techniques for potential f... http://www.epmag.com/article/print/63211

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Geoscientists and Engineers) 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.


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The magnitude magnetic anomaly on a logarithmic scale is shown.

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.

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.

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


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For this experiment, MaGSoundFDST performed best in detecting

the deeper central parts of sources that almost crop out on the

surface.

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.

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.


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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.


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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.


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automatic interpretation techniques for potential fields data

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