Electricity: measuring and testing – Of geophysical surface or subsurface in situ – By magnetic means
Patent
1996-09-19
1998-10-13
Strecker, Gerard R.
Electricity: measuring and testing
Of geophysical surface or subsurface in situ
By magnetic means
324326, 364420, G01V 340, G01V 338, G01V 308
Patent
active
058217533
DESCRIPTION:
BRIEF SUMMARY
FIELD OF THE INVENTION
This invention relates to the analysis of subterranean objects and, more particularly, to the determination of properties of subterranean objects by using principles of computerised tomography to interpret magnetic anomaly data associated with those objects.
BACKGROUND OF THE INVENTION
Magnetic surveying is a well-established method of conducting geophysical exploration based on detecting anomalies in the Earth's magnetic field. A limitation of this method at present is that it is difficult to use wish three dimensional modelling in order to obtain vertical geological sections or profiles from measured magnetic anomaly field data. In the past, efforts have been made to derive automatic methods for interpretation of the magnetic or potential anomaly profiles, but the most widely used methods at present are still various trial-and-error methods which require good a priori knowledge concerning the object being analyzed.
In the specification, natural numbers in brackets refer to the list of references at the end of the specification. Suppose that there is a buried two-dimensional magnetic source body of area S with constant magnetic dipole moment per unit area M whose direction is determined by its direction cosines P=cos.alpha. and Q=cos.beta. where .alpha. is M's angle from the (horizontal) x-axis and .beta. is M's angle from the (vertical) z-axis. The Earth's magnetic field is measured along a line parallel to the X-axis at elevation z.sub.0 above the Earth's surface. Suppose also that the direction of the total magnetic field at measuring point (x',z.sub.0) is a unit vector t whose direction cosines are p=cos.alpha.' and q=cos.beta.'. Then the total magnetic field measured by a magnetometer anomaly field of the source body and (x,z) are the coordinates of a point within the source body. The gradient operator .EPSILON. is defined as ##EQU1## where i and j are unit vectors in the directions of the x and z axes, and G(x',z.sub.0,x,z) is the so-called magnetic scalar potential which is defined as ##EQU2## where M is the magnitude of vector M, we have ##EQU3## Similarly, because ##EQU4## equation (1) becomes ##EQU5## where K is the data kernel defined as ##EQU6##
Here, P, Q, p and q are considered as constants. Modern magnetometers, such as three-component magnetometers and differential vector magnetometers, can provide information about these parameters. Thus, the data kernel can be considered to be a known function.
The interpretation task is to solve equation (3) to find M and to determine the boundary of S from the measured field data. From the point of view of image processing, this interpretation task is to reconstruct, from the measured signal, a magnetic dipole density distribution function which describes the source body.
If there is a priori knowledge about the shape of the boundary, the location, and the value of M for the source body, then the interpretation can be accomplished in a straightforward manner using least squares curve fitting. This is the principle of various trial-and-error strategies where the a priori knowledge may either come from well-log data or the interpreter's guess work.
Without good a priori knowledge, an hypothesis that is often adopted is that the boundary of S is contained in an area of interest S'(i.e., S.OR ##EQU7## Therefore the governing formula for the interpretation of the magnetic anomaly profile becomes ##EQU8## Equation (6) is a Fredholm integral equation of the first kind, and is an distribution function w(x,z) could be reconstructed by solving the integral equation then the interpretation of magnetic anomaly profile is accomplished or, in other words, the image of the source body is reconstructed from the measured signal.
Since the real data are measured at discrete points (x',z.sub.0) rather than continuously for all values of x', one method of solving equation (6) is to convert it into a system of linear equations of the form vectors, respectively. There are many numerical quadrature schemes available for approximating an integral eq
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Lee et al., Geophysics (USA), vol. 46, No. 5, dated May 1981, pp. 796-805.
McFee et al., IEEE Transactions on Geoscience and Remote Sensing (USA), vol. GE24, No. 5, Sep. 1986, pp. 663-673.
Stanley John
Zhou Jun
Geophysical Technology Limited
Strecker Gerard R.
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