2D potential theory using complex algebra: New equations and visualization for the interpretation of potential field data

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. J1-J13 ◽  
Author(s):  
Pauline Le Maire ◽  
Marc Munschy
Keyword(s):  
Magnetic Field ◽  
Complex Plane ◽  
Potential Field ◽  
Single Point ◽  
Magnetic Anomalies ◽  
Analytic Signal ◽  
Power Functions ◽  
Field Equations ◽  
Complex Algebra ◽  
Location Depth

The shape of an anomaly (magnetic or gravity) along a profile provides information on the geometry, horizontal location, depth, and magnetization of the source. For a 2D source, the horizontal location, depth, and geometry of a source are determined through the analysis of the curve of the analytic signal. However, the amplitude of the analytic signal is independent of the dips of the structure, the apparent inclination of magnetization, and the regional magnetic field. To better characterize the parameters of the source, we have developed a new approach for studying 2D potential field equations using complex algebra. Complex equations for different geometries of the sources are obtained for gravity and magnetic anomalies in the spatial and spectral domains. In the spatial domain, these new equations are compact and correspond to logarithmic or power functions with a negative integer exponent. We found that modifying the shape of the source changes the exponent of the power function, which is equivalent to differentiation or integration. We developed anomaly profiles using plots in the complex plane, which is called mapping. The obtained complex curves are loops passing through the origin of the plane. The shape of these loops depends only on the geometry and not on the horizontal location of the source. For source geometries defined by a single point, the loop shape is also independent of the source depth. The orientation of the curves in the complex plane is related to the order of differentiation or integration, the geometry and dips of the structures, and the apparent inclination of magnetization and of the regional magnetic field. The application of these equations and mapping on total field magnetic anomalies across a magmatic dike in Norway shows coherent results, allowing us to determine the geometry and the apparent inclination of magnetization.

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

Large scale magnetic anomalies over western Canada and the Arctic: a discussion

1976 ◽  
Vol 13 (6) ◽  
pp. 790-802 ◽  
Author(s):  
R. L. Coles ◽  
G. V. Haines ◽  
W. Hannaford
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Elevated Temperatures ◽  
Magnetic Anomalies ◽  
The Arctic ◽  
Evolutionary Development ◽  
Magnetic Feature ◽  
Western Canada ◽  
Arctic Regions ◽  
The Magnetic Field

A contoured map of vertical magnetic field residuals (relative to the IGRF) over western Canada and adjacent Arctic regions has been produced by amalgamating new data with those from previous surveys. The measurements were made at altitudes between 3.5 and 5.5 km above sea level. The map shows the form of the magnetic field within the waveband 30 to 5000 km. A magnetic feature of several thousand kilometres wavelength dominates the map, and is probably due in major part to sources in the earth's core. Superimposed on this are several groups of anomalies which contain wavelengths of the order of a thousand kilometres. The patterns of the short wavelength anomalies provide a broad view of major structures and indicate several regimes of distinctive evolutionary development. Enhancement of viscous magnetization at elevated temperatures may account for the concentration of intense anomalies observed near the western edge of the craton.

Euler’s differential equation and the identification of the magnetic point‐pole and point‐dipole sources

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1549-1553 ◽  
Author(s):  
J. O. Barongo
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Magnetic Anomalies ◽  
Field Vector ◽  
Magnetic Data ◽  
Dipole Source ◽  
Point Dipole ◽  
Main Subject ◽  
Depth Extent ◽  
Dipole Sources

The concept of point‐pole and point‐dipole in interpretation of magnetic data is often employed in the analysis of magnetic anomalies (or their derivatives) caused by geologic bodies whose geometric shapes approach those of (1) narrow prisms of infinite depth extent aligned, more or less, in the direction of the inducing earth’s magnetic field, and (2) spheres, respectively. The two geologic bodies are assumed to be magnetically polarized in the direction of the Earth’s total magnetic field vector (Figure 1). One problem that perhaps is not realized when interpretations are carried out on such anomalies, especially in regions of high magnetic latitudes (45–90 degrees), is that of being unable to differentiate an anomaly due to a point‐pole from that due to a point‐dipole source. The two anomalies look more or less alike at those latitudes (Figure 2). Hood (1971) presented a graphical procedure of determining depth to the top/center of the point pole/dipole in which he assumed prior knowledge of the anomaly type. While it is essential and mandatory to make an assumption such as this, it is very important to go a step further and carry out a test on the anomaly to check whether the assumption made is correct. The procedure to do this is the main subject of this note. I start off by first using some method that does not involve Euler’s differential equation to determine depth to the top/center of the suspected causative body. Then I employ the determined depth to identify the causative body from the graphical diagram of Hood (1971, Figure 26).

scholarly journals Measurements of vector magnetic anomalies on board the icebreaker Shirase and the magnetization of the ship

1999 ◽  
Vol 42 (2) ◽  
Author(s):  
Y. Nogi ◽  
K. Kaminuma
Keyword(s):  
Magnetic Field ◽  
Geomagnetic Field ◽  
Magnetic Anomalies ◽  
The Other ◽  
South Indian Ocean ◽  
Permanent Magnetic Field ◽  
South Indian ◽  
Antarctic Research ◽  
Permanent Magnetization ◽  
Made In

Vector measurements of the geomagnetic field have been made in the South Indian Ocean since 1988 when a Shipboard Three Component Magnetometer (STCM) was installed on board the icebreaker Shirase by the 30th Japanese Antarctic Research Expedition (JARE-30). Twelve constants related to the ship's induced and permanent magnetic field were determined by the data obtained from the JARE-30 to the JARE-35. The constants related to the ship's magnetic susceptibility distribution are almost stable throughout the cruise and mostly depend on the ship's shape. On the other hand, the constants related to the ship's permanent magnetization are variable. However, absolute values of total intensity geomagnetic field calculated from vector geomagnetic field is possible to use, if the constraints from total intensity geomagnetic field measured by the proton magnetometer and/or satellite derived magnetic anomalies are applied.

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