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This paper develops a minimum-support focusing stabilizer to perform a joint inversion of the vertical components of gravity and magnetic data using fuzzy c-means clustering (FCM) with the regularized Newton method in a space of weighted parameters. Not only does this joint inversion technology arrive at the conditionally well-posed traditional potential field inversion, but it also increases the structural correlation between multiple inverted models. The FCM and the focusing stabilizer make it possible to balance the convergence of the data space (D) and the model space (M), guiding multimodal geophysical parameters toward assigned petrophysical values, which makes the results more stable and realistic. Two model studies are presented to illustrate the method, a simple synthetic model with two rectangular bodies in a homogenous background and a realistic model of the Volcanogenic Massive Sulfide (VMS) deposits in northeastern New Brunswick, Canada. These models demonstrate that the new focusing joint inversion algorithm produces better images than traditional methods because the FCM function uses the structural correlation of density contrast and magnetic susceptibility as constraints. [ABSTRACT FROM AUTHOR]

Remanent magnetizations of magnetites between single-domain (SD) threshold size (≈0.1 μm) and ≈20 μm have SD-like intensities and coercivities. This paper shows for the first time that magnetite's induced magnetization also has pseudo-single-domain behaviour. The first part of the paper reports temperature-dependent initial susceptibility data, k0(T), of sized magnetites and assesses their granulometric potential. The second part transforms coercive force data, Hc(T), for the same magnetites into simulated k0(T) curves. The third part considers k0(T) results of coarse-grained mafic rocks as candidate sources of deep-seated magnetic anomalies.High-temperature susceptibility k0 measured with a Kappabridge for eight fractions of crushed natural magnetites (median sizes of 0.6, 1, 3, 6, 9, 14, 110 and 135 μm) shows a progressive increase in the height of the Hopkinson peak below the Curie point as grain size decreases. The trend is systematic and has granulometric potential in the 1–14 μm range. Self-demagnetization should produce almost flat k0(T) in grains larger than SD size but experimentally, well-defined Hopkinson peaks are not limited to the finest grains. 1-μm magnetites have a peak 1.5 times k0 at 20 °C and 14-μm grains have a peak of 1.25. Only 110 and 135 μm grains have T-independent k0.Using an empirical relationship between coercive force Hc and k0, Hc(T) data for the sized magnetites were used to simulate k0(T) results. A hump in the k0 heating curve around 250 °C was traced to annealing out internal strains, evident in Hc data measured in first heatings. For sizes ≤6 μm, observed Hopkinson peaks were smaller than predicted, possibly because of a previously unrecognized grain-size dependence of the empirical constant relating Hc and k0.Two crystalline rocks, a gabbro and a diabase, combine SD-like Hopkinson peaks and multidomain (MD) flat ramps in their k0(T) data. In the diabase, a Hopkinson peak is prominent in separated plagioclase grains containing submicron magnetite, but is masked in whole-rock data. The gabbro has a clear superposition of SD and MD k0(T) functions in its whole-rock data, with a Hopkinson peak of 1.35. If oceanic layer-3 gabbros have similar susceptibility enhancement above 500 °C, they could be more important magnetic anomaly sources than room-temperature k0 measurements on dredged or fault-uplifted samples would suggest. [ABSTRACT FROM AUTHOR]

Magnetic susceptibility and natural remanent magnetization of rocks are useful parameters to study geological structures and geodynamic processes. Traditional widely used algorithms for the inversion of magnetic data can recover the distribution of the apparent susceptibility or total magnetization intensity, but do not provide information on the remanent magnetization. In this paper, we propose a framework to directly invert for the magnetic susceptibility and the natural remanent magnetization vector using surface or airborne magnetic data, assuming that the Köenigsberger ratio of the rock is known or approximately deducible. The susceptibility and remanence are computed using two different approaches: (1) the susceptibility, intensity, and direction of the remanent magnetization are continuously recovered for each discretized cell and (2) the remanence direction is assumed to be uniform in each subzone and is iteratively computed as discrete values. Both processes are implemented using the preconditioned conjugate gradient algorithm. The method is tested on three synthetic models and one field data set from the Zaohuohexi iron-ore deposit, Qinghai Province, northwest China. The results of the continuous inversion show the trend of the remanent magnetization directions, while the discrete inversion yields more specific values. This inversion framework can determine the source bodies' geometry and position, and also provide superposed and comprehensive information on the natural remanent magnetization, which may be useful to investigate geological bodies bearing stable primary remanent magnetization. [ABSTRACT FROM AUTHOR]

In the absence of quantitative relationships, a cross-gradient function can be used to correlate unknown physical properties in a joint inversion of geophysical data sets. It introduces a structural correlation between properties. A commonly used, inexact approach adds a weighted cross-gradient term as a penalty to the cost function being minimized during inversion. This weighting factor needs to be tuned to balance the regularization and cross-gradient terms. In this paper we propose nonlinear weighting for the cross-gradient function which addresses the very different magnitudes of the cross-gradient and regularization terms. This approach also couples the weighting factors for the regularization and correlation terms reducing the number of tuning parameters. The approach is investigated for a synthetic case. Results are also shown for the 3-D joint inversion of high-resolution magnetic and gravity anomaly data from Southern Queensland in Australia with over 30 million cells. [ABSTRACT FROM AUTHOR]

One of the main applications of magnetic field measurements in boreholes is the detection of unexploded ordnance or buried utility structures like pipes or tiebacks. Even though the advantage of fully oriented magnetic vector measurements have long been recognized and could significantly reduce costs and risks, the tools used for those purposes typically measure only the total magnetic field, the vertical and horizontal components or gradients thereof. The Göttingen Bohrloch Magnetometer uses three fibre optic gyros to record its orientation and thus enables us to compute high-quality three-component magnetic vector data regardless of borehole orientation. The measurements described in this paper were run in the scientific borehole Cuxhaven Lüdingworth 1/1A, which was drilled as a part of the 'Coastal Aquifer Test field' project to study the dynamics of the saltwater/freshwater interface. As the drill string got stuck during drilling of the first borehole, a second hole was drilled in the immediate vicinity. The drill string lies at a depth between 80 and 114 m at a distance of only 2.5 m southeast of the borehole used for the measurements, making it an ideal target to demonstrate the benefits of vector magnetic surveys. Although the theories to calculate magnetic fields of objects with different shapes is well established and do not need to be tested, they almost exclusively include approximations of the geometry. It is not obvious whether these approximations are suited to describe real data, or whether additional effects or refinements have to be considered. We use both a simplified monopole model and a cylinder model to fit the data and are able to determine the position of the drill string within a statistical error of approximately 10 cm. Additionally, we show that the location of the drill string could not have been determined by measurements of the total field or its horizontal and vertical component alone and that those methods would require the drilling of additional boreholes to obtain an unambiguous result. [ABSTRACT FROM AUTHOR]

We examined the mathematical and computational aspects of the magnetic potential, vector and gradient tensor fields of a tesseroid in a geocentric spherical coordinate system (SCS). This work is relevant for 3-D modelling that is performed with lithospheric vertical scales and global, continent or large regional horizontal scales. The curvature of the Earth is significant at these scales and hence, a SCS is more appropriate than the usual Cartesian coordinate system (CCS). The 3-D arrays of spherical prisms (SP; 'tesseroids') can be used to model the response of volumes with variable magnetic properties. Analytical solutions do not exist for these model elements and numerical or mixed numerical and analytical solutions must be employed. We compared various methods for calculating the response in terms of accuracy and computational efficiency. The methods were (1) the spherical coordinate magnetic dipole method (MD), (2) variants of the 3-D Gauss-Legendre quadrature integration method (3-D GLQI) with (i) different numbers of nodes in each of the three directions, and (ii) models where we subdivided each SP into a number of smaller tesseroid volume elements, (3) a procedure that we term revised Gauss-Legendre quadrature integration (3-D RGLQI) where the magnetization direction which is constant in a SCS is assumed to be constant in a CCS and equal to the direction at the geometric centre of each tesseroid, (4) the Taylor's series expansion method (TSE) and (5) the rectangular prism method (RP). In any realistic application, both the accuracy and the computational efficiency factors must be considered to determine the optimum approach to employ. In all instances, accuracy improves with increasing distance from the source. It is higher in the percentage terms for potential than the vector or tensor response. The tensor errors are the largest, but they decrease more quickly with distance from the source. In our comparisons of relative computational efficiency, we found that the magnetic potential takes less time to compute than the vector response, which in turn takes less time to compute than the tensor gradient response. The MD method takes less time to compute than either the TSE or RP methods. The efficiency of the (GLQI and) RGLQI methods depends on the polynomial order, but the response typically takes longer to compute than it does for the other methods. The optimum method is a complex function of the desired accuracy, the size of the volume elements, the element latitude and the distance between the source and the observation. For a model of global extent with typical model element size (e.g. 1 degree horizontally and 10 km radially) and observations at altitudes of 10s to 100s of km, a mixture of methods based on the horizontal separation of the source and observation separation would be the optimum approach. To demonstrate the RGLQI method described within this paper, we applied it to the computation of the response for a global magnetization model for observations at 300 and 30 km altitude. [ABSTRACT FROM AUTHOR]