Inversion of magnetic data is complicated by the presence of remanent magnetization. To deal with this problem, we invert magnetic data for a three-component subsurface magnetization vector, as opposed to magnetic susceptibility (a scalar). The magnetization vector can be cast in a Cartesian or spherical framework. In the Cartesian formulation, the total magnetization is split into one component parallel and two components perpendicular to the earth’s field. In the spherical formulation, we invert for magnetization amplitude and the dip and azimuth of the magnetization direction. Our inversion schemes contain flexibility to obtain different types of magnetization models and allow for inclusion of geologic information regarding remanence. Allowing a vector magnetization increases the nonuniqueness of the magnetic inverse problem greatly, but additional information (e.g., knowledge of physical properties or geology) incorporated as constraints can improve the results dramatically. Commonly available information results in complicated nonlinear constraints in the Cartesian formulation. However, moving to a spherical formulation results in simple bound constraints at the expense of a now nonlinear objective function. We test our methods using synthetic and real data from scenarios involving complicated remanence (i.e., many magnetized bodies with many magnetization directions). All tests provide favorable results and our methods compare well against those of other authors.

Seismic methods continue to receive interest for use in mineral exploration due to the much higher resolution potential of seismic data compared to the techniques traditionally used, namely gravity, magnetics, resistivity and electromagnetics. However, the complicated geology often encountered in hard-rock exploration can make data processing and interpretation difficult. Inverting seismic data jointly with a complimentary dataset can help overcome these difficulties and facilitate the construction of a common Earth model. We consider the joint inversion of seismic traveltimes and gravity data. Our joint inversion approach incorporates measures of model similarity (i.e. slowness versus density) that are both compositional and structural in nature and follow naturally from this specific data combination. We perform the inversions on unstructured grids comprised of triangular cells in 2D, or tetrahedral cells in 3D. We present our joint inversion method on a scenario inspired by the Voisey's Bay massive sulphide deposit in Labrador, Canada.

Seismic methods continue to receive interest for use in mineral exploration due to the much higher resolution potential of seismic data compared to the techniques traditionally used, namely, gravity, magnetics, resistivity, and electromagnetics. However, the complicated geology often encountered in hard-rock exploration can make data processing and interpretation difficult. Inverting seismic data jointly with a complementary data set can help overcome these difficulties and facilitate the construction of a common earth model. We considered the joint inversion of seismic first-arrival traveltimes and gravity data to recover causative slowness and density distributions. Our joint inversion algorithm differs from previous work by (1) incorporating a large suite of measures for coupling the two physical property models, (2) slowly increasing the effect of the coupling to help avoid potential convergence issues, and (3) automatically adjusting two Tikhonov tradeoff parameters to achieve a desired fit to both data sets. The coupling measures used are both compositional and structural in nature and allow the inclusion of explicitly known or implicitly assumed empirical relationships, physical property distribution information, and cross-gradient structural coupling. For any particular exploration scenario, the combination of coupling measures used should be guided by the geologic knowledge available. We performed our inversions on unstructured grids comprised of triangular cells in 2D, or tetrahedral cells in 3D, but the joint inversion methods are equally applicable to rectilinear grids. We tested our joint inversion methodology on scenarios based on the Voisey’s Bay massive sulfide deposit in Labrador, Canada. These scenarios present a challenge to the inversion of first-arrival traveltimes and we show how joint inversion with gravity data can improve recovery of the subsurface features.

S U M M A R YWe develop an algorithm to invert geophysical magnetic data to recover 3-D distributions of subsurface magnetic susceptibility when the bodies have complicated geometry and possibly high magnetic susceptibility. For the associated forward modelling problem, a full solution to Maxwell's equations for source-free magnetostatics is developed in the differential equation domain using a finite volume discretization. The earth region of interest is discretized into many prismatic cells, each with constant susceptibility. The resulting system of discrete equations is solved using an ILU-preconditioned Bi-Conjugate Gradient Stabilized (BiCGStab) algorithm. Formulations for total and secondary field computations are developed and tested against analytic solutions and against a solution in the integral equation domain. The finite volume forward modelling method forms the foundation for a subsequent inversion algorithm. The underdetermined inverse problem is solved as an unconstrained optimization problem and an objective function composed of data misfit and a regularization term is minimized using a Gauss-Newton search. At each iteration, the CGLS algorithm is used to solve for the search direction. The inversion code is tested on synthetic data from both geometrically simple and complicated bodies and on field survey data collected over a planted ferrous shipping container.In this paper we tackle the problem of inverting geophysical magnetic data that is collected above regions of high magnetic susceptibility. Section 1.1 introduces self-demagnetization effects associated with high magnetic susceptibility. Section 1.2 explains why, and demonstrates how, the standard approximate magnetic inversion approach can fail in the presence of high susceptibility. In Section 2 we formulate a forward solution to accurately model the response of general 3-D distributions of highly magnetic material. Discretization choices and accuracy concerns are discussed. Our magnetostatic problem is similar to the electrostatic DC resistivity problem and the saturated steady-state fluid flow problem. To invert we follow the common approach of Li & Oldenburg (1996) and a compendious discussion is given in Section 3. In Section 4, we provide a comprehensive treatment of important practical inversion aspects that arise for the high susceptibility magnetic inverse problem. The inversion code is tested on synthetic and field survey data in Section 5. To our knowledge, this study is the first to produce a working, practical solution to the high susceptibility magnetic inverse problem for general 3-D distributions. Self-demagnetization effectsIn the presence of an inducing magnetic field, H, the magnetization, M, acquired by a volume of magnetic material is(1)Here, χ is magnetic susceptibility, H 0 is the Earth's magnetic field (or geomagnetic field) and H s includes any anomalous fields associated with magnetic material in the region. In the interpretation of magnetic data from geophysical surveys it is often assumed that anomalous fields a...

S U M M A R YIn this paper, we investigate options for incorporating structural orientation information into under-determined inversions in a deterministic framework (i.e. minimization of an objective function). The first approach involves a rotation of an orthogonal system of smoothness operators, for which there are some important practical details in the implementation that avoid asymmetric inversion results. The second approach relies on addition of linear constraints into the optimization problem, which is solved using a logarithmic barrier method. A 2-D synthetic example is provided involving a synclinal magnetic structure and we invert two sets of real survey data in 3-D (one gravity data, the other magnetic data). Using those examples, we demonstrate how different types of orientation information can be incorporated into inversions. Incorporating orientation information can yield bodies that have expected aspect ratios and axis orientations. Physical property increase or decrease in particular directions can also be obtained.To be reliable, earth models used for mineral exploration should be consistent with all available geophysical and geological information. Due to data uncertainty and other aspects inherent to the under-determined geophysical inverse problem, there are an infinite number of models that can fit the geophysical data to the desired degree (i.e. the problem is non-unique). Further information is essential for a unique solution. Incorporating prior geological knowledge can reduce ambiguity and enhance inversion results, leading to more reliable earth models.An important form of available geological information is structural orientation. This can involve the orientation of a body (i.e. the strike, dip, and tilt of its major axes), aspect ratios (i.e. the relative lengths of a body's major axes) and physical property trends (i.e. increase, decrease, or constant in a particular direction). The ability to specify such information becomes especially important for survey methods with limited depth resolution. The lack of resolution can lead to recovery of an object with an incorrect or distorted dip and by including orientation information the results can be dramatically improved at depth.Many researchers have provided functionality for incorporating different types of geological information into their particular inversion frameworks. In this paper, we investigate how orientation information can be placed into our deterministic inversion framework in which a computationally well-behaved function is minimized subject to optional constraints. Before introducing our methods we provide an overview of some techniques used by other authors for comparison. Bosch et al. (2001) and Guillen et al. (2008) work in a stochastic inversion framework that directly recovers rock type (i.e. a lithologic inversion) from a list of those assumed present. Prior information is placed into the problem through probability density functions and topology rules (relationships between rock units). The model space (i.e. all p...