Peter G. Lelièvre

A 3D total magnetization inversion applicable when significant, complicated remanence is present

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 informa...

Integrating geological and geophysical data through advanced constrained inversions

To be reliable, Earth models used for mineral exploration should be consistent with all available geological and geophysical information. During the past several years an important focus of inversion research has been towards advancing the integration of geological data (such as lithology and structure), physical property data (measurements taken on rock samples) and geophysical survey data through appropriate inversion methodologies. We expand the types of geological information that can be incorporated into ‘minimum structure’ type deterministic inversions involving minimisation of an objective function. These include orientation information and physical property trends. We also present an iterative cooperative inversion strategy for combining multiple types of geophysical data and recovering geologically realistic models involving sharp interfaces between rock units. We provide a synthetic example to illustrate our methods.

Unified geophysical and geological 3D Earth models

Three-dimensional geological Earth models typically comprise wireframe surfaces of connected triangles that represent geological contacts. In contrast, Earth models used by most current 3D geophysical numerical modeling and inversion methods are built on rectilinear meshes. This is because the mathematics for computing data responses are simpler on rectilinear meshes. In such a model, the relevant physical properties are uniform within each brick-like cell but possibly different from one cell to the next, producing a pixellated representation of the Earth. In principle, arbitrary spatial variations can be represented if a sufficiently fine discretization is used. However, no matter how fine the discretization of the rectilinear mesh, such a mesh is always incompatible with geological models comprising wireframe surfaces. Also, because the computational resources required by 3D numerical modeling and inversion methods increase dramatically as the discretization of a model is refined, it is never really pos...

Integrated Imaging of the Earth: Theory and Applications

Description: Reliable and detailed information about the Earth s subsurface is of crucial importance throughout the geosciences. Quantitative integration of all available geophysical and geological data helps to make Earth models more robust and reliable. The aim of this book is to summarize and synthesize the growing literature on combining various types of geophysical and other geoscientific data. The approaches that have been developed to date encompass joint inversion, cooperative inversion, and statistical post–inversion analysis methods, each with different benefits and assumptions.

Constraining Geophysical Inversions With Geologic Information

Earth models used for mineral exploration should be reliable and consistent with all information available. The current focus of the Geophysical Inversion Facility at the University of British Columbia (UBC-GIF) is towards the development of a new generation of geophysical inversion codes and utilities to advance the integration of geologic and geophysical data through appropriate inversion methodologies. This research will provide more functional methods for applying geophysics to general mineral exploration problems. Here we outline some of the available types of geologic information that can be incorporated into UBC-GIF inversions and we provide an example that illustrates some of our methods.

Magnetic Forward Modeling And Inversion For Materials of High Susceptibility

Summary Magnetic data collected over bodies of high susceptibility contain significant self-demagnetization effects. Examples include mineral exploration surveys over banded iron formations and surveys for detection and discrimination of unexploded ordinance. Standard forward modeling methods that neglect the effects of self-demagnetization can produce inaccurate results and subsequent deterioration in performance of the inverse solution. Here we solve the full Maxwell’s equations for electrostatics using a finite volume discretization. This forward modeling forms the foundation for a subsequent inversion algorithm. Standard Magnetic Forward Modeling Methods The secondary (anomalous) magnetic field strength Hs at any point P due to a distribution of induced magnetization M within a region R is given by

JMorph: Software for performing rapid morphometric measurements on digital images of fossil assemblages

Abstract Quantitative morphometric analyses of form are widely used in palaeontology, especially for taxonomic and evolutionary research. These analyses can involve several measurements performed on hundreds or even thousands of samples. Performing measurements of size and shape on large assemblages of macro- or microfossil samples is generally infeasible or impossible with traditional instruments such as vernier calipers. Instead, digital image processing software is required to perform measurements via suitable digital images of samples. Many software packages exist for morphometric analyses but there is not much available for the integral stage of data collection, particularly for the measurement of the outlines of samples. Some software exists to automatically detect the outline of a fossil sample from a digital image. However, automatic outline detection methods may perform inadequately when samples have incomplete outlines or images contain poor contrast between the sample and staging background. Hence, a manual digitization approach may be the only option. We are not aware of any software packages that are designed specifically for efficient digital measurement of fossil assemblages with numerous samples, especially for the purposes of manual outline analysis. Throughout several previous studies, we have developed a new software tool, JMorph, that is custom-built for that task. JMorph provides the means to perform many different types of measurements, which we describe in this manuscript. We focus on JMorphs ability to rapidly and accurately digitize the outlines of fossils. JMorph is freely available from the authors.

Joint Inversion Using Multi-objective Global Optimization Methods

The standard deterministic approach to joint inversion is to combine the multiple objectives (data misfits, regularization and joint coupling terms) into a weighted sum (aggregate) and minimize using a descent-based method. This approach has some disadvantages: appropriate weights must be determined for the aggregate, the use of local optimization requires that the objective functions be differentiable and well behaved, and there is the potential for entrapment in local minima. Pareto Multi-Objective Global Optimization (PMOGO) algorithms can overcome these issues. Also, PMOGO algorithms generate a suite of solutions representing the best compromises between the multiple objectives. We have implemented a PMOGO genetic algorithm and applied it to three classes of inverse problems: standard mesh-based problems for which the physical property values in each mesh cell are treated as continuous variables; mesh-based problems in which the cells can only take discrete physical property values corresponding to known or assumed rock units (a lithological inversion); and a fundamentally different type of inversion for which a model comprises wireframe surfaces representing contacts between rock units (essentially a geometry inversion). Joint inversion is greatly simplified for the latter two classes because no additional mathematical coupling measure is required in the objective function.

Towards Real Earth Models - Computational Geophysics on Unstructured Tetrahedral Meshes?

Using unstructured tetrahedral meshes to specify 3D geophysical Earth models has a numer of advantages. Such meshes can conform exactly to the triangularly tessellated wireframe surfaces in the 3D Earth models used by geologists. This offers up the possibility of both geophysicists and geologists working with a single unified Earth model. Unstructured tetrahedral meshes are extremely flexible, and so can accurately mimic arbitrarily complicated subsurface structures and topography. Also, in the context of electromagnetic methods, unstructured tetrahedral meshes can be very finely discretized around sources and yet can transition to a coarse discretization in the extremities of the solution domain without, in principle, affecting the quality of the mesh. However, using unstructured tetrahedral meshes for geophysical Earth models has its challenges. The tessellated surfaces in wireframe geological models are often not immediately suitable for computational techniques as they can contain intersecting facets and facets with extreme aspect ratios. Generating tetrahedral meshes that are of sufficient quality from real wireframe geological models can therefore be difficult. This presentation will aim to discuss the pros and cons of using unstructured tetrahedral meshes for geophysical Earth models, keeping in mind the complexities of the real subsurface that we are ultimately trying to represent.