GP53A-01 INVITED
Multiple joint inversion of gravity, magnetic, electromagnetic and seismic data under a common structural framework for subsurface material discrimination
The combined analysis of multiple geophysical observations on geological targets makes possible the discrimination and classification of subsurface materials and processes. Unfortunately, the individual uncertainties and low resolution of some data may mislead the integrated interpretation. It is now emerging that some of these limitations can be reduced in a joint inversion process by adopting the basic principle that collocated measurements should be influenced by a common underlying geology. A joint inversion approach that has been increasingly popular is that based on cross-gradient constraints; this approach basically seeks collocated subsurface images of two physical properties with a common structural signature defined by parallel property changes. This methodology has been successfully applied to the joint inversion of electromagnetic and seismic data; however, it has not yet been applied to geopotential data, which are thought to suffer from more severe limitations in resolution. As gravity and magnetic data constitute the geophysical evidence of two very characteristic properties of the subsurface materials, it is desirable to extend the cross-gradient philosophy to the joint inversion of geopotential data. This will address some relevant issues such as: Should several physical properties, like density and magnetization, follow a common underlying structural framework in actual geological terrains? If so, how much can geopotential data contribute to the search for such a common structure? Conversely, can the estimations of density and magnetization, as well as other physical parameters, be more accurate when a common structure is adopted? To address these questions, I developed a multiple joint inversion procedure founded on a generalized cross- gradient constraint that incorporates gravity, magnetic, dc resistivity and seismic data all together in the search for multiple property images that follow a common structural framework. I show some comparative results incorporating individual and combined data in test and field examples for two-dimensional profiles. The results show that the jointly estimated images can be readily incorporated in an integrated model from where the constituent materials could be more easily discriminated and characterized.
GP53A-02 INVITED
Detph-to-the-bottom Optimization for Potential-field Data Inversion
We show an algorithm for the linear inversion of 2D surface magnetic data to obtain 3D models of the susceptibility of the source. After showing a novel characterization of the ambiguity domain in the Fourier space, which has a simple geometrical interpretation, we will demonstrate that a depth-weighting function is useful to significantly reduce the ambiguity domain in order to characterize the main source properties. The forward model is discretized by a mesh of prismatic cells with constant magnetization that allows the recovery of a complete 3D generating source. As the number of cells are normally grater than the amount of available data, we are left with an underdetermined linear inverse problem, which can be regularized in order to obtain an unique solution by a depth-weighting function, adapted from Li and Oldenburg (1996) to close the source towards its bottom. The main novelty of this method is a first-stage optimization that gives information about the depth-to-the-bottom (dtb) of the generating source. This parameter permits both the evaluation of the appropriate vertical extension of the mesh, and the definition of the shape of the regularizing depth-weighting distribution. The adopted method is suitable under appropriate changes to deal also with gravity data. After showing which kind of a priori information is introduced by this particular regularization, we will describe its limits and its possible improvements and then we will show the results of some synthetic tests. As a final application we will show the 3D magnetic model of an interesting volcanic region in Italy.
GP53A-03 INVITED
What can we Expect From Present Geomagnetic Field Studies in the Next Years?
The International Decade of Geopotential Field Research, firstly proposed by a resolution of the International Association of Geomagnetism and Aeronomy in 1997, is changing our approaches towards the study of the present geomagnetic field. In a few years, Swarm satellites will complete the cycle of missions started few years ago with Orsted, Champ, and SAC-C with the objective of undertaking high-resolution mapping of the magnetic field from space. The new global models will theoretically be able to go up to degree 130 and beyond, filling the traditional gap in the power spectrum between near-surface and satellite data. Moreover, the availability of satellite data for a long period has allowed the development of preliminary models of the secular variation of the magnetic field using only satellite data. Traditional modeling of the magnetic field using spherical harmonics expansion is now used alongside other techniques such as wavelet analysis and regional techniques like R- SCHA. This latter technique, due to its capacity to represent very short wavelengths, will have a great importance in the exploitation of the World Digital Magnetic Anomaly Map and in all the geological implications that can be derived from it. In addition, the use of a Geographical Information System approach has been shown to be a fundamental tool for the compilation of this magnetic anomaly map of the world. As well as newly obtained data, the reanalysis of old surveys and compilations with new approaches and techniques is giving interesting results, like the recent discovery of ultrafast oceanic spreading in some areas of the Mediterranean Sea. Scientists are also questioning the role of the magnetic field on climate change, and geophysical prospecting techniques will be employed by organizations like UN to unveil hidden nuclear explosions. In this talk I will try to give an overview of the major issues that have happened in recent years, on these and other topics, as an approach to what can be expected in the near future.
GP53A-04 INVITED
Inversion of magnetic data in three steps
We present a three step magnetic inversion procedure in which invariant quantities with respect to source parameters are sequentially inverted to give i) shape cross-section, ii) magnetization intensity, and iii) magnetization direction for a two-dimensional (elongated) magnetic source. The quantity first inverted (called here the shape function) is obtained from the ratio of the gradient intensity of the total field anomaly to the intensity of the anomalous vector field. For homogenous sources, the shape function is invariant with source magnetization and allows reconstruction of the source geometry by attributing an arbitrary magnetization to trial solutions. Once determined, the source shape is fixed and magnetization intensity is estimated by fitting the total gradient of the total field anomaly (equivalent to the amplitude of the analytic signal of magnetic anomaly). Finally, the source shape and magnetization intensity are fixed and the magnetization direction is determined by fitting the magnetic anomaly. As suggested by numerical modeling and real data application, stepped inversion allows checking if causative sources are homogeneous or not. This is possible because the shape function from inhomogeneous sources can be fitted by homogeneous models but a model obtained in this way neither fits the total gradient of the magnetic anomaly nor the magnetic anomaly itself. Such a criterion seems effective in recognizing strongly inhomogeneous sources. Stepped inversion is tested with numerical experiments, and used to model a magnetic anomaly from intrusive basic rocks from the Parana Basin, Brazil.
GP53A-05 INVITED
Monte Carlo Inversion of Gravity and Magnetic Data in 3D
Inference of earth medium structure and properties is based on multidisciplinary data and information. Commonly, geophysics, petrophysics and geology need to be integrated to produce a realistic description of earth structures, basins and reservoirs. To achieve a quantitative combination of such different types of information we use a statistical approach that begins with defining a common model jointly describing structural, petrophysical and physical properties of the medium. This prior statistical model represents the knowledge of the medium structure and properties before taking into account the information provided by the geophysical surveys. By inverting the geophysical data onto the common model, we further constraint the model to jointly explain the geophysical observations and comply with the petrophysical and geological information. The related calculations are developed using sampling (Monte Carlo) techniques. We follow this approach for the joint inversion of gravity and magnetic data to infer the 3D structure and properties of an earth volume. We model the major lithotype regions and the medium mass density and magnetic susceptibility fields. The three model properties (lithotype, density and susceptibility) are linked by conditioning the physical property statistics to the lithotype using petrophysical and geostatistical information. In this way the gravity and magnetic data are coupled to a common model structure. We generate a large number of model realizations that jointly honour the prior structural and geostatistical information, and the likelihoods with the gravity and magnetic observations, calculating final estimates and probabilities of the medium model parameters. We have applied the joint gravity and magnetic inversion approach to infer sedimentary basin and crustal structure in 3D, with interest to regional exploration of hydrocarbon resources. The statistical model in this case constraints the structure of the basin and the rock properties using information obtained from the geology, seismic surveys and rock sample measurements. With the method we obtain basement and Moho estimates and full description of their probabilities. In a different application we study the region of interaction between the South American and Caribbean plates to infer the lithospheric structure and the low angle subduction of the latter beneath South America.
GP53A-06
Apparent Density Mapping Using Entropic Regularization
We present a new apparent density mapping on the horizontal plane, which combines the minimization of the first-order entropy with the maximization of the zeroth-order entropy of the estimated density contrasts. The interpretation model consists of a grid of vertical, juxtaposed prisms in both horizontal directions. We assume that the top and the bottom of the gravity sources are flat and horizontal and we estimate the prisms density contrasts. The minimization of the first-order entropy favors solutions presenting sharp borders, and the maximization of the zeroth-order entropy prevents the tendency of the source to collapse to a single prism, so a judicious combination of both constraints may lead to solutions characterized by regions with virtually constant estimated density contrasts separated by sharp discontinuities. The method has been applied to synthetic data from simulated intrusive bodies in sediments, presenting flat and horizontal tops. By comparing our results with those obtained with the smoothness constraint, we show that both methods produce good and equivalent locations of the sources' central positions, but the entropic regularization delineates the boundaries of the bodies with greater resolution. Both the proposed and the global smoothness constraints have been applied to real anomalies from the eastern Alps, and from the Matsitama intrusive complex, northeastern Botswana. In the first case, the entropic regularization delineates two sources with horizontal and nearly flat top being consistent with the known geological information. In the second case, both constraints produced virtually the same estimate indicating, in agreement with results of synthetic tests, that the tops of the sources are neither flat nor horizontal.
GP53A-07
Determining the optimal Bouguer density for a gravity data-set
Two methods are commonly adopted to evaluate the optimal Bouguer density for a given data-set, starting from different data characteristics or geological regime, giving in many cases different results. We propose some simple extension of these methods in order to make their results compatible. To this aim, we have used free-air gravity satellite data from Geosat and ERS-1 missions in order to compile a Bouguer gravity map of the Mediterranean Sea. The complete Bouguer correction has been applied by using the method of Parker (1972), that acts in the Fourier domain and allows for an exact evaluation of the gravity contribution from an highly sampled topographic model of the land. The density used for the Bouguer reduction has been obtained thus from the gravity data-set itself, by using two different optimization methods that have given the same optimal result of 2400 kg/m3. We have studied the radial power spectrum of the data, choosing the optimal Bouguer density as the one that minimizes its slope, i.e. the fractal dimension of the resulting gravity map in the band of wavelength from 45 km to 105 km. The second approach consists of studying the correlation between topography and Bouguer anomaly by spatial crossplots for a significant sub-set of the data. In the past these methodologies were applied alternatively since they gave different optimization values, especially the second method that seems to ignore large-wavelength isostatic effects. The main novelty of our work is represented by the combined application of both the approaches having as common goal the reduction of the short-wavelength effects of topography in the gravity map. Actually we have revisited both the methodologies, proposing slight modifications to make their efforts compatible. Their coincident results confirm their validity of application and give reliability to the recovered value of the Bouguer optimal density. As a first result we have obtained a revised Bouguer map for the Mediterranean Sea, that is useful for large-scale geological studies. Moreover, studying the correlation between Bouguer anomaly and bathymetry, we propose the compilation of a new interpretative tool that may be considered a sort of normalized correlation map defining the 2D isostatic setting of the investigated region, without introducing any lithospheric model. In a direct way we have found that the over-all region seems to be in a complete isostatic equilibrium apart from the young basins of Tyrrhenian Sea and Aegean Sea, confirming previous similar results.