Luis A. Gallardo

Cross-gradients joint 3D inversion with applications to gravity and magnetic data

We extend the cross-gradient methodology for joint inversion to three-dimensional environments and introduce a solution procedure based on a statistical formulation and equality constraints for structural similarity resemblance. We apply the proposed solution to the joint 3D inversion of gravity and magnetic data and gauge the advantages of this new formulation on test and field-data experiments. Combining singular-value decomposition (SVD) and other conventional regularizing constraints, we determine 3D distributions of the density and magnetization with enhanced structural similarity. The algorithm reduces some misleading features of the models, which are introduced commonly by conventional separate inversions of gravity and magnetic data, and facilitates an integrated interpretation of the models.

A quadratic programming approach for joint image reconstruction: mathematical and geophysical examples

Although a comparative analysis of multiple images of a physical target can be useful, a joint image reconstruction approach should provide better interpretative elements for multi-spectral images. We present a generalized image reconstruction algorithm for the simultaneous reconstruction of band-limited images based on the novel cross-gradients concept developed for geophysical imaging. The general problem is formulated as the search for those images that stay within their band limits, are geometrically similar and satisfy their respective data in a least-squares sense. A robust iterative quadratic programming scheme is used to minimize the resulting objective function. We apply the algorithm to synthetic data generated using linear mathematical functions and to comparative geophysical test data. The resulting images recovered the test targets and show improved structural semblance between the reconstructed images in comparison to the results from two other conventional approaches.

New insights into Archean granite-greenstone architecture through joint gravity and magnetic inversion

Archean tectonic evolution and metallogenic endowment in cratonic areas are intrinsically linked to lithological diversity and complex architectures. Unfortunately, reliable models of the deep structure of such areas are scarce due to poor surface exposure and limited availability of drill holes and high-resolution geophysical information. By combining multiple geophysical data sets, the strategy of cross-gradient joint geophysical inversion permits improved subsurface imaging of geological heterogeneity and structure. In this work we showcase the application of cross-gradient joint inversion of gravity and magnetic data to characterize the heterogeneity of the Leonora district in the eastern Yilgarn Craton, Western Australia. Our results harmonize both geophysical data types into integrated images of the top 15 km of the crust and successfully predict observations made by a seismic experiment and surface geological mapping.

Crustal structure of the northern Menderes Massif, western Turkey, imaged by joint gravity and magnetic inversion

In western Anatolia, the Anatolide domain of the Tethyan orogen is exposed in one of the Earth’s largest metamorphic core complexes, the Menderes Massif. The Menderes Massif experienced a two-stage exhumation: tectonic denudation in the footwall of a north-directed Miocene extensional detachment, followed by fragmentation by E–W and NW–SE-trending graben systems. Along the northern boundary of the core complex, the tectonic units of the Vardar–Izmir–Ankara suture zone overly the stage one footwall of the core complex, the northern Menderes Massif. In this study, we explore the structure of the upper crust in the northern Menderes Massif with cross-gradient joint inversion of gravity and aeromagnetic data along a series of 10-km-deep profiles. Our inversions, which are based on gravity and aeromagnetic measurements and require no geological and petrophysical constraints, reveal the salient features of the Earth’s upper crust. We image the northern Menderes Massif as a relatively homogenous domain of low magnetization and medium to high density, with local anomalies related to the effect of interspersed igneous bodies and shallow basins. In contrast, both the northern and western boundaries of the northern Menderes Massif stand out as domains where dense mafic, metasedimentary and ultramafic domains with a weak magnetic signature alternate with low-density igneous complexes with high magnetization. With our technique, we are able to delineate Miocene basins and igneous complexes, and map the boundary between intermediate to mafic-dominated subduction–accretion units of the suture zone and the underlying felsic crust of the Menderes Massif. We demonstrate that joint gravity and magnetic inversion are not only capable of imaging local and regional changes in crustal composition, but can also be used to map discontinuities of geodynamic significance such as the Vardar–Izmir–Ankara suture and the West Anatolia Transfer Zone.

Geometry of ophiolites in eastern Cuba from 3D inversion of aeromagnetic data, constrained by surface geology

This study combined geophysical, geologic, and topographic information to investigate the Mayari-Baracoa ophiolitic belt in eastern Cuba. A recently developed interpretation technique for 3D inversion of magnetic data was employed to determine the geometry at depth of ophiolitic and other rocks. Based on measured susceptibilities, lithologies were divided into four groups. The geophysical data allowed 3D imaging of ophiolites (serpentinized peridotites and gabbros), as well as sedimentary and volcanic rocks. The study verified that both the Pinares de Mayari Plateau and the Sagua de Tanamo Basin have been strongly influenced by tectonic activity. The modeling showed evidence of more east-west structural deformation of the ophiolite belt than had been previously reported. The depth of the depocenter of the Sagua de Tanamo basin and its rate of subsidence were determined. We identified some areas with potential for economic deposits of chromium, cobalt, and nickel, as well as precious metals; these were related to the thickness of the peridotite layer. The modeling also corroborated the presence of previously mapped faults and revealed other previously unrecognized faults.

Joint Interpretation of Maps Using Gradient Directions, Cross and Dot‐Product Values to Determine Correlations Between Bathymetric and Gravity Anomaly Maps

We present the results of joint image interpretation method application to determine correlations between spatially distributed data sets. This method uses angles between gradients, cross and dot-products values maps and their statistical distribution as criteria to evaluate correlations between images. We applied this method to investigate the relations between free-air gravity anomaly (FA) and bathymetry maps. Two synthetic models were created to test and evaluate methods main results. Obtained results allowed us to develop qualitative and quantitative criteria to evaluate correlations in data spatial distribution. We applied this method for the southern segment of Eastern-Brazilian coast. Based on the developed criteria we can conclude that for the studied region the observed FA are strongly correlated with the bathymetry. Method and the obtained results are discussed.

Two dimensional cross-gradient joint inversion of gravity and magnetic data sets constrained by airborne electromagnetic resistivity in the Capricorn Orogen, Western Australia

In many geological scenarios, the interpretation of multiple geophysical datasets through the use of joint inversion has become a common practice provided all data share compatible spatial resolution. Unfortunately, this requirement has also limited the application of airborne electromagnetic (AEM) data in joint inversion. For instance, we commonly assume that airborne gravity and magnetic datasets largely originate at a depth of a few kilometres, whereas co-located AEM signals can only penetrate a few hundred metres, thus rendering spatially incompatible datasets. We believe, however, that a fraction of these datasets originate from the same structures and provide a common ground for structural joint inversion strategies. We aim to explore the viability of jointly inverting such datasets using potential and AEM field data acquired in Western Australia with three comparative experiments. First, we generate conventional 2D separated models for each dataset to gauge their individual resolution capability. We then perform the 2D cross-gradient joint inversion of gravity and magnetic datasets. Finally, we adapt the structural joint inversion to include the AEM resistivity model as a constraint. We show that there is an area commonly sensed by the three datasets and that the coupled resolution influences both shallow and deep structures of the joint models. This yields a coherent integrated interpretation of shallow and deep structures of the studied section, which is validated when compared to a nearby seismic traverse section. Airborne collection of electromagnetic and potential field data is a common strategy for extensive resource exploration and reconnaissance. Since these datasets contain information about different properties at different depths, they are normally considered complementary and are interpreted separately. Using airborne data acquired in Western Australia, we explore the viability of their joint inversion and show the advantages of their combined analysis and interpretation.

Cross-gradients joint inversion of disparate geophysical data for improved subsurface characterization: multiple-physics field examples

The characterization and monitoring of hydrogeological and other complex subsurface processes requires a detailed knowledge of several properties of the composing rocks and fluids. Whilst some of these properties can be measured directly, other properties have to be estimated by indirect measurements such as geophysical data. However, it is not uncommon that the geophysical data yield models of limited accuracy that may not contribute significantly to our understanding of the subsurface processes. Interestingly, the distribution of apparently uncorrelated physical properties seems to be controlled by common subsurface attributes that, when taken into account, can improve the accuracy and meaning of the otherwise independent geophysical models. For instance, a highly porous rock that is saturated with water can be sharply defined by a combined low seismic velocity-low electrical resistivity area. However, such a correlation can not be generalised to different environments. An outstanding feature of the subsurface that is common to the geophysical data is the geometrical distribution of the physical properties which can be measured by the physical property changes. This condition of commonality can be incorporated in the process of estimation to obtain meaningful and more reliable subsurface models in a process of joint inversion. In this work I define the joint inversion of disparate geophysical data as the search of those models that satisfy their respective geophysical data in a least squares sense and are geometrically similar. I quantify the geometrical similarity with the null values of the cross-products of the gradients of two physical properties and pose solutions for these objective functions that account for multiple-physics models (P- and S-wave velocities as well as DC- and MT- resistivity). I present several test and field examples that show the improvements attained in parameter accuracy and geometrical resemblance as well as their implications for petrophysical and structural associations for several near-surface field sites.