3D Convolution Conjugate Gradient Inversion of Potential Fields in Acoculco Geothermal Prospect, Mexico

Potential field data have long been used in geophysical exploration for archeological, mineral, and reservoir targets. For all these targets, the increased search of highly detailed three-dimensional subsurface volumes has also promoted the recollection of high-density contrast data sets. While there are several approaches to handle these large-scale inverse problems, most of them rely on either the extensive use of high-performance computing architectures or data-model compression strategies that may sacrifice some level of model resolution. We posit that the superposition and convolutional properties of the potential fields can be easily used to compress the information needed for data inversion and also to reduce significantly redundant mathematical computations. For this, we developed a convolution-based conjugate gradient 3D inversion algorithm for the most common types of potential field data. We demonstrate the performance of the algorithm using a resolution test and a synthetic experiment. We then apply our algorithm to gravity and magnetic data for a geothermal prospect in the Acoculco caldera in Mexico. The resulting three-dimensional model meaningfully determined the distribution of the existent volcanic infill in the caldera as well as the interrelation of various intrusions in the basement of the area. We propose that these intrusive bodies play an important role either as a low-permeability host of the heated fluid or as the heat source for the potential development of an enhanced geothermal system.

Mapping Main Structures and Related Mineralization of the Arabian Shield (Saudi Arabia) Using Sharp Edge Detector of Transformed Gravity Data

Saudi Arabia covers most of the Arabian Peninsula and is characterized by tectonic regimes ranging from Precambrian to Recent. Using gravity data to produce the lateral boundaries of subsurface density bodies, and edge detection of potential field data, a new subsurface structural map was created to decipher the structural framework controls on the distribution of gold deposits in Saudi Arabia. Moreover, we detected the relationships between major structures and mineral accumulations, thereby simultaneously solving the problem of edge detectors over complex tectonic patterns for both deeper and shallower origins. Analytic signal (ASg), theta map (TM), TDX, and softsign function (SF) filters were applied to gravity data of Saudi Arabia. The results unveil low connectivity along the Najd fault system (NFS) with depth, except perhaps for the central zones along each segment. The central zones are the location of significant gold mineralization, i.e., Fawarah, Gariat Avala, Hamdah, and Ghadarah. Moreover, major fault zones parallel to the Red Sea extend northward from the south, and their connectivity increases with depth and controls numerous gold mines, i.e., Jadmah, Wadi Bidah, Mamilah, and Wadi Leif. These fault zones intersect the NFS in the Midyan Terrane at the northern part of the AS, and their conjugation is suggested to be favorable for gold mineralization. The SF maps revealed the boundary between the Arabian Shield and Arabian Shelf, which comprises major shear zones, implying that most known mineralization sites are linked to post-accretionary structures and are not limited to the Najd fault system (NFS).

Potential field data interpolation by Taylor series expansion

Data interpolation is critical in the analysis of geophysical data when some data is missing or inaccessible. We propose to interpolate irregular or missing potential field data using the relation between adjacent data points inspired by the Taylor series expansion (TSE). The TSE method first finds the derivatives of a given point near the query point using data from neighboring points, and then uses the Taylor series to obtain the value at the query point. The TSE method works by extracting local features represented as derivatives from the original data for interpolation in the area of data vacancy. Compared with other interpolation methods, the TSE provides a complete description of potential field data. Specifically, the remainder in TSE can measure local fitting errors and help obtain accurate results. Implementation of the TSE method involves two critical parameters – the order of the Taylor series and the number of neighbors used in the calculation of derivatives. We have found that the first parameter must be carefully chosen to balance between the accuracy and numerical stability when data contains noise. The second parameter can help us build an over-determined system for improved robustness against noise. Methods of selecting neighbors around the given point using an azimuthally uniform distribution or the nearest-distance principle are also presented. The proposed approach is first illustrated by a synthetic gravity dataset from a single survey line, then is generalized to the case over a survey grid. In both numerical experiments, the TSE method has demonstrated an improved interpolation accuracy in comparison with the minimum curvature method. Finally we apply the TSE method to a ground gravity dataset from the Abitibi Greenstone Belt, Canada, and an airborne gravity dataset from the Vinton Dome, Louisiana, USA.

Estimating the Extreme Values in Gridding Data using Gauss Elimination Method: A New Approach in Potential Field Processing

The position of a maximum point of a function depends on its coefficients and order. The maximum horizontal gradient method is a popular method that greatly contributes to the detection of maximum points and approximation of geological structures edges. By adopting a mathematical logic, Blakely and Simpson established a quadratic function based on the characteristic of three points of a straight line in the fundamental directions. However, for potential field data like gravity and magnetic data, the coefficients of a quadratic function in each direction are not only dependent on the values of three points on a straight line, but also, they depend on the values of the surrounding points. This article proposes an algorithm which can detect maximum points more effectively in order to delineate geological structures boundaries from potential field data. The proposed algorithm uses a 3×3 neighborhood data grid to establish a two-variables function and to determine its coefficients by applying the Gaussian elimination method. After the two-variables function has been established, the algorithm estimates any extreme points and their positions from a set of four single-variable functions which correspond to the horizontal, vertical and the two diagonal directions by the cases x = 0, y = 0, y = -x and y = x of the main function. Finally, the conditions to detect the maximum point from the extreme points are defined. The validity of the algorithm was demonstrated on synthetic datasets generated by two different model structures. A real data application of the method has also been realized by estimating the geological boundaries by gravity data in the Vietnam’s continental shelf. The results obtained from the synthetic applications of the algorithm proved that it can determine more maximum points as compared to Blakely and Simpson method, and as a result, in all the test cases, it has drawn the real boundaries of the model structures more accurately. The application results of the method on real data revealed new boundary delineations in the research area, interpreted to be faults or fractures which lies between deep trench in the East Vietnam Sea.

Structural, petrophysical, and geological constraints in potential field inversion using the Tomofast-x v1.0 open-source code

The quantitative integration of geophysical measurements with data and information from other disciplines is becoming increasingly important in answering the challenges of undercover imaging and of the modelling of complex areas. We propose a review of the different techniques for the utilisation of structural, petrophysical, and geological information in single physics and joint inversion as implemented in the Tomofast-x open-source inversion platform. We detail the range of constraints that can be applied to the inversion of potential field data. The inversion examples we show illustrate a selection of scenarios using a realistic synthetic data set inspired by real-world geological measurements and petrophysical data from the Hamersley region (Western Australia). Using Tomofast-x's flexibility, we investigate inversions combining the utilisation of petrophysical, structural, and/or geological constraints while illustrating the utilisation of the L-curve principle to determine regularisation weights. Our results suggest that the utilisation of geological information to derive disjoint interval bound constraints is the most effective method to recover the true model. It is followed by model smoothness and smallness conditioned by geological uncertainty and cross-gradient minimisation.

Insights and Lessons from 3D Geological and Geophysical Modeling of Mineralized Terranes in Tasmania

Over the last two decades, Mineral Resources Tasmania has been developing regional 3D geological and geophysical models for prospective terranes at a range of scales and extents as part of its suite of precompetitive geoscience products. These have evolved in conjunction with developments in 3D modeling technology over that time. Commencing with a jurisdiction-wide 3D model in 2002, subsequent modeling projects have explored a range of approaches to the development of 3D models as a vehicle for the better synthesis and understanding of controls on ore-forming processes and prospectivity. These models are built on high-quality potential field data sets. Assignment of bulk properties derived from previous well-constrained geophysical modeling and an extensive rock property database has enabled the identification of anomalous features that have been targeted for follow-up mineral exploration. An aspect of this effort has been the generation of uncertainty estimates for model features. Our experience is that this process can be hindered by models that are too large or too detailed to be interrogated easily, especially when modeling techniques do not readily permit significant geometric changes. The most effective 3D modeling workflow for insights into mineral exploration is that which facilitates the rapid hypothesis testing of a wide range of scenarios whilst satisfying the constraints of observed data.

Integration of magnetic, gravity, and well-logging data interpretation to delineate the structural framework and formation evaluation of Bahariya Formation, North Diyur area, northern Western Desert, Egypt

The Bahariya Formation in Egypt's Western Desert is a major source for minerals and hydrocarbon accumulation. It is also characterized by a relatively high radiation content because it contains iron oxide deposits that attract radioactive elements. The main objectives of our study are to establish depth to basement, basement configuration and related structural elements, and thickness and configuration of the overlain sedimentary section. In addition to the analysis of well-logging data, many advanced techniques have been applied to analyze magnetic and gravity data, including depth estimation, 2D magnetic and gravity modeling, and 3D inversion of potential field data. By integrating all available data, we can determine the structural control of the study area and evaluate the subsurface parameters. Well logging has been used for interpretation of porous and permeable zones, water saturation calculation, and basic lithology identification. The depth to basement in our study ranges from −1700 to −4500 m. The basement is shallow in the northern parts of the study area and deeper in the southern parts. The main clay minerals of the formation are montmorillonite, chlorite, and a mixed clay layer. The Bahariya Formation is composed mainly of sandy clay and sandstone, and therefore it is considered an excellent reservoir.