Cross-gradient Joint Inversion Research Articles

Use of three-dimensional crossgradient joint inversion of marine controlled-source electromagnetic (CSEM) and seismic refraction data for overburden geohazards mapping.

Offshore energy-transition activities typically require the construction of new subsurface facilities where overburden heterogeneity and deformation pattern may not be fully understood. Anisotropic marine controlled-source electromagnetic (CSEM) and seismic refraction imaging can be adapted to geohazards assessment of the overburden to mitigate safety and costs risks in such areas. This is investigated using an area in deepwater NW Borneo as the type-example. For this proof-of-concept study, a well-established Multiphysics joint inversion code was extended to handle marine seismic refraction data from conventional towed streamers. Realistic field-scale synthetic models with anomalous resistivities and velocities in the shallow section (∼50-200 m below mudline) were built and their CSEM and seismic refraction responses were first inverted separately and then jointly in 3D using the crossgradient method. The joint inversion recovered the anomalous bodies better than the separate inversions. The velocity model from the joint inversion showed improvement from the separate inversion but required a good starting model. As a further test of the methodology, first-break travel times were picked from legacy 3D seismic data and inverted with the available sparse CSEM data. For model verification, resistivity and velocity profiles from separate and joint inversion models were extracted at a well location in the survey area and compared with actual well logs. The joint inversion models matched the well logs better than the separate inversion models. Moreover, known geohazards (complex fault-sets and lateral-inflows) from independent geomatic study were imaged in the joint inversion models. Also, the resistivity anisotropy ratio tracked anomalous zones that correspond to zones of recent complex faulting and potential lateral inflows in the overburden mass transport systems. Thus, joint inversion of CSEM and seismic refraction data has potential to improve the mapping of overburden hazards offshore, with the associated resistivity anisotropy serving as a proxy for active ground deformation.

Cross-gradient joint inversion and clustering of ERT and SRT data on structured meshes incorporating topography

Summary The combination of electrical resistivity and seismic refraction tomography is a common practice for the characterization of subsurface features. Presently, the cross-gradient inversion scheme stands out as one of the most robust joint approaches, and some authors modified it to manage complex topographies on unstructured meshes even if at the expense of introducing additional parameters in the inversion process. We propose in this work a cross-gradient algorithm for jointly inverting electrical and seismic tomographic data on structured meshes in cases with non-flat topography. The proposed approach preserves the benefit of the classical cross-gradient approach without the need to impose physical length scales, as for irregular meshes. The quality of the results is evaluated in comparison with independent inversion through a new standardized cross-gradient index and a fuzzy c-means analysis that provides an assessment of the reconstruction accuracy through the membership function. The proposed method was applied to both synthetic models and field-scale examples located in Central Italy, where an accurate geophysical reconstruction is needed for the rehabilitation of existing dams. For all cases, joint inversion yielded superior results compared to independent inversion, demonstrating better agreement with available borehole data. The effectiveness of the joint approach was also demonstrated by the post-inversion tools, where the new cross-gradient index highlighted changes in structural similarity whilst fuzzy c-means clustering allowed for a quantitative reconstruction (position and shape) of the main units at the sites, facilitating the detection of site layering modifications.

Binary structure constrained gravity inversion based on seismic first arrival travel time data

Gravity exploration method is one of the important methods for deep mineral resource exploration, but gravity data inversion has limited resolution ability in the vertical direction. In order to improve the vertical resolution of gravity data inversion, we propose a binary structure constrained gravity inversion method based on seismic first arrival travel time data. This method effectively reconstructs a density model with high vertical resolution by transferring the structural information of a high-resolution velocity model reconstructed by seismic data inversion to gravity data inversion through the binary structure constrained technique. This strategy eliminates the need to integrate both gravity and seismic methods into a single inversion framework, avoiding both the difference in convergence speeds between the two methods, as well as getting rid of the complexity associated with calculating structural coupling terms. Theoretical simulations show that the fuzzy c-means cluster analysis technique can accurately extract the target region of the velocity model reconstructed by seismic data inversion. Under the constraint of seismic structural information, the resolution of reconstructed density model is much higher than that of separate gravity data inversion, which proves that high resolution seismic information can improve the vertical resolution of gravity data inversion. Compared with the traditional cross-gradient joint inversion, the binary structure constrained gravity inversion method can further improve the resolution of the density model, especially in the reconstruction of the anomaly interface, which verifies that the method has certain effectiveness.

Gravity inversion with a binary structure constraint imposed by magnetotelluric data and its application to a Carlin-type gold deposit

With characteristics of low cost and high efficiency, the gravity method is one of the most important means for the deep exploration of mineral resources. However, due to its inherent physical properties, its inversion results provide a limited vertical resolution. To reduce the uncertainty of gravity inversion, it is necessary to impose constraints from other geophysical methods, drilling, or geologic models. Based on the high vertical resolution of the multifrequency magnetotelluric (MT) data, we have developed a novel 2D gravity inversion method with a binary structure constraint imposed by MT data. The guided model is the density model reconstructed by the cross-gradient joint inversion of MT and gravity data, and the target and background regions of the guided model are divided using a fuzzy c-means clustering algorithm. The obtained binary target-background model is used as a structural constraint of the gravity inversion. The gravity inversion changes the density values of the target region rather than the background region, which can significantly reduce the dimensions of the inversion solution equation. The experimental results demonstrate that, even if the resistivity model and the density model indicate an inconsistent structure, the binary structure-constrained gravity inversion can reconstruct the density model with a higher degree of resolution than the traditional gravity inversion and cross-gradient joint inversion. Finally, we apply this algorithm to density modeling for the exploration of Carlin-type gold deposits in the southeast of the Jilin province, China, where the image determines the distribution of deep Paleoproterozoic Formation and high-density deposits, providing important technical support for the exploration of Carlin-type gold deposits.

Fast 3D joint inversion of gravity and magnetic data based on cross gradient constraint

The gravity and magnetic data can be adopted to interpret the internal structure of the Earth. To improve the calculation efficiency during the inversion process and the accuracy and reliability of the reconstructed physical property models, the triple strategy is adopted in this paper to develop a fast cross-gradient joint inversion for gravity and magnetic data. The cross-gradient constraint contains solving the gradients of the physical property models and performing the cross-product calculation of their gradients. The sparse matrices are first obtained by calculating the gradients of the physical property models derived from the first-order finite difference. Then, the triple method is applied to optimize the storages and the calculations related to the gradients of the physical property models. Therefore, the storage compression amount of the calculations related to the gradients of the physical property models and the cross-gradient constraint are reduced to one-fold of the number of grid cells at least, and the compression ratio increases with the increase of the number of grid cells. The test results from the synthetic data and field data prove that the structural coupling is achieved by using the fast cross-gradient joint inversion method to effectively reduce the multiplicity of solutions and improve the computing efficiency.

An Efficient Cross-Gradient Joint Inversion Algorithm for Gravity and Magnetic Data Using a Sequential Strategy

The joint inversion methods of gravity and magnetic data have been presented in numerous literatures and implemented in many real applications. However, almost all of these existing methods still face the problem of low computational efficiency, although some targeted improvements have been put forwarded. To further address this issue, this study proposes an efficient algorithm for the joint inversion of gravity and magnetic data. The new algorithm is developed from the idea of structural coupling by using the cross-gradient function and employs a sequential strategy. A new formula for efficient minimization of the structural similarity term is derived innovatively, in which the minimization of the structural coupling term is obtained by a technical combination of an alternating strategy and the randomized singular value decomposition (RSVD) algorithm. Using the proposed new formula, the dimension of the original inverse problem can be reduced greatly. Furthermore, the RSVD algorithm is utilized to perform the independent inversion and determine an optimal regularization parameter. Several comparative tests on a synthetic example show that the proposed efficient method poses great advantage in efficiency compared with the conventional sequential cross-gradient joint inversion (CSCGJI) method. The proposed algorithm is also successfully applied to the real data from a metallic deposit area in Xinjiang province, China.

Cross-Gradient Joint Inversion of Gravity and Seismic Data With Triangular Grid Division by the Second-Order Finite-Difference Method

Cross-Gradient Joint Inversion of Gravity and Seismic Data With Triangular Grid Division by the Second-Order Finite-Difference Method

3-D Cross-Gradient Joint Inversion Method for Gravity and Magnetic Data With Unstructured Grids Based on Second-Order Taylor Formula: Its Application to the Southern Greater Khingan Range

3-D Cross-Gradient Joint Inversion Method for Gravity and Magnetic Data With Unstructured Grids Based on Second-Order Taylor Formula: Its Application to the Southern Greater Khingan Range

Data of Three-dimensional Cross-gradient Joint Inversion Method

Data of Three-dimensional Cross-gradient Joint Inversion Method

Data of Three-dimensional Cross-gradient Joint Inversion Method

Data of Three-dimensional Cross-gradient Joint Inversion Method

Interpretation of gravity and magnetic data on the hot dry rocks (HDR) delineation for the enhanced geothermal system (EGS) in Gonghe town, China

As a new kind of renewable and environmental-friendly energy to generate electricity, hot dry rocks (HDR) geothermal reservoirs have been studied, along with the enhanced geothermal system (EGS). Geophysical methods have been used for the geological characterisation in different scales. The small-scale geophysical data are required for the local geological analysis so as to provide prior information for HDR modelling. Gonghe basin is in the northeast margin of the Qinghai–Tibet Plateau. Several drilling records indicate that this basin is a potential HDR prospecting area with high geothermal gradient, high heat flow and widespread igneous rock distribution, especially the Gonghe town (Qiabuqia) along with its neighbouring area. Gravity and magnetic surveys were carried out here. To better understand the areal and vertical distribution of the HDR, the gravity and magnetic data were inverted using 2D manual inversion and 3D cross-gradient joint inversion based on the smooth $${l}^{0}$$ norm constraint of minimum support functional stabiliser. The 2D model showed the sedimentary cap with a thickness of around 1000–1500 m. Granites of different periods and intrusion process were widely distributed and underlined the sediments accompanied by some deep faults. As for the HDR delineation, 3D models showed a potential area along Gonghe town and Dongba. The density and susceptibility were estimated at over 2.6 g/cm3 and 4 × 10–3 SI separately, when referred with exiting HDR distribution along the geological profile of DR4–QR1–DR3–DR2 wells. The upper boundary of HDR was outlined at the depth of around 2000 m, and the volume of HDR was then estimated around 6100 km3 above 3500 m depth. The appearance of the density and susceptibility models was affected by the lithology, stress and hydrothermal alteration. More precise geophysical methods including the microgravity, seismic and MT (magnetotelluric) surveys would be more applicable at the HDR exploitation stage.

Gravity-magnetic cross-gradient joint inversion by the cyclic gradient method

In this paper, we consider a joint-inversion problem using different types of geophysical data: gravity and magnetism. We first formulate two kinds of inverse problems in the famework of the first kind Fredholm integral equations, and then build up a sparse inversion model combining the two inverse problems as well as the cross-gradient term. The cyclic gradient method for quadratic function minimization is extended for solving the corresponding optimization problem. We update the stepsizes in a cyclic way, by combining the approximated Cauchy steps and the fixed steplengths. Theoretical analysis shows that the algorithm converges R-linearly. Experimental tests show that the proposed joint inversion sparse model as well as the proposed cyclic gradient method improve the numerical performances effectively, compared to the state of the art.

Structurally tailored 3D anisotropic controlled-source electromagnetic resistivity inversion with cross-gradient criterion and simultaneous model calibration

Geologic interpretation of 3D anisotropic resistivity models from conventional marine controlled-source electromagnetic (CSEM) data inversion faces difficulties in low-resistivity contrast sediments and structurally complex environments that typify the new frontiers for hydrocarbon exploration. Currently, the typically reconstructed horizontal resistivity [Formula: see text] and vertical resistivity [Formula: see text] models often have conflicting depth structures that are difficult to explain in terms of subsurface geology, and the resulting resistivities may not be close to the true formation resistivities required for estimating reservoir parameters. We have investigated the concept that an objective geologically oriented or structurally tailored inversion can be achieved by requiring that the cross-product of the gradient of horizontal resistivity and the gradient of the vertical resistivity is equal to zero at significant geologic boundaries. We incorporate this boundary-shape criterion in our 3D inverse problem formulations, implemented within nonlinear model-space and conjugate-gradient contexts, for cases in which a priori calibration data from wells and/or seismically derived subsurface boundaries are available and for cases in which these are lacking. The resulting fit-for-purpose solutions serve to better analyze the peculiarity of a given data set. We applied these algorithms to synthetic and field CSEM data sets representing a fold-thrust environment with low-resistivity and low-contrast sediments. The resulting [Formula: see text] and [Formula: see text] models from cross-gradient joint inversion of synthetic data of appropriate frequency bandwidth without a priori information are structurally similar and consistent with the test models, whereas those from the inversions of band-limited field data are consistent with the available seismic and resistivity well-log data. This particular approach will thus be useful for lithologic correlation in frontier regions with limited a priori information using broadband CSEM data. For these band-limited field data, we found that the anisotropic bulk resistivities of the low-contrast sediments are better determined by incorporating a priori calibration data from triaxial resistivity logs and seismic horizons.

Formation and evolution of Paleoproterozoic orogenic belt in southern Jilin, Jiao–Liao–Ji Belt, North China Craton: Constraints from geophysics

The tectonic setting and depositional environments of the Laoling and Ji’an groups in the northeastern Jiao–Liao–Ji Belt, northeastern China, are controversial. These Paleoproterozoic stratigraphic units are exposed sporadically (in Baishan and Tonghua) beneath a thick cover of Quaternary basalts, meaning that only limited information can be obtained by traditional geological methods. Therefore, using geophysical techniques in this region is pertinent. Here we present new data on the petrophysical properties (density, magnetic susceptibility, and specific resistivity) obtained from 2D cross-gradient joint inversion profiles. The results allow us to establish the relationships between the Laoling and Ji’an groups, interpret the tectonic setting of deposition, and locate the subsurface margins of the Jiao–Liao–Ji Belt. Petrophysical parameters from the Dataishan Formation (density of 2.58 g/cm3, zero magnetic susceptibility, and specific resistance of 103.04 Ω m) indicate that these rocks were derived predominantly from the Longgang Block in the north. For the Zhenzhumen Formation, the petrophysical parameters (high density, weak magnetic susceptibility, and high specific resistivity) are consistent with deposition in a passive margin that received detrital material sediments from the Longgang Block and the Liaoji granitoids. The Mayihe and Huangchagou formations (intermediate to high density, strong magnetic susceptibility, and intermediate specific resistivity) were deposited closer to a magmatic arc, with the detritus derived from the Liaoji granitoids. The low to intermediate density, stronger magnetic susceptibility, and intermediate specific resistivity of the Huashan–Linjiang, Dalizi, and Dadongcha formations indicate that these rocks were deposited in a pre-orogenic setting, with the detritus derived from the Longgang Block, Liaoji granitoids, and other felsic igneous rocks. Based on the geophysical profiles, we conclude that the Jiao–Liao–Ji Belt extends under Quaternary basalt, from Linjiang to Baishan, and eastward towards North Korea. Two basin-controlling faults (F1 and F2) represent the northern and eastern boundaries between the Longgang Block and the Jiao–Liao–Ji Belt. We interpret geophysical anomalies and variations in the petrophysical parameters in the context of subduction and collision processes.

Structure of the Cerro Prieto Pull-apart basin from joint inversion of gravity, magnetic and magnetotelluric data

The large transform fault system that separates the Pacific and the North American plates in the Gulf of California is conformed by a system of oblique rifts and large dextral transform faults. Besides their seismogenic importance, several of these structures are related to geothermal resources in the area. This system originates the Cerro Prieto Pull-apart basin (CPPAB), which is particularly important as it hosts the world's third largest geothermal field. It is remarkable that, despite intensive geological and geophysical exploration in the CPPAB, there is no published geophysical image of the basin that gives clear evidence of the underlying basement and the existence of an active pull-apart basin and whether it may be the source of heat of the reservoir. We posit that the joint inversion of multiple geophysical data can unveil the underlying CPPAB structure. We then applied the cross-gradient joint inversion to recently collected gravity, magnetic and magnetotelluric data on three intersecting profiles. From the joint models, we could clearly distinguish the major geometry of the basin and classify the basement units by their characteristic geophysical signatures, as well as propose the occurrence of various suites of intrusives. The interpreted models correlate well with surface geology and geophysical maps and depict a likely structure for the active pull apart basin in the area.

Integrated 2D joint inversion models of gravity, magnetic, and MT for geothermal potentials: a case study from Gujarat, India

Joint Inversion of different geophysical potentials promises to reduce chances of uncertainties which are more probable in case of independent inversions. In this paper, cross-gradient Joint Inversion was applied for gravity, magnetic, and MT data to understand the subsurface geothermal potential in Dholera and Unai, Gujarat, India. This paper narrates the understanding of individual inversion for gravity, magnetic, and MT data followed by joint inversion to delineate more clear understanding of geological and geothermal bodies in the subsurface. To formulate data space, a generalized cross-gradient inversion for data set and model set parameters are discussed. On the basis of the algorithm proposed, an integrated subsurface model for Dholera and Unai was prepared which depicts geological as well as lithological characteristics of the area. For the structural coupling, a Lagrange data multiplier was applied in an iterative manner to reach a global minima. Fluid flow models of Dholera and Unai were prepared where “J” type drilling is suggested up to a depth of 800 m and 700 m, respectively.

Structurally based joint inversion of electromagnetic, seismic and potential field data for improved classification and characterization: Field examples from the vadose zone

A key strategy to characterize subsurface materials is the integrative analysis of tomograms of several physical properties provided by different geophysical data. Among the recent strategies to produce these tomograms is the joint inversion. Unfortunately, most joint inversion techniques are based on hypothetical property relationships that hinder the site-specific property correlations that characterize individual materials. Differently, a recently developed cross-gradient joint inversion technique is underpinned by the hypothesis of structural resemblance and permits the coexistence of natural property correlations that provide the key to unravel the signatures of subsurface materials. In the present work, electromagnetic, seismic and potential field data are jointly inverted for several field sites with near surface targets. The results show not only a clearer disposition of the mapped units in structural terms, but also a sound evidence of their actual fluid-mineral characteristics. In general, the results demonstrate the power of analyzing multiple-property images when they are structurally consistent.

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.

An efficient sequential strategy for realizing cross-gradient joint inversion: method and its application to 2-D cross borehole seismic traveltime and DC resistivity tomography

An efficient sequential strategy for realizing cross-gradient joint inversion: method and its application to 2-D cross borehole seismic traveltime and DC resistivity tomography

2D data-space cross-gradient joint inversion of MT, gravity and magnetic data

We have developed a data-space multiple cross-gradient joint inversion algorithm, and validated it through synthetic tests and applied it to magnetotelluric (MT), gravity and magnetic datasets acquired along a 95km profile in Benxi-Ji'an area of northeastern China. To begin, we discuss a generalized cross-gradient joint inversion for multiple datasets and model parameters sets, and formulate it in data space. The Lagrange multiplier required for the structural coupling in the data-space method is determined using an iterative solver to avoid calculation of the inverse matrix in solving the large system of equations. Next, using model-space and data-space methods, we inverted the synthetic data and field data. Based on our result, the joint inversion in data-space not only delineates geological bodies more clearly than the separate inversion, but also yields nearly equal results with the one in model-space while consuming much less memory.