Joint Inversion Algorithm Research Articles

Innovative imaging of iron deposits using cross‐gradient joint inversion of potential field data with petrophysical correlation

AbstractThis study demonstrates the application of the cross‐gradient joint inversion method to investigate iron mineralization zones within a volcano‐sedimentary environment. The presence of minerals with intense contrasts in density or magnetic susceptibility, such as hematite or magnetite, facilitates modelling the distribution of ore bodies with depth. Our approach involves establishing a unified interpretation of reconstructed density and susceptibility models through both independent and joint inversion with sparsity regularization in conjunction with a petrophysical model resulting from core data. This approach provides an ideal strategy to uncover the realistic geologic setting of iron ore deposits. We initially simulated a synthetic model closely resembling real‐case scenarios to assess the efficacy of the cross‐gradient joint inversion algorithm in comparison to independent inversion. Subsequently, the inversion algorithms were implemented on gravity and magnetic data, collected over an area of 500 × 600 m2 in Shavaz iron‐bearing deposits located in the central Iranian block. The primary iron oxide–apatite type mineralization in the study area is associated with the Nain–Dehshir–Baft fault as a NW–SE trending strike‐slip fault. Although both inversion methods yield satisfactory models, incorporating the cross‐gradient constraint in joint inversion resulted in a more constrained delineation of iron–oxide ore deposits in the fault system. This improvement facilitates the differentiation between hematite and a small percentage of magnetite, providing a more accurate estimation of ore depth. Inversion results suggest that the magnetite mineralization is coated with extensive hematite mineralization and both are positioned relatively within the same depth interval, covered by approximately a 15–25 m sequence of sediments.

Near-surface imaging by joint inversion of ERT and seismic traveltime data with guided FCM clustering

We present a novel joint inversion strategy for electrical resistivity tomography (ERT) and seismic first-arrival traveltime data with guided fuzzy c-means (GFCM) clustering coupling to increase the accuracy of inversion results and improve the characterization of heterogeneous near-surface materials. The physical parameter correlation between the resistivity and seismic velocity is enforced using a GFCM clustering coupling term in the objective function, which also includes misfit and regularization terms. The physical property models estimated by joint inversion are guided by the clustering centers of a priori petrophysical parameters. A limited-memory quasi-Newton approach is used to optimize the objective function. To validate the proposed approach and describe its implementation in detail, tests were first performed using two synthetic models. The stratigraphic structures recovered by joint inversion with GFCM clustering coupling are more consistent with the true model than those inverted by individual inversion, cross-gradient and fuzzy c-means (FCM) joint inversion. Furthermore, the physical parameters estimated using GFCM joint inversion are significantly more accurate than those estimated using individual inversion and the other two joint inversion methods. The joint inversion algorithm was applied to field data from the Liangzhu site in Hangzhou, China. The depth and shape of the stratigraphic interface imaged by GFCM joint inversion are consistent with the drilling results. However, when using individual inversion and the other two joint inversion methods, the recovered stratigraphic structures have some differences with the drilling data. Therefore, GFCM joint inversion is an effective and reliable method for near-surface fine imaging.

Joint Gramian inversion of gravity, magnetic and gravity gradient tensor data for the modelling of Mesoproterozoic iron oxide deposits, southeast Missouri, USA

SUMMARY Within the iron metallogenic province of southeast Missouri, USA, there are several mines that contain not only economic iron resources, magnetite and/or hematite, but also contain rare earth elements, copper and gold. An area including three major deposits, Pea Ridge, Bourbon and Kratz Spring, was selected for detailed modelling for the upper crustal magnetic susceptibility and density structures. For the study area, ground gravity and high-resolution airborne magnetic and gravity gradiometry data sets are available. An efficient and novel joint inversion algorithm for the simultaneous inversion of these multiple data sets is presented. The Gramian coupling constraint is used to correlate the reconstructed density and magnetic susceptibility models. The implementation relies on the structures of the sensitivity matrices and an efficient minimization algorithm to achieve significant reductions in the memory requirements and computational costs. Consequently, it is feasible to use a laptop computer for the inversion of multiple data sets, each containing thousands of data points, for the recovery of models on the study area, each including approximately one million model parameters. This is the first time that these multiple data sets have been simultaneously inverted for this area. The L1-norm stabilizer is used to provide compact and focused images of the ore deposits. For contrast, independent inversions of each data set are also discussed. In general, our results provide new insights about the concealed ore deposits in the Mesoproterozoic basement rocks of southeast Missouri. Both short- and long-wavelength anomalies exist in the recovered models; these provide a high-resolution image of the subsurface. The geometry and physical properties of the known deposits are determined very well. Additionally, some unknown concealed deposits are revealed; these could be economically valuable and should be considered in future geophysical and geological investigations.

Three-Dimensional Joint Inversion of the Resistivity Method and Time-Domain-Induced Polarization Based on the Cross-Gradient Constraints

The resistivity method and time-domain-induced polarization (TDIP) are two branches of electric exploration that are used to solve problems in mineral exploration, hydrogeology and engineering geology. In recent years, integrating different physical parameters for joint inversion to improve the accuracy of inversion results has been extensively examined; however, three-dimensional joint inversion of the two methods above has not been realized. To further address this issue, in this research, we used the limited-memory BFGS (L-BFGS) method to develop a three-dimensional joint inversion algorithm of the resistivity method and TDIP based on the cross-gradient constraints. In the new algorithm, the resistivity method and TDIP inversion were iteratively updated alternately to ensure that the inversion results can simultaneously meet the two conditions of obtaining minimum data misfits and finding structural similarity. The three-dimensional synthetic dataset inversion results showed that the models obtained by joint inversion are more accurate in the recovery of both the boundaries and the values of the anomalies. Especially in the background of high noise, joint inversion has higher resolution for the target body. The joint inversion algorithm was also successfully applied to a groundwater detection practice in Beijing, China, in which the practicability of the algorithm was confirmed.

Seismogenic Structure of the 2014 M6.5 Ludian Earthquake From Three‐Dimensional Joint Inversion of Magnetotelluric Data and Seismic Arrival Times

AbstractOn 3 August 2014, a destructive earthquake with a magnitude of 6.5 occurred in the Ludian region in Yunan, China, causing heavy casualties. However, the seismogenic structure of the Ludian earthquake is still unclear. To address this issue, we have developed a three‐dimensional joint inversion algorithm for magnetotelluric data and seismic body wave arrival times based on the cross gradient structural similarity constraint, which utilizes the complementary advantages of the two different datasets. We use arrival times of P‐ and S‐waves from 6,369 local earthquakes recorded by 30 seismic stations and magnetotelluric impedances from 127 MT stations to perform the joint inversion to construct a combined 3‐D P‐wave velocity (Vp), S‐wave velocity (Vs), and resistivity models and the locations of relocated aftershocks in the source region of the Ludian earthquake. Our models show significant low Vp/Vs ratios and low resistivity in the upper crust of the main shock zone, and the relocated aftershocks form an L‐shaped zone. Based on petrophysical studies and analysis of the cross‐plots of different physical properties, we infer the existence of cracks/fractures and fluids as well as high quartz contents in the source region. These fluids may play a key role in promoting the Ludian earthquake by reducing the effective normal stress of the fault zone, and the existence of high quartz contents further makes the crustal rocks in the source region more brittle. Our study provides a new evidence how the properties of the crust in the focal area have some control on the genesis of moderate to large earthquakes.

Joint inversion of two-dimensional magnetotelluric and ambient noise data constrained with cross gradient

We present an alternating joint two-dimensional inversion algorithm for imaging integrated magnetotelluric (MT) and ambient noise dispersion data sets. This approach is based on the limited-memory quasi-Newton method and enforced with cross-gradient constraints that seeks the geometrically similar structural features from multi-geophysical data. A classic synthetic model with same geometric boundaries has been used to test the stability and effectiveness of the joint inversion algorithm. Compared with individual MT and ambient noise tomography (ANT) inversion results, the resistivity and velocity models are captured with higher resolution, especially the electric structures below conductive units are recovered more correctly. The algorithm is also performed on another synthetic example with partial inconsistent boundaries in the resistivity and velocity models more analogous to the realistic scenario. The result demonstrates that, at the inconsistent boundaries, the resistivity model is still imaged correctly but the velocity model is constructed with some artificial structures. We suggest that, in the application of the actual case, the resistivity model obtained from joint inversion is superior and the velocity model should be evaluated comprehensively from individual and joint inversion results.

Geophysical joint inversion based on mixed structural and rock-physics coupling constraints

Joint inversion algorithms continue to receive a lot of interest in the application of geophysical interpretation due to the reduction of uncertainty of the inverse solutions. Over the past decade, several coupling constraints, structural or rock physics, have been introduced to the joint inversion of multiple geophysical data sets. However, a single coupling constraint may not provide the optimum solution for all geologic scenarios. To improve the application of the multiple geophysical data sets, in which some rock-physics information is available, we have developed a new joint inversion algorithm based on a mixed structural and rock-physics coupling constraints. The presented algorithm incorporates the cosine dot product gradient function, a structural coupling constraint, with a guided fuzzy c-means clustering strategy, which is a rock-physics coupling constraint. The former imposes the structural similarity among different model parameters, whereas the latter improves the linear or nonlinear correlation among model parameters. We use the exact structural resemblance algorithm to numerically solve the mixed coupling constraint joint inversion objective function. The developed algorithm is applied on 2D synthetic and field data examples. Our results find a significant improvement in the resolution of the reconstructed models, in comparison with traditional single coupling algorithms, even when the rock-physics information is not complete. This algorithm is more conducive to obtaining clear geologic unit boundaries and provides a favorable basis for delineating metallogenic target areas.

Nature-inspired stochastic hybrid technique for joint and individual inversion of DC and MT data

Here, a new naturally-inspired stochastic nonlinear joint and individual inversion technique for integrating direct current (DC) and magnetotelluric (MT) data interpretation-based simulation of a swarm intelligence combo with specific capabilities for exploitation of the variable weight particle swarm optimizer (vPSO) and exploration of the grey wolf optimizer (GWO), vPSOGWO, is used. They are particularly notable for their capacity for information exchange while hunting for food. Through synthetic MT and DC data contaminated with various sets of random noise, the applicability of the anticipated vPSOGWO algorithm based joint and individual inversion algorithm was assessed. The field examples, collected from diversified different geological terrains, including Digha (West Bengal), India; Sundar Pahari (Jharkhand), India; Puga Valley (Ladakh), India; New Brunswick, Canada; and South Central Australia, have shown the practical application of the proposed algorithm. Further, a Bayesian probability density function (bpdf) for estimating a mean global model and uncertainty assessment in posterior; and a histogram for model resolution assessment have also been created using 1000 inverted models. We examined the inverted outcomes and compared them with results from other cutting-edge methodologies, including the GWO, PSO, genetic algorithm (GA), Levenberg–Marquardt (LM), and ridge-regression (RR). Our findings showed that the current methodology is more effective than the GWO, PSO, GA, LM, and RR techniques at consistently improving the convergence of the global minimum. In contrast to earlier approaches, the current cutting-edge strategy vPSOGWO offers an improved resolution of an additional significant crustal thickness of about 65.68 ± 1.96 km over the Puga Valley, in which the inverted crustal thickness determined by vPSOGWO agrees well with the published crustal thickness over the Puga Valley. The new technology brings simulations closer to genuine models by significantly reducing uncertainty and enhancing model resolution.

3D joint inversion of airborne ZTEM and ground MT data using the finite element method with unstructured tetrahedral grids

As an airborne electromagnetic method induced by natural sources, the Z-axis tipper electromagnetic (ZTEM) system can primarily recover near-surface shallow structures, due to band-limited frequencies (usually 30–720 Hz) of the airborne survey and high sample rate acquisition along the terrain. In contrast, traditional ground magnetotellurics (MT) allows better recovery of deep structures as the data acquired are typical of large site intervals (usually higher than 1 km) and lower frequencies (usually lower than 400 Hz). High-resolution MT surveys allow for shallow small and deep large anomalies to be adequately interpreted but need large site intervals and broadband frequency range, which are seldom used as they are quite costly and laborious. ZTEM data are tippers that relate local vertical to orthogonal horizontal fields, measured at a reference station on the ground. As the 1D structures produce zero vertical magnetic fields, ZTEM is not sensitive to background resistivity. Thus, in general, ZTEM can only reveal relative resistivities and not real resistivities. A combination of the ZTEM and MT methods can be an effective technique, alleviating the shortcomings of the individual methods. At present, complex underground structures and topography introduce difficulties for data inversion and interpretation, as conventional ZTEM and MT forward modeling are generally used on structured grids with limited accuracy. To effectively recover complex underground structures with topography, we developed a 3D framework for joint MT and ZTEM inversion with unstructured tetrahedral grids. The finite element method is used for the forward problem because of its flexibility with unstructured tetrahedral meshes. The limited-memory quasi-Newton algorithm (L-BFGS) for optimization is used to solve the joint inverse problem, which saves memory and computational time by avoiding the explicit calculation of the Hessian matrix. To validate our joint inversion algorithm, we run numerical experiments on two synthetic models. The first synthetic model uses two conductive anomalous bodies of different sizes and depths. At the same time, a simple quadrangular is used for comparing the inversions with and without topography. In contrast, the second synthetic model represents a realistic topography with two different conductivities and the same depth. Both single-domain and joint inversions of the ZTEM and MT data are carried out for the two synthetic models to demonstrate the complementary advantages of joint inversion, while the second model is also used to test the adaptability of the joint inversion to complex topography. The results demonstrate the effectiveness of the finite element method with unstructured tetrahedral grids and the L-BFGS method for joint MT and ZTEM inversion. In addition, the inversion results prove that joint MT and ZTEM inversion can recover deep structures from the MT data and small near-surface structures from the ZTEM data by alleviating the weaknesses of the individual methods.

Two‐dimensional joint inversion of electromagnetic soundings at low induction numbers and direct current resistivity

AbstractDirect current resistivity and electromagnetic methods at low induction numbers are commonly used to characterize near‐surface structures. Although both methods are related to the same property, resistivity or conductivity, they have different sensitivities. The electromagnetic method at low induction numbers is more sensitive to conductive structures, but faces problems resolving resistive bodies, whereas the direct current method can image conductive and resistive variations. Additionally, the electromagnetic method at low induction numbers is less expensive and faster to collect the data, which seems a promising way to provide information at a low cost to enhance the model robustness. Aside from that, the exploration depth in both methods is not the same, but they can complement each other. In this work, a joint inversion algorithm based on a linear approximation was developed to incorporate both data. To achieve the goal, we rewrite the linear integral equations of electromagnetic data at low induction numbers in terms of resistivity logarithm to overcome the differences in magnitude and incorporate both data sets. We explore the potential of the joint inversion testing the algorithm with two synthetic models. In our tests, the joint model improvements are mainly in the conductive geometry and show favourable influence compared to the individual models. Finally, we tested the algorithm with field data collected in the coastal aquifer at Maneadero Valley. Despite the high anthropogenic electromagnetic noise in the area, the joint inversion results are coherent with the individual inversions of electromagnetic soundings at low induction numbers and direct current resistivity along with the geological setting.

A deep learning-enhanced framework for multiphysics joint inversion

Joint inversion has drawn considerable attention due to the availability of multiple geophysical data sets, ever-increasing computational resources, the development of advanced algorithms, and its ability to reduce inversion uncertainty. A key issue of joint inversion is to develop effective strategies to link different geophysical data in a unified mathematical framework, in which the information obtained from different models can complement each other. We have developed a deep learning-enhanced joint inversion framework to simultaneously reconstruct different physical models by fusing different types of geophysical data. Traditionally, structure similarity constraints are pursued by joint inversion algorithms using manually crafted formulations (e.g., cross gradient). The constraint is constructed by a deep neural network (DNN) during the learning process. The framework is designed to combine the DNN and a traditional independent inversion workflow and improve the joint inversion result iteratively. The network can be easily extended to incorporate multiphysics without structural changes. Numerical experiments on the joint inversion of 2D DC resistivity data and seismic traveltime are used to validate our method. In addition, this learning-based framework demonstrates excellent generalization abilities when tested on data sets using different geologic structures. It also can handle different sensing configurations and nonconforming discretization.

Application of induced polarization imaging across different scales to understand surface and groundwater flow at the Hofermuehle landslide

Understanding changes in hydraulic properties of the subsurface is critical to delineate areas susceptible for groundwater accumulation and the triggering of landslides. Laboratory studies have demonstrated the possibility to estimate the hydraulic conductivity from induced polarization (IP) measurements. However, to-date only rare studies have been applied at the field scale and none has evaluated the frequency-dependence in field IP imaging data. We show that the application of petrophysical models linking hydraulic conductivity (K) and IP at 1 Hz, resolves for the same estimations from frequency-domain measurements as well as from time-domain IP. Moreover, our IP images reveal an evident frequency-dependence between 0.1 and 240 Hz in the electrical properties, which is also observed in lab measurements conducted in soil samples. To account for this, we fit a Cole-Cole model to our multi-frequency IP results and evaluate models linking K and the normalized chargeability, gaining a subsurface model of the hydraulic conductivity with enhanced resolution. Our results reveal clear variations at depth in the electrical conductivity and polarization associated with the presence of a plane of instability and the sliding plane. We also resolve lateral changes delineating areas with K below 10-6 m/s, which may act as barriers for groundwater flow. To evaluate our results we also estimate the hydraulic conductivity using a joint inversion algorithm that directly solves for porosity and saturation through the simultaneous inversion of seismic refraction and electrical resistivity tomography data. We observed consistent hydraulic conductivity images obtained through the inversion of the IP data and the joint inversion, with such model being in agreement with existing information of the site. We resolve a 3D model of the hydraulic conductivity at the Hofermuehle landslide from IP data that reveals the geometry of areas with poor drainage that may lead to land sliding.

Joint Inversion of Body Wave Arrival Times, Surface Wave Dispersion Data and Receiver Functions: Method and Application to South China

AbstractWe have developed a new joint inversion method that incorporates body wave arrival times, surface wave dispersion and receiver functions to simultaneously update earthquake locations and constrain three‐dimensional P‐wave (Vp) and S‐wave velocity (Vs) models. Due to complementary sensitivities of the three types of data, the proposed joint inversion algorithm can reduce the intrinsic non‐uniqueness of inversions using fewer types of data and better determine smooth velocity variations and velocity discontinuities. Synthetic tests demonstrate the advantages of this new joint inversion algorithm in resolving velocity structures, especially in constraining velocity gradients across the Moho interface. We have applied the proposed joint inversion algorithm to image the lithosphere velocity structure of south China. The inverted Vp and Vs models fit body wave arrival times, surface wave dispersion and receiver functions well. We further analyzed the distribution of Vs gradients across the Moho interface in detail, which helps us better understand tectonics in south China.

3-D data-space joint inversion of gravity and magnetic data using a correlation-analysis constraint

Non-uniqueness, low computational efficiency and large memory requirements are main issues for geophysical data inversion. In this paper, we propose an efficient algorithm for 3D correlationanalysis joint inversion of gravity and magnetic data with high accuracy and low computation effort. Firstly, since the number of the observed field data is smaller than the number of inverted parameters, the calculations of the correlation-analysis for joint inversion of gravity and magnetic data in model space (MS) are transformed into the equivalent calculations in data space (DS), which can reduce the dimensions of the calculation domain, improve the computation efficiency and reduce the non-uniqueness. Then, an improved conjugate gradient (ICG) method is employed for the optimization algorithm, which can facilitate the use of stable functions with sparse factors and improve the accuracy of the inversion. The inversion performed by the combined DS-ICG method for synthetic data tests shows the calculation effort can be effectively reduced, and the issues with non-uniqueness are improved. Finally, the test by real field data can delineate the distribution of underground geological bodies, which illustrates the strong stability and good applicability of our extended method.

Physically Constrained 2D Joint Inversion of Surface and Body Wave Tomography

Joint inversion of different geophysical methods is a powerful tool to overcome the limitations of individual inversions. Body wave tomography is used to obtain P-wave velocity models by inversion of P-wave travel times. Surface wave tomography is used to obtain S-wave velocity models through inversion of the dispersion curves data. Both methods have inherent limitations. We focus on the joint body and surface waves tomography inversion to reduce the limitations of each individual inversion. In our joint inversion scheme, the Poisson ratio was used as the link between P-wave and S-wave velocities, and the same geometry was imposed on the final velocity models. The joint inversion algorithm was applied to a 2D synthetic dataset and then to two 2D field datasets. We compare the obtained velocity models from individual inversions and the joint inversion. We show that the proposed joint inversion method not only produces superior velocity models but also generates physically more meaningful and accurate Poisson ratio models.

Research on oil exploration seismic Rayleigh wave imaging based on multi-channel analysis of surface waves and genetic-damped least squares joint inversion

Rayleigh waves in oil exploration seismic records usually have strong energy and are considered as noise, but Rayleigh waves also carry information about subsurface. In this paper, we process Rayleigh waves from a set of oil seismic data to detect underground structures of shear-wave velocity (vs) using multi-channel analysis of surface waves (MASW). Fundamental mode and higher order mode dispersion curves of the Rayleigh wave were automatically extracted by a modified phase shift method. We then use the genetic and damped least squares (DLS) joint inversion algorithm to inverse the dispersion curves and obtain a one-dimensional (1D) vs structure under each shot gather. Finally, all 1D vs structures were combined to create a 3.2 km long two-dimensional (2D) section, revealing a stratum structure down to 80 m depth. The results show that MASW technology successfully improves the use of oil seismic data, the automatic dispersion extraction method based on modified phase shift improves the efficiency of data processing, and the joint inversion algorithm reduces the dependence of the Rayleigh wave dispersion inversion on initial model.

Crustal Structure across the West Antarctic Rift System from Multicomponent Ambient Noise Surface Wave Tomography

Abstract Approximately 2 yr (2010–2011) of continuous seismic records from a subset of the Antarctic component of the Polar Earth Observing Network (POLENET-ANET) seismic network deployed in West Antarctica are used to compute the nine components of the correlation tensor between each pair of stations in the network. Rayleigh wave velocity information from the vertical and radial components was extracted in the form of group and phase velocity dispersion curves, whereas the transverse component provided complimentary Love wave velocity information. The multicomponent Rayleigh wave measurements (ZZ, RR, ZR, and RZ) were averaged and used to infer the measurement uncertainties. The Rayleigh and Love wave group and phase velocities were then regionalized in space using a 2D deterministic tomography. A transect that spans the West Antarctic rift system was extracted from the tomography at individual periods between 7 and 60 s for the four types of surface wave velocities (i.e., Rayleigh and Love phase and group velocities). A transdimensional Bayesian joint inversion algorithm was used to invert these four datasets for a 1D model of isotropic shear-wave velocity versus depth at each point along the transect. In this way, surface wave dispersion curves from multicomponent noise correlations were used to build a 2D isotropic shear-wave velocity model down to ∼55 km depth. In this model, the top of the large low-velocity zone beneath Marie Byrd Land was imaged (up to a 5% decrease in velocity at ∼50 km depth), which provides further evidence for a mantle hot spot beneath the crust that supports the high topography in this region. We also observed a large velocity contrast in the lower crust beneath Marie Byrd Land at a depth where previous long-period seismicity has been observed. This strong contrast occurs more shallow than in previous crustal models, which compared to our model identify a deeper Moho (∼5–10 km deeper) beneath Marie Byrd Land. This new model has implications for interpreting earthquake locations in this region and perhaps necessitates that we revisit past hypocenter estimation studies using updated velocity models for the region.

Large-scale focusing joint inversion of gravity and magnetic data with Gramian constraint

SUMMARYA fast algorithm for the large-scale joint inversion of gravity and magnetic data is developed. The algorithm uses a non-linear Gramian constraint to impose correlation between the density and susceptibility of the reconstructed models. The global objective function is formulated in the space of the weighted parameters, but the Gramian constraint is implemented in the original space, and the non-linear constraint is imposed using two separate Lagrange parameters, one for each model domain. It is significant that this combined approach, using the two spaces provides more similarity between the reconstructed models. Moreover, it is shown theoretically that the gradient for the use of the unweighted space is not a scalar multiple of that used for the weighted space, and hence cannot be accounted for by adjusting the Lagrange parameters. It is assumed that the measured data are obtained on a uniform grid and that a consistent regular discretization of the volume domain is imposed. Then, the sensitivity matrices exhibit a block-Toeplitz-Toeplitz-block structure for each depth layer of the model domain, and both forward and transpose operations with the matrices can be implemented efficiently using two dimensional fast Fourier transforms. This makes it feasible to solve for large scale problems with respect to both computational costs and memory demands, and to solve the non-linear problem by applying iterative methods that rely only on matrix–vector multiplications. As such, the use of the regularized reweighted conjugate gradient algorithm, in conjunction with the structure of the sensitivity matrices, leads to a fast methodology for large-scale joint inversion of geophysical data sets. Numerical simulations demonstrate that it is possible to apply a non-linear joint inversion algorithm, with Lp-norm stabilisers, for the reconstruction of large model domains on a standard laptop computer. It is demonstrated, that while the p = 1 choice provides sparse reconstructed solutions with sharp boundaries, it is also possible to use p = 2 in order to provide smooth and blurred models. The methodology is used for inverting gravity and magnetic data obtained over an area in northwest of Mesoproterozoic St Francois Terrane, southeast of Missouri, USA.

High-resolution Vs tomography of South China by joint inversion of body wave and surface wave data

To take advantage of complementary strengths of earthquake body wave data and surface wave data from both earthquake and ambient noise sources, we have jointly used them to determine a high-resolution 3D Vs model of the lithosphere in South China by the joint inversion algorithm of Zhang et al. (2014). For body wave data, we assembled P- and S-wave arrival times for 40,028 earthquakes during the period of 2008/10–2018/06 recorded by 676 stations in South China. For surface wave dispersion dataset, it includes Rayleigh wave phase velocity maps at periods of 8–70 s and group velocity maps at periods of 8–50 s from Shen et al. (2016). Due to the complementary strengths of the two data types, the resolution of the jointly inverted Vs model has improved compared to the separately inverted models. The joint inversion model can also fit both data types at a similar level compared to separate inversions. In comparison with previous models, the new velocity model better delineates the sedimentary basins in the shallow crust and high velocity root in the lithosphere beneath the Sichuan basin, as well as better resolves the velocity variations between western and eastern Yangtze craton, thin lithosphere beneath eastern Yangtze craton and Cathaysia block, and helps us to better understand the mechanism of the lithosphere thinning. From the correlation between high velocity anomalies in the middle crust and the distribution of Neoproterozoic basalt samples, we propose the amalgamation suture between the Yangtze craton and Cathaysia block is along the eastern segment of the Jiangshan-Shaoxing fault and the west margin of the Jiangnan orogen volcanic rocks. Our new joint inversion model is useful for constructing a community velocity model and for better understanding the complex tectonics of the South China block.

2-D joint inversion of semi-airborne CSEM and LOTEM data in eastern Thuringia, Germany

SUMMARY Various electromagnetic (EM) techniques have been developed for exploring natural resources. The novel frequency-domain semi-airborne controlled source electromagnetic (semi-AEM) method takes advantages of both ground and airborne techniques. It combines ground-based high-power electrical dipole sources with large-scale and spatially densely covered magnetic fields measured via airborne receivers. The method can survey the subsurface down to approximately 1000 m and is particularly sensitive towards conductive bodies (e.g. mineralized bodies) in a more resistive host environment. However, the signal-to-noise ratio of semi-AEM is lower than that of ground-based methods such as long-offset transient electromagnetics (LOTEM), mainly due to the limited stacking time and motion-induced noise. As a result, the semi-AEM often has reduced depth of investigation in comparison to LOTEM. One solution to overcome these flaws is to analyse and interpret semi-AEM data together with information from other EM methods using a joint inversion. Since our study shows that LOTEM and semi-AEM data have complementary subsurface resolution capabilities, we present a 2-D joint inversion algorithm to simultaneously interpret frequency-domain semi-AEM data and transient electric fields using extended dipole sources. The algorithm has been applied to the field data acquired in a former mining area in eastern Thuringia, Germany. The 2-D joint inversion combines the complementary information and provides a meaningful 2-D resistivity model. Nevertheless, obvious discrepancies appear between the individual and joint inversion results. Consequent synthetic modelling studies illustrate that the discrepancies occur because of (i) differences in lateral and depth resolution between the semi-AEM and LOTEM data caused by different measuring configurations, (ii) different measured EM components and (iii) differences in the error weighting of the individual data sets. Additionally, our synthetic study suggests that more flexible land-based configurations with sparse receiver locations are possible in combination with semi-AEM without a significant loss of target resolution, which is promising for accelerating data acquisition and for survey planning and logistics, particularly when measuring in inaccessible areas.