3D Inversion Research Articles

Three-Dimensional Inversion Algorithm with A Footprint Computational Domain for Underground Engineering

Granite bodies pose a common geohazard in urban underground engineering. The GEM-2 system, employing small coils as transmitter and receiver (Tx-Rx), has gained widespread adoption for efficiently and non-invasively delineating low resistivity targets with 1D results in the near-surface. In this paper, we propose a 3D inversion algorithm based on the footprint-guided compact finite element method and Gauss-Newton optimization to accurately delineate the 3D structure of granite boulders. To demonstrate the effectiveness of our 3D inversion method, we conducted a GEM-2 test survey in a scenario featuring a granite boulder. The inversion results exhibit superior horizontal resolution compared to the current 1D inversion methods. The three-dimensional contour of the boulder is clearly depicted by areas of relatively high resistance, showcasing the capability of our inversion algorithm.

РЕЗУЛЬТАТЫ ГЛУБИННЫХ МАГНИТОТЕЛЛУРИЧЕСКИХ ИССЛЕДОВАНИЙ В РАЙОНЕ СЛОБОДСКОГО ГЕОДИНАМИЧЕСКОГО УЗЛА (ВОСТОЧНО-ЕВРОПЕЙСКАЯ ПЛАТФОРМА)

The Sloboda Geodynamic Intersection is considered as an area of convergence for major segments, aulacogens, faults, and suture zones of the East European Platform.Between 2020 and 2022, researchers from the Geological Faculty of Lomonosov Moscow State University and the Geoelectromagnetic Research Center (GEMRC IPE RAS) conducted deep magnetotelluric surveys in this region. The surveys were performed along the Pushkiny Gory – Andreapol, Sebezh – Velikiye Luki – Rzhev, and Ostrov – Ostashkov profiles. Through qualitative analysis of the collected data, the dimensionality of the studied medium, the total longitudinal conductance of the sedimentary cover, and the dominant strike direction of conductive structures were assessed. Quantitative interpretation using 1D, 2D, and 3D inversions resulted in geoelectric models comprising a conductive sedimentary cover and a highly resistive basement. Within the depth range of 10–40 km, transcrustal zones of enhanced electrical conductivity were consistently identified, interpreted as the southwest extension of the Ilmen-Ladoga anomaly. These conductivity anomalies are attributed to the deep submergence of heavily tectonized and metamorphosed sedimentary rocks, initially saturated with organic and carbonate matter.

Audio Magnetotelluric Imaging of a Concealed Mineral Deposit: A Case Study of Carbonate Hosted Zhugongtang lead-zinc Deposit, NW Guizhou Province, China

Non-intrusive geophysical exploration methods play a major role in ore deposit detection. This study aimed to characterize the subsurface electrical resistivity structure across the recently discovered super-large Zhugongtang lead-zinc deposit in north-western Guizhou province of China, using audio magnetotellurics (AMT) method. The results of this procedure were compared with available geological information. The estimated geoelectrical strike by impedance tensor invariants ranged between N285°E and N315°E. This range is consistent with known NW-SE trending structures in the Zhugongtang mining area. The obtained 2D inversion models revealed the presence of formations with an exceptionally low resistivity (< 15 Ωm), which corresponded to the known location of lead-zinc bearing formations. Moderate to low resistivity anomalies (< 63 Ωm) were observed at both shallow and greater depths. These anomalies were interpreted as indicative of geological formations composed of shale, sandstone, claystone, and silty mudstone. In addition, the resistivity models also revealed widespread high resistivity anomalies (> 1000 Ωm). These anomalies were thought to represent dolomite and limestone lithologies. In summary, the results presented in this study make a valuable contribution to the existing body of literature on the Zhugongtang deposit.

Identification of Geothermal System in Cisolok, West Java based on the Correlation of Gravity Method, ADMT (Active Directory Magnetotelluric), and Drill Log Data

Indonesia has 40% geothermal potential of the world’s geothermal potential. One proof of its potential is in Cisolok, West Java. The method used in this study is the gravity method from 2013 GGMPlus satellite with First Horizontal Derivative (FHD) analysis which is correlated with ADMT and drill log data. Based on overlaid between Land Surface Temperature (LST) map and residual anomaly map, Cisolok has a temperature of around 23.8 – 26.5 °C. These correlations describe the normal fault structure in the south that controls the Cisolok geothermal system. The results of the 3D inversion modeling show alternating layers of tuff, tuff breccia and silt as a cap rock with a density contrast of 0 – 0.2 gr/cc at a depth of 0 – 325 m, thick limestone layers with a density contrast of -0.1 – (-0.05) gr/cc at a depth of 325 – 700 m, and a layer of granodiorite rock as an intrusion body with a density contrast of -0.2 – (-0.15) gr/cc at a depth of 700 – 900 m. Based on the results obtained, it can be proven that the gravity method and the ADMT method have a fairly good correlation in geothermal exploration activities.

3D Forward and Inversion Research on Frequency Domain Electromagnetic Tipper Data

The tipper is one of the main parameters of the electromagnetic exploration data in the frequency domain and has an important role and significant advantage in the exploration under complex geological conditions. In this paper, the 3D forward modeling is carried out based on the staggered grid finite difference method, and the analytical solution of the layered medium is used to verify its correctness; the L-BFGS algorithm is used to perform the 3D inversion of the tipper data. Through the three-dimensional complex model, the forward response characteristics and spatial distribution of the tipper are analyzed. The inversion results show that the inversion using the inversion data has less influence on static displacement and better inversion results.

Energy transfer in reactive movements as a function of individual stretch load

Background: By directly recording electromyographic activity profiles and muscle-tendon interaction, this study aimed to elucidate the mechanisms why well-trained track and field athletes (experts) are able to outperform untrained individuals without former systematic experience in reactive jump training (novices). In particular, reactive power output and the elastic recoil properties of the muscle-tendon unit (MTU) were of special interest. For this purpose, stiffness regulation on muscle and joint level, energy management in terms of storing or dissipating elastic energy were compared between experts and novices during various stretch loads.Methods: Experts were compared with novices during reactive drop jumps (DJs) from drop heights ranging between 25 and 61 cm. Delta kinetic energy (Ekin) was calculated as the difference between the Ekin at take-off and ground contact (GC) to determine energy management. By recording electromyography of the lower limb muscles, in vivo fascicle dynamics (gastrocnemius medialis) and by combining kinematics and kinetics in a 3D inverse dynamics approach to compute ankle and knee joint kinetics, this study aimed to compare reactive jump performance, the neuromuscular activity and muscle-tendon interaction between experts and novices among the tested stretch loads.Results: Experts demonstrated significantly higher power output during DJs. Among all drop heights experts realized higher delta Ekin compared to novices. Consequently, higher reactive jump performance shown for experts was characterized by shorter GC time (GCT), higher jump heights and higher neuromuscular activity before and during the GC phase compared to novices. Concomitantly, experts were able to realize highest leg stiffness and delta Ekin in the lowest stretch load; however, both groups compensated the highest stretch load by prolonged GCT and greater joint flexion. On muscle level, experts work quasi-isometrically in the highest stretch load, while in novices GM fascicles were forcefully stretched.Conclusion: Group-specific stiffness regulation and elastic recoil properties are primarily influenced by the neuromuscular system. Due to their higher neuromuscular activity prior and during the GC phase, experts demonstrate higher force generating capacity. A functionally stiffer myotendinous system through enhanced neuromuscular input enables the experts loading their elastic recoil system more efficiently, thus realizing higher reactive power output and allowing a higher amount of energy storage and return. This mechanism is regulated in a stretch load dependent manner.

Regularization and L-curves in ice sheet inverse models: a case study in the Filchner–Ronne catchment

Abstract. Over the past 3 decades, inversions for ice sheet basal drag have become commonplace in glaciological modeling. Such inversions require regularization to prevent over-fitting and ensure that the structure they recover is a robust inference from the observations, confidence which is required if they are to be used to draw conclusions about processes and properties of the ice base. While L-curve analysis can be used to select the optimal regularization level, the treatment of L-curve analysis in glaciological inverse modeling has been highly variable. Building on the history of glaciological inverse modeling, we demonstrate general best practices for regularizing glaciological inverse problems, using a domain in the Filchner–Ronne catchment of Antarctica as our test bed. We show a step-by-step approach to cost function normalization and L-curve analysis. We explore the spatial and spectral characteristics of the solution as a function of regularization, and we test the sensitivity of L-curve analysis and regularization to model resolution, effective pressure, sliding nonlinearity, and the flow equation. We find that the optimal regularization level converges towards a finite non-zero limit in the continuous problem, associated with a best knowable basal drag field. Nonlinear sliding laws outperform linear sliding in our analysis, with both a lower total variance and a more sharply cornered L-curve. By contrast, geometry-based approximations for effective pressure degrade inversion performance when added to a sliding law, but an actual hydrology model may marginally improve performance in some cases. Our results with 3D inversions suggest that the additional model complexity may not be justified by the 2D nature of the surface velocity data. We conclude with recommendations for best practices in future glaciological inversions.

Density and magnetization models for the Acoculco geothermal field by joint 3D inversion

We determined density and magnetization magnitude in the Acoculco geothermal field, Mexico. For that purpose, we used terrestrial gravity and aerial magnetometry data. For the joint inversion of both sets of data, we assumed a petrophysical relation between density and magnetization that is also unknown. Along the inversion process, we estimated density, magnetization in every single prism in a 3D mesh and the coefficients from the petrophysical equation. The deeper part of the 3D model seems to describe a semicircular shape, that are apparently filled of intrusions. The difference between density and magnetization inside this semicircular shape can give us some insight about the characteristics of such intrusions, The shallowest part of the model keeps very good relation with the surface faults mapped.

Crustal electrical structure and seismicity of the Weiyuan shale gas block in Sichuan Basin, southwest China

Abstract Hydraulic fracturing, a significant contributor to seismic activity within and around operational fields, has been extensively used in shale gas production. Magnetotelluric (MT) sounding is an effective geophysical tool for identifying high-conductivity fluid-filled and/or molten regions. In this study, we deploy a dense grid of rectangular MT sites to investigate the 3D geoelectrical resistivity structure beneath the Weiyuan shale gas block (WSGB) and subsequently examine the causes of seismic activity. The resistivity data, obtained through 3D inversion accounting for topography using ModEM, reveals a shallow low-resistivity layer (&amp;lt;10 Ω-m) within the WSGB, ranging from ∼2 to 5 km in depth. This layer exhibits multiple isolated areas with very low resistivity (&amp;lt;5 Ω-m), indicative of fluid-filled zones associated with hydraulic fracturing or shale gas-bearing formations. In the northwestern WSGB, the Weiyuan anticline presents a high-resistivity dome extending possibly to depths beyond 20 km, without extending beyond the northern boundary of our study area. Conversely, the sedimentary zone in the southeastern WSGB displays a low-resistivity feature, with an extremely low-resistivity center (&amp;lt;1 Ω-m). Since a consistent high-resistivity zone exists beneath each fault and its top depth is &amp;lt;5 km, so faults might not extend downward below 5 km. Earthquakes with magnitudes (ML) of 3.0 or higher predominantly occur close to the faults, when considering industrial production data, we found a noteworthy correlation between earthquakes with ML &amp;lt; 3.0 and annual shale gas production within the WSGB. Tectonic faulting is not the leading cause for ML &amp;lt; 3.0 earthquakes but likely the primary contributor to seismic events with ML ≥ 3.0.

Modeling the Colatina lineament using geophysical methods: Insights into the geology of ES, Brazil

The study of the primary dikes in a given region is essential for comprehending its geological evolution. This study focuses on the offshore region in the state of Espírito Santo (ES), which encompasses one of the major oil sedimentary basins in the country, namely the Espírito Santo Basin. The study area is considered structurally complex due to the presence of numerous structural features, and the present work focuses on the Colatina Lineament. Despite several decades of oil and rock prospecting studies, the lateral and depth boundaries of the lineament are still unknown. Therefore, this study aims to utilize geophysical methods, including magnetic.and gravity, obtained from aerial and terrestrial surveys, respectively, to characterize the Colatina Lineament structurally. The study generated thematic maps using highlight filters to investigate the structural importance of the zone of influence. Additionally, 2.5D forward modeling was performed from gravity data, revealing numerous geological structures generated by crustal movements. To visualize the geological encompassed by the Colatina Lineament, a 3D inversion of the magnetic data was performed. The outcomes facilitated the visualization and mapping of the dike bundle and confirmed the impact of tectonic processes in the region.

Comparative 3D inversion of magnetotelluric phase tensors and impedances reveals electrically anisotropic base of Gawler Craton, South Australia

Isotropic three-dimensional (3-D) inversion has become a standard tool in the interpretation of magnetotelluric (MT) data. 3-D anisotropic inversion codes are under development, yet the number of unknowns increases by a factor of 6 rendering the problem extremely ill-posed. The presence of anisotropy is usually inferred from (i) spurious sequences of conductive and resistive bodies or (ii) comparison with two-dimensional anisotropic modelling approaches. Here, we investigate the 3-D structure of the Gawler Craton down to ∼250 km depth using 282 sites of the AusLAMP array located in the southern half of South Australia. Inversions of the MT impedance as phase tensors and real and imaginary parts result in diverging structures at depths > 70 km. We demonstrate that a unifying model that explains all data types similarly well is suggestive of an anisotropic resistivity structure at the base of the Gawler Craton lithosphere at depths of 120–210 km. Depth location and orientation of the anisotropy agree well with results from the analysis of seismic receiver functions. We suggest that electric anisotropy in the Gawler Craton is a result of lattice-preferred orientation of olivine crystals and metasomatic processes with macroscopic preferential orientation. Our results illustrate that inversion of phase tensor data is superior for the direct imaging of anisotropic resistivity contrasts in otherwise isotropic resistivity models; inversion models obtained with impedances may miss such structures. “Comparable” overall RMS misfits are often meaningless when comparing inversion results for various data types since sensitivities differ between data types. Reliable inversion results consistent with the entire data set can only be recovered if data fits are assessed systematically for all data representations. We also discuss the influence of error settings for phase tensors on the inversion. Our study also revealed that, if persistent across large areas, (i) parallel orientation of phase tensor major axes, (ii) constantly high phase tensor maximum phases or (iii) diverging directions of phase tensor major axes and induction arrows are suggestive of anisotropic structures and corresponding hypotheses should be evaluated.

3D gravity fast inversion based on Krylov subspace methods

Abstract Mapping the density contrast through the 3D gravity inversion can help detect goals under the subsurface. However, it is a challenge to accurately and efficiently solve the 3D gravity inversion. The Krylov subspace method is commonly used for large linear problems due to its high computational efficiency and low storage requirement. In this study, two classical algorithms of Krylov subspace method, namely the generalized minimum residual method and the conjugate gradient method, are applied to 3D gravity inversion. On the basis of the recovered models of the deep mineral and the shallow L-shaped tunnel models, it was found that the generalized minimum residual method provided similar density contrast results to the conjugate gradient method. The obtained inversion results of density contrast corresponded well to the position of the deep mineral resources model and the L-shaped tunnel model. The 3D distribution of Fe content underground was obtained by inverting the measured gravity data from the Olympic Dam in Australia. The recovered results correspond well with the distribution of Fe content in the geological profile collected. The accuracy of inversion using the generalized minimum residual method was similar to that of the conjugate gradient method under the same conditions. However, the generalized minimum residual method had a faster convergence speed and increased inversion efficiency by ∼90%, greatly reducing the inversion time and improves the inversion efficiency.

TransInver: 3D data-driven seismic inversion based on self-attention

Recently, convolutional neural network (CNN)-based deep learning (DL) for impedance inversion has been extended to multiple dimensions. Training multidimensional DL inversion requires extracting supervised information from sparse 1D well-log labels. Fully convolutional networks rely on their parameter sharing mechanism and receptive fields to achieve this, but their perceptual range is limited, making it difficult to capture long-term correlations in seismic data. The transformer is a type of network that is entirely based on self-attention, and it has demonstrated remarkable performance across various tasks and domains. However, its suitability for 3D seismic inversion is restricted by its high computational workload, fixed input size requirement, and inadequate handling of low-level details. The primary goal was to reengineer the self-attention mechanism to optimize its applicability for seismic impedance inversion tasks. The high-dimensional self-attention is decoupled into dual low-dimensional attention paths to reduce the computation of dense connections and matrix dot products. Shared parameters are used instead of full connection, allowing for flexible changes in input sizes by the network. In addition, its local modeling capabilities are enhanced by integrating it with the residual structure of the CNN. We name the resulting structure Self-Attention ResBlock, which is used as the basic unit for constructing TransInver. Comparative experiments indicate that TransInver performs significantly better than 3D methods such as UNet, TransUNet, HRNet, and 1D inversion methods. TransInver produces reliable inversion results using only nine well logs for SEAM Phase I and three well logs for the field data set of the Netherlands F3. This backbone network can deliver excellent inversion performance without depending on any auxiliary means such as low-frequency constraints or semisupervised frameworks.

Geothermal field model in the southeast of Shijiazhuang Region (China) deduced from magnetotelluric data

Shijiazhuang is located in the contact area between the Taihang Mountain Uplift and the Jizhong Depression of the North China Plain, adjacent to the eastern Taihang Mountain Fault. The major geothermal fields are located to the southeast of the Shijiazhuang region. Considering that the origin of these geothermal fields can be better delineated via geophysical methods, in this study, broadband magnetotelluric data were acquired from 51 stations. The aim of this study was to understand the underlying mechanism of the action of a geothermal system in terms of resistivity and other known information. Before inversion, the data were processed via remote reference technique, and the dimensionality and geoelectric strike directions were analyzed. 2D inversion of the TM-mode data was performed via the non-linear conjugate gradient method, and a deep electrical structure was imaged. Combining the data with previous data, the tectonic units and fault distribution of study area were comprehensively interpreted. The four components of the geothermal system have been identified: a heat source, channel, thermal reservoir, and caprock. The low-resistivity layer in the middle crust was considered as a deep heat source, and the fault was a heat diffusion channel. The high-porosity carbonate rock in the uplift area was considered as a thermal reservoir, and the overlying Neogene and Quaternary strata were considered as caprocks for thermal insulation. This study provides valuable reference basis for studying geothermal fields in this area.

Grounded source transient electromagnetic 3D forward modeling with the spectral-element method and its application in hydraulic fracturing monitoring

A long wire with large current source transient electromagnetic (TEM) monitoring, with a large detection depth, low cost, safety, and environmental protection, has unique advantages in the testing and identification of unconventional reservoir fluid and the evaluation of stimulated reservoir volume. So, the TEM 3D forward modeling method has become a research hotspot. Although the finite-element method (FEM) is a type of numerical algorithm that has been widely applied in three-dimensional (3D) electromagnetic field forward modeling, the efficiency and accuracy of FEM require further improvement in order to meet the demand of fast 3D inversion. By increasing the order of the basis function and adjusting the principle of mesh discretization, the precision of the mixed-order spectral-element (SEM) result will be increased. The backward Euler scheme is an unconditionally stable technique which can ignore the impact of the scale of the time step. To achieve a better description of the nonlinear electromagnetic (EM) response of the grounded source TEM method and to optimize the efficiency and accuracy/precision of the 3D TEM forward modeling method significantly, we proposed the use of 3D TEM forward modeling based on the mixed-order SEM and the backward Euler scheme, which can obtain more accurate EM results with fewer degrees of freedom. To check its accuracy and efficiency, the 1D and 3D layered models are applied to compare the SEM results with the semi-analytical and FEM solutions. In addition, we analyzed the accuracy and efficiency of the SEM method for different types of order basis functions. Finally, we calculated the long-wire source TEM response for a practical 3D earth model of a shale gas reservoir for fracturing monitoring and tested the feasibility of the TEM method in a hydraulic fracturing monitoring area to further demonstrate the flexibility of the SEM method.

A new technique inversion Time-Domain electromagnetic data

Time-Domain Electromagnetic (TDEM) data modeling, especially for central-loop configurations, is often achieved through 1D inversion models. This study aims to enhance the accuracy and efficiency of TDEM data inversion by employing the Born Approximation method to address calculation and convergence speed issues. We also utilize the modified Symbiotic Organism Search (mSOS), a global optimization algorithm capable of handling multi-minimum problems in non-linear objective functions, to optimize the inversion process. Our research includes the assessment of the accuracy and performance of this approach through inversion modeling on both synthetic and field data. The accuracy of the synthetic data was evaluated based on the algorithm's capability to retrieve the values of the synthetic data, as indicated by the small relative error between the synthetic model parameters and the calculated model. In the case of field data modeling, the accuracy relied on the consistency achieved when modeling the data with different numbers of layers. Additionally, we considered the time required to perform the inversion as an evaluation metric for inversion performance. For the synthetic data case, the algorithm produced relatively accurate models with misfit values of approximately 0 % and low relative error values. In the field data case, the inversion models demonstrated consistency and reduced misfit values when the data was modeled with different numbers of layers, specifically 8.72 % for the 2-layer model, 3.92 % for the 3-layer model, and 2.61 % for the 4- and 5-layer models. Both datasets required less than 19 min for 10,000 iterations. These findings highlight the innovative nature of the mSOS algorithm and its potential for practical applications in TDEM inversion studies.

3D phase-sensitive inversion recovery sequence for intracranial vertebrobasilar artery dissection

BackgroundT1-weighted 3D turbo spin echo (T1W-3D-TSE) sequences with variable refocusing flip angle are commonly used to diagnose intracranial vertebrobasilar artery dissection (iVAD). However, magnetic susceptibility artifacts of the cavernous sinus may cause loss of the basilar and vertebral arteries. This study investigated the effectiveness of a 3D phase-sensitive inversion recovery (3D-PSIR) sequence in reducing magnetic susceptibility artifacts in the cavernous sinus, and its imaging findings for iVAD. MethodsTwelve volunteers and eleven patients with iVAD were included. Magnetic resonance imaging (MRI) was performed using a 3.0-T MRI system. 3D-PSIR and T1W-3D-TSE sequences were used. Vessel wall defects and contrast-to-noise ratio (CNR) were evaluated. The MRI findings were visually evaluated. ResultsIn the 3D-PSIR images, one volunteer (8 %) had vessel wall defects, and five (42 %) had vessel wall defects (p = 0.046) in the T1W-3D-TSE images. CNR was higher in 3D-PSIR images for vessel wall-to-lumen, whereas it was higher in T1W-3D-TSE images for vessel wall-to-CSF (p < 0.001). Visual evaluation revealed similar MRI findings between the two sequences. ConclusionsThe 3D-PSIR sequence may be able to improve the vessel wall defects and achieve MRI findings comparable to those of the T1W-3D-TSE sequence in iVAD. The 3D-PSIR sequence can be a useful tool for the imaging-based diagnosis of iVAD.

MRI-detected intraosseous bone marrow edema recedes after effective therapy of periodontitis

ObjectivesT2 STIR MRI sequences can detect preclinical changes associated with periodontal inflammation, i.e. intraosseous edema in the tooth-supporting bone. In this study, we assessed whether MRI can be used for monitoring periodontal disease.Material and methodsIn a prospective cohort study, we examined 35 patients with periodontitis between 10/2018 and 04/2019 by using 3D isotropic T2-weighted short tau inversion recovery (STIR) and Fast Field Echo T1-weighted Black bone sequences. All patients received standardized clinical exams before and three months after non-surgical periodontal therapy. Bone marrow edema extent was quantified in the STIR sequence at 922 sites before and after treatment. Results were compared with standard clinical findings. Non-parametric statistical analysis was performed.ResultsNon-surgical periodontal treatment caused significant improvement in mean probing depth (p < 0.001) and frequency of bleeding on probing (p < 0.001). The mean depth of osseous edema per site was reduced from a median [IQR] of 2 [1, 3] mm at baseline to 1 [0, 3] mm, (p < 0.001). Periodontal treatment reduced the frequency of sites with edema from 35 to 24% (p < 0.01).ConclusionThe decrease of periodontal bone marrow edema, as observed with T2 STIR MR imaging, is indicative of successful periodontal healing.Clinical relevance statementT2 STIR hyperintense bone marrow edema in the periodontal bone decreases after treatment and can therefore be used to evaluate treatment success. Furthermore, MRI reveals new options to depict hidden aspects of periodontitis.Key Points• T2 STIR hyperintense periodontal intraosseous edema was prospectively investigated in 35 patients with periodontitis before and after treatment and compared to clinical outcomes.• The frequency of affected sites was reduced from 35 to 24% (p < 0.001), and mean edema depth was reduced from a median [IQR] of 2 [1, 3] mm at baseline to 1 [0, 3] mm 3 months after treatment. (p < 0.001).• T2 STIR sequences can be used to monitor the posttreatment course of periodontitis.

Common modelling assumptions affect the joint moments measured during passive joint mobilizations

Joint resistance to passive mobilization has already been estimated in-vivo in several studies by measuring the applied forces and moments while manipulating the joint. Nevertheless, in most of the studies, simplified modelling approaches are used to calculate this joint resistance. The impact of these simplifications is still unknown. We propose a protocol that enables a reference 3D inverse dynamics approach to be implemented and compared to common simplified approaches. Eight typically developed children and eight children with cerebral palsy were recruited and underwent a passive testing protocol, while applied forces and moments were measured through a 3D handheld dynamometer, simultaneously to its 3D kinematics and the 3D kinematics of the different segments. Then, passive joint resistance was estimated using the reference 3D inverse dynamics approach and according to 5 simplified approaches found in the literature, i.e. ignoring either the dynamometer kinematics, the measured moments alone or together with the measured tangential forces, the gravity and the inertia of the different segments, or the distal segments kinematics. These simplifications lead to non-negligible differences with respect to the reference 3D inverse dynamics, from 3 to 32% for the ankle, 4 to 34% for the knee and 1 to 58% for the hip depending of the different simplifications. Finally, we recommend a complete 3D kinematics and dynamics modelling to estimate the joint resistance to passive mobilization.

Robust 3D Joint Inversion of Gravity and Magnetic Data: A High-Performance Computing Approach

One of the fundamental challenges in geophysics is the calculation of distribution models for physical properties in the subsurface that accurately reproduce the measurements obtained in the survey and are geologically plausible in the context of the study area. This is known as inverse modeling. Performing a 3D joint inversion of multimodal geophysical data is a computationally intensive task. Additionally, since it involves a modeling process, finding a solution that matches the desired characteristics requires iterative calculations, which can take days or even weeks to obtain final results. In this paper, we propose a robust numerical solution for 3D joint inversion of gravimetric and magnetic data with Gramian-based structural similarity and structural direction constraints using parallelization as a high-performance computing technique, which allows us to significantly reduce the total processing time based on the available Random-Access Memory (RAM) and Video Random-Access Memory (VRAM)and improve the efficiency of interpretation. The solution is implemented in the high-level programming languages Fortran and Compute Unified Device Architecture (CUDA) Fortran, capable of optimal resource management while being straightforward to implement. Through the analysis of performance and computational costs of serial, parallel, and hybrid implementations, we conclude that as the inversion domain expands, the processing speed could increase from 4× up to 100× times faster, rendering it particularly advantageous for applications in larger domains. We tested our algorithm with two synthetic data sets and field data, showing better results than standard separate inversion. The proposed method will be useful for joint geological and geophysical interpretation of gravimetric and magnetic data used in exploration geophysics for example minerals, ore, and petroleum search and prospecting. Its application will significantly increase the reliability of physical-geological models and accelerate the process of data processing.