Least-squares Inversion Research Articles

English

The Osogbo central solid waste dumpsite in Osun State, Nigeria falls within the Ilesha Schist Belt, southwestern basement complex of Nigeria. Thirty-three (33) Vertical Electric Sounding (VES), and 2-D Electric Resistivity Tomography (ERT) data were acquired across various locations in the study area using ABEM Terrameter SAS 300, respectively. Schlumberger configuration with a maximum spread length of 100 m, for the VES was used, while four traverses of ERT were conducted, using Dipole-Dipole Array with average traverse length of 112.50 m. A smoothness-constrained least-squares inversion was then applied to the ERT data using a 2-D inversion algorithm [that is, DIPRO for Windows, version 4.01. Generally, the results defined the contaminated leachate plumes as electrically conductive, with anomalous resistivity values. Both the VES and the 2-D tomography identified zones of low resistivity values, between 24 and 67 ?m, from 10 to 20 m deep, as leachate contaminant plumes. Some of the weathered and fractured basement rocks indicated that the subsurface soil and groundwater have been contaminated by the leachates, which appears to have migrated outside landfill site. Zones within the sub-surface, with resistivity values relatively high (> 300 Ωm) and depth above 30 m might be pollutant free. Solid wastes management calls for the adoption of the best practicable environmental management approach through the governments’ enforcement of circular economic policies, using extended producer responsibility (EPR) model and construction of engineered landfills to replace unsanitary landfills. The conduct of environmental impact assessment (EIA), prior to commencement of operations and phytoremediation of closed sites is also crucial. Key words: Tomography, leachate, pollution, contaminant plume.

Least-squares interferometric migration of microseismic source location with a deblurring filter

Microseismic source locations play an important role in monitoring hydraulic fracturing in unconventional oil and gas exploration. Waveform-based source location methods can reliably and automatically image source locations without phase identification. A widely used and representative waveform-based method is interferometric migration (IM), which can eliminate the excitation-time term and image the source location in space by using correlograms of pairwise receivers. IM can avoid the trade-off between the inversions of excitation time and source location, but provides low-resolution source location images with strong migration artifacts. To improve the spatial resolution, we first developed a least-squares interferometric migration (LSIM). LSIM iteratively minimizes the correlogram residuals using the conjugate-gradient (CG) method. It provides a significant improvement in spatial resolution compared with conventional IM but requires a large number of iterations and high computational costs. To overcome this drawback, we develop an efficient least-squares interferometric migration with a deblurring filter (DLSIM) for high-resolution microseismic source locations. We introduce the Hessian matrix into the microseismic source location problem and approximate the inverse Hessian with a relatively inexpensive deblurring filter. The deblurring filter is applied to the updated gradient matrix in the CG algorithm. It could significantly accelerate the convergence rate of the least-squares inversion and meanwhile, provide a high spatial resolution. We use synthetic and real hydraulic fracturing data to demonstrate the robustness and effectiveness of DLSIM. Data noise, velocity error, and wavelet error are considered in the synthetic tests to simulate actual situations. The inverted results find that DLSIM achieves high-resolution source location images after 5–10 iterations that are equivalent to those of LSIM after approximately 50 iterations. Therefore, DLSIM can dramatically reduce the computational cost owing to its fewer number of iterations compared with LSIM.

Rapid Object Depth Estimation From Position-Referenced EMI Data Using Machine Learning

State-of-the-art methods for localization and detection of small metallic objects using electromagnetic induction (EMI) sensing usually struggle due to the strong correlation between the intrinsic parameters of the object and the object’s depth. In this article, we present a machine-learning-based approach for rapid estimation of metallic object depth from line-scan EMI data. The 1-D-convolutional neural network (1D-CNN), trained on a simulated dataset, takes advantage of metal detector (MD) spatial response to extract features from which depth is inferred. Experimental evaluation using a mono-coil pulse induction MD and an electromagnetic (EM) tracking system was performed under laboratory conditions on a large dataset containing arbitrarily oriented objects of different sizes, shapes, and materials. The nonlinear least-squares (NLSs) inversion was employed as the benchmark method for comparison. The proposed solution shows superior performance over NLS at depths >10 cm. From two passes of MD over the object at depths within the range of 2.5–15 cm, our method yields a median absolute error (MedAE) on the order of millimeters.

Vertical transversely isotropic elastic least-squares reverse time migration based on elastic wavefield vector decomposition

Anisotropic elastic reverse time migration (RTM) is a promising technique for imaging complex oil and gas reservoirs. However, the migrated images often suffer from low spatial resolution, migration artifacts, wave-mode crosstalk, and unbalanced amplitude response. Conventional vertical transversely isotropic elastic least-squares reverse time migration (VTI-elastic LSRTM) defines stiffness parameter perturbations as elastic images, which have different physical meanings from VTI-elastic RTM images. We have developed a VTI-elastic LSRTM method based on elastic wavefield vector decomposition that is a natural extension of VTI-elastic RTM. More specifically, our method applies least-squares inversion to VTI-elastic RTM and defines the compressional- and shear-wave reflectivity as elastic images (PP, PS, SP, and SS images). When computing the elastic images, we decompose the elastic wavefields into compressional and shear wavefields and cross-correlate the corresponding wave modes. We derive the reverse time demigration operator by taking the adjoint of the RTM operator. Using the migration and demigration operators, we formulate the VTI-elastic LSRTM as a linear inverse problem with the least-squares criterion. The conjugate gradient method is used to solve the optimization problem. Three numerical examples are presented to test the feasibility of our method. The VTI-elastic LSRTM images have higher resolution, fewer migration artifacts and wave-mode crosstalk, and improved amplitude response when compared with VTI-elastic RTM images.

Shallow crustal model of the DehDasht in Zagros, Iran, using Rayleigh wave tomography

Surface wave tomography is considered an efficient method to reveal the physical properties of subsurface geological structures, particularly beneath geologically complex areas where conventional active seismic methods are problematic. The salt-rich DehDasht structural basin, in the SW of Iran, is an example of this area, which is characterized by high seismicity. Despite the complex geology and the great thickness of evaporitic deposits in this region, surface wave tomography can retrieve high-resolution images by applying a dense network of stations. Therefore, >11,000 micro-earthquakes (M ≤ 3.0) recorded by 116 broadband stations in 9 months were processed to detect geological structures and a crustal model beneath the DehDasht region. After selecting strict data selection criteria, the observed dispersion curves of Rayleigh waves were then measured using the multiple filter analysis method, and the 2D tomography was done for periods of 0.3 to 5.0 s. A non-linear iterative damped least-squares inversion procedure was then applied to each local dispersion curve to obtain the 1D VS model of the uppermost 5 km, and the results were inserted into the original cells to construct a quasi-3D VS model. Although our resulted VS model has high correlations with known geological units and tectonic features of the study area, we validated it by inverting the observed gravity data independently and consequently recovering the location of the anomalies at the basin and/or around faults, anticlines, and synclines. Generally, the observed low-and high-velocity anomalies are associated with the sedimentary materials.

Deep unfolding dictionary learning for seismic denoising

Seismic denoising is an essential step for seismic data processing. Conventionally, dictionary learning (DL) methods for seismic denoising always assume the representation coefficients to be sparse and the dictionary to be normalized or a tight frame. Current DL methods need to update the dictionary and the coefficients in an alternating iterative process. However, the dictionary obtained from the DL method often needs to be recalculated for different input data. Moreover, the performance of DL for seismic noise removal is related to the parameter selection and the prior constraints of dictionary and representation coefficients. Recently, deep learning demonstrates promising performance in data prediction and classification. Following the architecture of DL algorithms strictly, we have developed a novel and interpretable deep unfolding dictionary learning (DUDL) method for seismic denoising by unfolding the iterative algorithm of DL into a deep neural network (DNN). The proposed architecture of DUDL contains two main parts: the first is to update the dictionary and representation coefficients using least-squares inversion and the second is to apply a DNN to learn the prior representation of dictionary and representation coefficients, respectively. Numerical synthetic and field examples find the effectiveness of our method. More importantly, this method for seismic denoising obtains the dictionary for different seismic data adaptively and is suitable for seismic data with different noise levels.

A Fault-Based Crustal Deformation Model with Deep Driven Dislocation Sources for the 2023 Update to the U.S. National Seismic Hazard Model

Abstract A fault-based crustal deformation model with deep driven dislocation sources is applied to estimate long-term on-fault slip rates and off-fault moment rate distribution in the western United States (WUS) for the 2023 update to the National Seismic Hazard Model (NSHM). This model uses the method of Zeng and Shen (2017) to invert for slip rate and strain-rate parameters based on inputs from Global Positioning System (GPS) velocities and geologic slip-rate constraints. The model connects adjacent major fault segments in California and the Cascadia subduction zone to form blocks that extend to the boundaries of the study area. Faults within the blocks are obtained from the NSHM geologic fault section database. The model slip rates are determined using a least-squares inversion with a normalized chi-square of 6.6. I also apply a time-dependent correction called “ghost transient” effect to account for the viscoelastic responses from large historic earthquakes along the San Andreas fault and Cascadia subduction zone. Major discrepancies between model slip rates and geologic slip rates along the San Andreas fault, for example, from the Cholame to the Mojave and San Bernardino segments of the San Andreas, are well reduced after the ghost transient correction is applied to GPS velocities. The off-fault moment rate distribution is consistent with regional tectonics and seismicity patterns with a total rate of 1.6×1019 N·m/yr for the WUS.

Improvement in magnetic nanoparticle tomography estimation accuracy by combining sLORETA and non-negative least squares methods

Imaging methods that can detect biofunctionalized magnetic nanoparticles (MNPs) accumulated at cancerous tumor sites are expected to be part of the in vivo cancer diagnostic techniques. An imaging technique called magnetic nanoparticle tomography (MNT), which uses a magnetic sensor array, has been proposed. High sensitivity and spatial resolution were achieved using the non-negative least-squares (NNLS) inverse solution in MNT. However, owing to the presence of measurement noise, the concentration and position of certain MNPs were estimated inaccurately, i.e., artifacts were generated. To overcome this issue, this study first applied standardized low-resolution brain electromagnetic tomography (sLORETA), a spatial filter method with no location bias, to approximate the position of MNPs. The region of analysis was restricted to where the estimated value exceeded the threshold. Subsequently, the NNLS method was applied to estimate the concentration and position of MNPs in the restricted region. In the experiment, two Resovist MNP samples (300 or 500 μgFe) were arranged at a distance of 25–502 mm, and the concentration and position estimation were performed. The estimation results demonstrated that the proposed method successfully suppresses artifacts and adequately estimates the concentration and position of MNPs within a position error of 10 mm and a concentration error of 20 %.

Genetic Algorithms for Interior Comparative Optimization of Standard BCS Parameters in Selected Superconductors and High-Temperature Superconductors

Inverse least squares numerical optimization, 3D/4D interior optimization, and 3D/4D graphical optimization software and algorithm programming have been presented in a series of previous articles on the applications of the BCS theory of superconductivity and TC dual/multiobjective optimizations. This study deals with the comparison/validation of the optimization results using several different methods, namely, classical inverse least squares (ILS), genetic algorithms (GA), 3D/4D interior optimization, and 2D/3D/4D graphical optimization techniques. The results comprise Tikhonov regularization algorithms and mathematical methods for all the research subjects. The findings of the mathematical programming for optimizing type I chrome isotope superconductors are validated with the genetic algorithms and compared to previous results of 3D/4D interior optimization. Additional rulings present a hypothesis of the new ‘molecular effect’ model/algorithm intended to be proven for Hg-cuprate-type high-temperature superconductors. In molecular effect optimization, inverse least squares and inverse least squares polynomial methods are applied with acceptable numerical and 2D graphical optimization solutions. For the BCS isotope effect and molecular effect, linearization logarithmic transformations for model formula software are implemented in specific programs. The solutions show accuracy with low programming residuals and confirm these findings. The results comprise two strands, the modeling for the isotope effect and molecular effect hypotheses and the development of genetic algorithms and inverse least squares-improved programming methods. Electronic physics applications in superconductors and high-temperature superconductors emerged from the rulings. Extrapolated applications for new modeling for the theory of superconductivity emerged from the numerical and image data obtained.

Performance Evaluation for an Optimized Wenner (ALPHA, BETA, AND GAMMA) Arrays Using Synthetic Geological Models

The study aimed at comparing the resolution and effectiveness of three-electrode arrays (Wenner-α, Wenner-β, and Wenner-γ) in the 2D Electrical resistivity method using Numerical analysis of geological models. Three synthetic geological models that simulate block-one dyke and water layer were generated using RES2DMOD software. The inversion used for the geological models was based on smoothness-constrained least-square inversion which was carried out with RES2DINV. The inversion results were imputed into surfer11 software to examine the image resolution, thereafter absolute percentage error (APE) was calculated to measure the effectiveness of the arrays. The result for the block-one model shows that the Wenner-β array has an APE of 14.45%, the Wenner-α array has an APE of 32.67%, and the Wenner-γ array with an APE of 29.15%. Similarly, for the dyke model, the Wenner-α array, Wenner-β array, and Wenner-γ array have an APE of 69.61%, 57.43%, and 45.49% respectively. However, the results for the water layer model show that the Wenner-α array has an APE of 17.11%, the Wenner-β array has an APE of 12.16%, and that the Wenner-γ array has an APE of 16.21%. Wenner-α is expected to produce an image with the best resolution having the highest APE, henceforth APE suggests the resolution capacity of an array.

3D Graphical Optimization for Molecular Effect Model in High Temperature Superconductors Thallium Class [ TC < 0° , TC > 0° ] without Lattice Tetragonal Compounds

In subsequent study series for 3D High Temperature Superconductors (HTCSs), Inverse Least Squares (ILS) and 3D Numerical/Graphical Optimization is the objective for this Molecular Effect Model (MEM) contribution. HTSCs class selected is Thallium group of [ Tl-Sn-Pb-Ba-Si-Mn-Mg-Cu-O ], constrained/extended to [T<sub>C</sub> ? 0° , T<sub>C</sub> > 0° ]. Tetragonal Lattice and Amorphous compounds of this Type II Thallium HTSCs class are not included in this study. Results obtained for Matlab 3D Graphical Optimization techniques are proven/presented. Numerical calculations include 3D Tikhonov Regularization algorithms with mathematical developments for this Thallium class. Thus, results show two strands, 3D surfaces for Graphical Optimization MEM Thallium HTSCs modelling, and MEM analysis of numerical equations. 3D MEM and Numerical Optimization get low error and residuals. Electronics Physics applications emerge from allteh research.

Analysis of direct current resistivity data using continuous wavelet transform

We have developed a new method for the direct current resistivity interpretation, based on the continuous wavelet transform (CWT) of electric potential-difference data. It exploits the main properties of the CWT, such as stability versus noise, and does not require a starting model or other a priori information such as a model weighting function or constraints. Because the approximate integral equation of the resistivity problem has the same form as the forward problem for potential fields, the authors analyze geoelectric data (with dipole-dipole configuration) using the wavelets belonging to the Poisson kernel semigroup. They find that the CWT analysis of the measured electric potential difference is able to identify buried bodies, defining their depth, position, and extent. Such parameters are estimated with no prior knowledge of the resistivity contrast between the bodies and the background. We consider several synthetic models, such as dikes, compact bodies, and contacts. In general, the depth and the lateral thickness of the buried bodies are estimated with good accuracy, using a diagram relating the singular point estimations to the different values of the dipole separation factor n. Thanks to the good results obtained from synthetic data, we test the method with data generated during laboratory experiments. In two laboratory-scale models, our method displays a better precision compared with smoothness-constrained least-squares inversion in identifying the exact position of the edges of a buried body. Finally, we find that combining CWT and inversion is advantageous: after constraining the inverse problem with a priori information from the CWT analysis, we obtain an improved inverse model.

Huber inversion-based reverse-time migration with de-primary imaging condition and curvelet-domain sparse constraint

Least-squares reverse-time migration (LSRTM) formulates reverse-time migration (RTM) in the least-squares inversion framework to obtain the optimal reflectivity image. It can generate images with more accurate amplitudes, higher resolution, and fewer artifacts than RTM. However, three problems still exist: (1) inversion can be dominated by strong events in the residual; (2) low-wavenumber artifacts in the gradient affect convergence speed and imaging results; (3) high-wavenumber noise is also amplified as iteration increases. To solve these three problems, we have improved LSRTM: firstly, we use Huber-norm as the objective function to emphasize the weak reflectors during the inversion; secondly, we adapt the de-primary imaging condition to remove the low-wavenumber artifacts above strong reflectors as well as the false high-wavenumber reflectors in the gradient; thirdly, we apply the L 1 -norm sparse constraint in the curvelet-domain as the regularization term to suppress the high-wavenumber migration noise. As the new inversion objective function contains the non-smooth L 1 -norm, we use a modified iterative soft thresholding (IST) method to update along the Polak-Ribière conjugate-gradient direction by using a preconditioned non-linear conjugate-gradient (PNCG) method. The numerical examples, especially the Sigsbee2A model, demonstrate that the Huber inversion-based RTM can generate high-quality images by mitigating migration artifacts and improving the contribution of weak reflection events.

Surface-wave tomography using SeisLib: a Python package for multiscale seismic imaging

Summary To improve our understanding of the Earth’s interior, seismologists often have to deal with enormous amounts of data, requiring automatic tools for their analyses. It is the purpose of this study to present SeisLib, an open-source Python package for multiscale seismic imaging. At present, SeisLib includes routines for carrying out surface-wave tomography tasks based on seismic ambient noise and teleseismic earthquakes. We illustrate here these functionalities, both from the theoretical and algorithmic point of view and by application of our library to seismic data from North America. We first show how SeisLib retrieves surface-wave phase velocities from the ambient noise recorded at pairs of receivers, based on the zero crossings of their normalized cross-spectrum. We then present our implementation of the two-station method, to measure phase velocities from pairs of receivers approximately lying on the same great-circle path as the epicentre of distant earthquakes. We apply these methods to calculate dispersion curves across the conterminous United States, using continuous seismograms from the transportable component of USArray and earthquake recordings from the permanent networks. Overall, we measure 144 272 ambient-noise and 2055 earthquake-based dispersion curves, that we invert for Rayleigh-wave phase-velocity maps. To map the lateral variations in surface-wave velocity, SeisLib exploits a least-squares inversion algorithm based on ray theory. Our implementation supports both equal-area and adaptive parametrizations, with the latter allowing for a finer resolution in the areas characterized by high density of measurements. In the broad period range 4–100 s, the retrieved velocity maps of North America are highly correlated (on average, 96 per cent) and present very small average differences (0.14 ± 0.1 per cent) with those reported in the literature. This points to the robustness of our algorithms. We also produce a global phase-velocity map at the period of 40 s, combining our dispersion measurements with those collected at global scale in previous studies. This allows us to demonstrate the reliability and optimized computational speed of SeisLib, even in presence of very large seismic inverse problems and strong variability in the data coverage. The last part of the manuscript deals with the attenuation of Rayleigh waves, which can be estimated through SeisLib based on the seismic ambient noise recorded at dense arrays of receivers. We apply our algorithm to produce an attenuation map of the United States at the period of 4 s, which we find consistent with the relevant literature.

Soil Mapping Using Electromagnetic Induction to Assess the Suitability of Land for Growing Leptospermum nitens in Western Australia

Leptospermum sp. with dihydroxyacetone in their nectar are a source of high-value medicinal honey production and can provide income from agriculturally marginal lands. The current study was from two newly planted Leptospermum nitens sites, one with duplex soil and the other in deep sandy soil, in the low rainfall areas of the south-west of Western Australia, with the aim of identifying key soil parameters influencing the plantation’s survival and growth. Electromagnetic induction (EMI) at different depths was used to investigate the possible impact of soil variability on the Leptospermum nitens plantations. Two EMI surveys were conducted at each site, at different times of the year, to account for soil moisture variability (relatively dry and wet conditions). A least-square inversion algorithm was used to determine true electrical conductivities at three different soil depths (0–0.5, 0.5–0.8, and 0.8–1.6 m) to produce quasi-3D maps of soil inverted electrical conductivity. Corresponding soil samples from each depth were used for the physico-chemical analysis of soil parameters and to develop laboratory-based electrical resistivity to soil volumetric moisture calibrations with R2 values between 0.95 and 0.99. Shrub survival and growth (canopy diameter) were estimated using unmanned aerial vehicle (UAV) images and machine learning. Comparing EMI soil mapping with UAV imagery results showed significantly greater shrub survival and growth (p < 0.001) in areas with higher ECa ranges of 12–24 mS m−1 at the variable textured site and 6–9 mS m−1 at the uniformly sandy site. Overall, the variable textured site, with an 82% survival rate, had a significantly higher shrub count and larger plants than the uniformly sandy site, with a 75% survival rate. A principal component analysis (PCA) identified inverted EC to be strongly correlated with soil moisture > pH > soil texture. Such soil mapping may be a robust and effective method for risk assessment of new shrub plantations.

Research on Remaining Oil Characterization in Superheavy Oil Reservoir by Microgravity Exploration

Some physical processes such as oil and gas development, metal deposit collection, and groundwater resource migration can cause density changes, for which microgravity monitoring is the most intuitive method to monitor the density change process. Based on the basic principle of microgravity measurement and the idea of multiscale separation, a multiscale, second-order, surface-fitting, residual gravity anomaly extraction method is proposed to separate superimposed microgravity fields. In this method, regional fields of different scales are fitted and calculated successively with the measurement points as the center, so as to separate the gravity anomalies produced by different-depth density bodies. Results from actual data show that this method extracts the reservoir’s residual density characteristics of plane gravity anomaly on the basis of remaining oil distribution characteristics, consistent with reservoir numerical simulation results. A three-dimensional least-squares inversion of the method for extracting residual gravity anomaly was carried out, with the inversion results consistent with the results of vertical remaining oil distribution characteristics and well-test production results.

DecNet: Decomposition network for 3D gravity inversion

Three dimensional gravity inversion is an effective way to extract subsurface density distribution from gravity data. Different from the conventional geophysics-based inversions, machine-learning-based inversion is a data-driven method mapping the observed data to a 3D model. We have developed a new machine-learning-based inversion method by establishing a decomposition network (DecNet). Unlike existing machine-learning-based inversion methods, the proposed DecNet method is a mapping from 2D to 2D, which requires less training time and memory space. Instead of learning the density information of each grid point, this network learns the boundary position, vertical center, thickness, and density distribution by 2D-to-2D mapping and reconstructs the 3D model by using these predicted parameters. Furthermore, by using the highly accurate boundary information learned from this network as supplement information, the DecNet method is optimized into a DecNetB method. By comparing the least-squares inversion and U-Net inversion on synthetic and real survey data, the DecNet and DecNetB methods have shown the advantage in dealing with inverse problems for targets with boundaries.

Mathematical optimization and approximation methods for primary molecular effect model in high temperature superconductors TL group [TC > 0°

Optimization-Modelling Molecular Effect methods for one HTSC group were approached/determined based on previous studies. Namely, Inverse Least Squares (ILS), 2D Numerical/Graphical Optimization in primary Molecular Effect model are presented. This contribution results deals with the Molecular Effect Model ILS Numerical/2D Graphical modelling for High Temperature Superconductors HTSCs group of [Tl- Sn-Pb-Ba-Si-Mn-Mg-Cu-O] whose TC > 0° C exclusively. This HTSCs class, among others, constitutes a recent materials innovation in HTSCs with both TC > 0° C and TC ˂ 0° C material compounds. It shows important recent/prospective electronics physics applications. For results with these optimization/simulations, classical ILS, 2D Interior Optimization, and 2D Graphical Optimization techniques are applied. Numerical-Imaging solutions comprise Tikhonov Regularization algorithms and mathematical modelling-methods for this HTSCs group. Primarily, results prove a 2D sinusoidal analytic geometry model curve. Findings for this Molecular Effect ILS optimization show acceptable theoretical Numerical, 2D Graphical Optimization outcomes with low residuals. Results comprise two strands, the modelling for TC Molecular Effect, and the ILS software/imaging methods. HTCS Electronics Physics applications emerge from numerical and graphical results.

Seismic hazard potential of Kachchh paleo-rift basin of Indian craton from seismic and geodetic strain rates

The Kachchh paleo-rift basin of western India which recently experienced Mw 7.6, 26th January 2001 Bhuj earthquake, is one of the most active and vulnerable intra-cratonic zones in the world categorized as seismic zone V, i.e. having potential to produce earthquakes of intensity IX or higher. We analysed the geodetic and seismic principal strain rates to reveal the seismic hazard potential of the Kachchh paleo-rift basin. The geodetic strain rates are calculated from the reported surface motion in the region using a modified least-square inversion scheme that utilizes distance and spatial coverage dependent weight factor on the uncertainty in the plate motion to get a reliable estimate of principal strain rates and their orientations at regular grid nodes. An optimal weighting factor yields a mean rate of compression of ~ − 16 ± 6 nano strain/yr towards north-northeast in the region. The seismic strain rates are estimated based on fault plane solutions of the significant past earthquakes (Mw ≥ 2.5) of the region using the Kostrov formulations. The seismic strain rate and stress inversion estimate indicate that the region released elastic strain at an average rate of ~ − 85 nano strain/yr towards north-south in the past 350 years. A composite analysis of the geodetic and seismic strain rates indicates 900–3000 years of recurrence interval of major (Mw 7.8–8) earthquakes in the region. Our analysis indicates a high rate of strain build-up on the reactivated major faults in the region that have the potential to generate devastating (Mw ≥6) earthquakes.

2D Graphical Optimization for Molecular Effect Model in High Temperature Superconductors Thallium Class [ TC < 0° , TC > 0° ] with Electronics Physics Multifunctional Transmission Line Design

Following High Temperature Superconductors (HTCSs) study series, Inverse Least Squares (ILS) 2D Numerical/Graphical Optimization is applied on Molecular Effect Model (MEM). Selected HTSCs class is Thallium group of [ Tl- Sn-Pb-Ba-Si-Mn-Mg-Cu-O ], constrained to [T<sub>C</sub> ? 0° , T<sub>C</sub> > 0° ]. Tetragonal Lattice and Amorphous compounds of this Type II Thallium HTSCs are not included at this research stage. Solutions with Matlab 2D Graphical Optimization techniques to validate primarily the MEM sinusoid-shape analytical geometry are presented. Programming-methods and imaging processing comparisons with GNU-Octave and Freemat software are also shown. Results comprise 2D Tikhonov Regularization algorithms with mathematical methods for this class. Findings obtain acceptable Numerical and 2D Graphical Optimization outcomes with low error-residuals. Results show two parts, the 2D Graphical Optimization MEM modelling, and MEM comparative imaging processing systems with examples and analysis of several numerical equations and predictions. Applications of MEM for the overview of the Multifunctional Transmission Line for SCs and HTSCs are included. Electronics Physics usages for Superconducting Multifunctional Transmission Lines, Superconductors in general, and HTSCs are presented.