Least-squares Inversion Research Articles

Non-stationary inversion of seismic data for fracture compliances in azimuthally anisotropic mediag

Fractures and tectonic settings cause azimuthal anisotropy in reservoirs. Recognizing the fracture model from the seismic data is a useful tool for identifying the productive zone in the reservoirs. We applied azimuthal velocity analysis in seismic processing to improve image quality and to estimate anisotropic model parameters. Using azimuthal residual moveout analysis, we predicted the direction of azimuthal anisotropy in the reservoir, and found that the results are consistent with fracture orientations obtained from the image logs in the reservoirs. Bayes’ theorem, and a cascaded procedure in least-squares inversion, matching observed amplitudes to linearized Zoeppritz equations, were used to estimate the elastic moduli in a first step and normal and tangential fracture weaknesses in a second step. We used laboratory experiments on core samples to validate the first step inversion results. We found that the propagation wavelet varied in space and reflection time, and so a library of extracted wavelets in the time-frequency domain was used for seismic inversion. Maps of computed fracture fluid index and the estimated fracture weaknesses help to visualize the role of fractures in reservoir productivity and revealed a consistency with the seismic peak frequency attribute in identifying zones of highly compliant fracture fill. The estimated fracture model demonstrates a good fit with the fractures seen in the available core samples and implies that the fracture fluid index is a useful attribute for determining the productive zones in the reservoir.

Audio magnetotelluric view of the giant carbonatite-hosted Bayan Obo REE deposit, Inner Mongolia, northern China

As critical minerals in low-carbon economies, rare-earth elements (REEs) are crucial for modern industry, technology, and medicine. The largest known REE resource in the world is the Bayan Obo (BO) deposit in northern China. However, BO features as complicated mineral compositions and has experienced several geological events. As a reuslt, controversy remains about the BO REE genesis and enrichment mechanism, and debates are also ongoing about the controlling structure of this giant deposit. We carried out an multiscale electromagnetism study on BO mineral deposits. The multiscale study consists a microscale on samples, a small scale targeting mineral deposits and a mid scale concerning the mine field. The small and mid scale study were conducted using audio-magnetotelluric (AMT). This study revealed the controlling structure using geoelectrical characteristics. AMT data were acquired from more than 590 stations, and the petro-electromagnetism of several samples was analyzed to understand the geoelectrical features of the ore deposits and their surrounding rocks. The data were interpreted using Bostick transformation and generalized least-squares inversions. We obtained the geoelectrical structure of the BO complex down to a maximum depth of 3500 m, and we present two-dimensional imaging based on the AMT conversion results. The results show that the BO deposit developed at the transition of the high- and low-resistivity geoelectrical structure from south to north. Our AMT results indicate that the tectonic setting of the BO deposit is the transition zone between the rift edge and craton margin slope. The ore geology is presently controlled by the complex slope and the rift remnant, the ore-bearing dolostone in the profiles is Y-shaped. It goes downward from south to north and potentially features a great mineral prospect deep in the BO deposit.

Earthquake source inversion by integrated fiber-optic sensing

We present an earthquake source inversion using a single time series produced by integrated fiber-optic sensing in a phase noise cancellation (PNC) system used for frequency metrology. Operating on a 123 km long fiber between Bern and Basel (Switzerland), the PNC system recorded the Mw3.9 Mulhouse earthquake that occurred on 10 September 2022 around 10 km north-west of the northern fiber end. A generalised least-squares inversion in the 4 - 13 s period band constrains the components of a double-couple moment tensor with an uncertainty that corresponds to around 0.2 moment magnitude units, nearly independent of prior information. Uncertainties for hypocenter location and original time are more variable, ranging between 4 - 20 km and 0.1 - 1 s, respectively, depending on whether injected prior information is realistic or almost absent. This work is a proof of concept that quantifies the resolvability of earthquake source properties under specific conditions using a single-channel stand-alone integrated (non-distributed) fiber-optic measurement. It thereby constitutes a step towards the integration of long-range phase-transmission fiber-optic sensors into existing seismic networks in order to fill significant seismic data gaps, especially in the oceans.

A validated numerical methodology for flow-induced vibration of a semi-spherical end cantilever rod in axial flow

This study presents a simulation method for turbulent flow-induced vibrations of cantilever rods with a semi-spherical end exposed to axial flow, a configuration investigated for the first time. This simulation strategy has been developed using solids4Foam, a toolkit for the open-source package OpenFOAM, which uses the finite-volume approach. The fluid and solid domain equations are solved separately. Coupling is achieved with the Interface Quasi-Newton Inverse Least-Squares (IQN-ILS) algorithm. The mean flow is described by the unsteady Reynolds-averaged Navier–Stokes equations. Turbulence is modeled through either the stress-transport model of Launder, Reece, and Rodi or the effective-viscosity k–ω shear stress transport model, both with the wall-function approach accounting for near-wall turbulence. The methodology is validated using experimental data produced during this study. The simulations show good agreement with the measured values of the oscillation amplitude and frequency for both flow directions (toward rod free-end and away from it). Turbulence model comparisons show that (a) Reynolds stress transport models are necessary to reproduce the vibration amplitude and (b) wall functions enable the simulations to be completed in realistic time scales. The significance to the fluid–solid-interaction (FSI) process of a so far overlooked (with the exception of a couple of recent studies) dimensionless number, the ratio of the flow dynamic pressure to the rod's Young's modulus of elasticity, is also explored. Simulations, which decouple the variation of this dimensionless number from that of the Reynolds number, demonstrate this number's strong effect on the vibration amplitude. This finding is important to the contact of further FSI studies and the scaling of FSI data.

PINNslope: Seismic data interpolation and local slope estimation with physics informed neural networks

Interpolation of aliased seismic data constitutes a key step in a seismic processing workflow to obtain high-quality velocity models and seismic images. Building on the idea of describing seismic wavefields as a superposition of local plane waves, we propose to interpolate seismic data by using a physics informed neural network (PINN). In the proposed framework, two feed-forward neural networks are jointly trained using the local plane wave differential equation as well as the available data as two terms in the objective function: a primary network assisted by positional encoding is tasked with reconstructing the seismic data, whereas an auxiliary, smaller network estimates the associated local slopes. Results on synthetic and field data validate the effectiveness of the proposed method in handling aliased (coarsely sampled) data and data with large gaps. Our method compares favorably against a classic least-squares inversion approach regularized by the local plane-wave equation as well as a PINN-based approach with a single network and precomputed local slopes. We find that introducing a second network to estimate the local slopes, whereas at the same time interpolating the aliased data enhances the overall reconstruction capabilities and convergence behavior of the primary network. Moreover, an additional positional encoding layer embedded as the first layer of the wavefield network confers to the network the ability to converge faster, improving the accuracy of the data term.

Geoelectric Modelling Based on Bessel Functions Integral and Damped Least-Square Inversion for Layered Earth Models

Apparent resistivity formulations of a geoelectric method for layered Earth have been obtained analytically in the Bessel functions integral. This formulation is obtained through the application of two boundary conditions. First, the current density is zero at the Earth's surface. Second, current density and electric potential are continuous at the boundary between the layers. Geoelectric modelling can be done using several model parameters through this formulation. The modelling results show that apparent resistivity formulations based on Bessel function integrals can simulate apparent resistivity curves for layered earth models. The inversion process uses the apparent resistivity formulation based on Bessel function integrals. In this study, the inversion process uses a dumped Least-squared inversion method. The first step begins by testing the inversion program using synthetic data. After that, the inversion program is used in field data. The inversion results using field data from geoelectric data in Mount Pandan, East Java, show that the program was well done, with a minimal error value of 1.24%.

Damping Factors in the Interpretation of Geoelectric Data (Case Study: Malalak Agam Rock Structure)

This research aims to optimize the damping factor so that the results of Geoelectric data inversion are stable and in accordance with current geological conditions in Malalak Agam. This type of research is a descriptive research using secondary data in the form of pseudo-type resistance data and electrode spacing obtained from research in the field of Geoelectric exploration in the Department of Physics at Padang State University (UNP). This data is obtained from Geoelectric secondary data and location supporting data. The geoelectric data processing stage is carried out using Res2dinv software which is used to model in 2-D using least-square inversion. The results showed that based on the interpretation of the data, the suitable damping factors in Malalak Agam District, West Sumatra, were the initial damping factor (0.2 – 0.25) and the minimum damping factor (0.01 – 0.1) because on trajectory 2 At the third measurement point 160 meters from point 0 was dominated by limestone and sandstone rocks. The existence of Limestone acts as a slip field, and there is Sandstone right above it which causes large-scale landslides from the first to fifth measurement points (315-160 meters from point 0) and on trajectory 3 at this time there is a landslide with a small volume, it is estimated that the avalanche is at the second measurement point 120 meters from point 0 with an avalanche thickness ranging from approximately 5 meters.

Least-squares reverse time migration of simultaneous sources with deep-learning-based denoising

Least-squares reverse time migration (LSRTM) is currently one of the most advanced migration imaging techniques in the field of geophysics. It uses least-squares inversion to fit the observed data, resulting in high-resolution imaging results with more accurate amplitudes and better illumination compensation than conventional reverse time migration (RTM). However, noise in the observed data and the Born approximation forward operator can result in high-wavenumber artifacts in the final imaging results. Moreover, iteratively solving LSRTM leads to one or two orders of computational cost higher than conventional RTM, making it challenging to apply extensively in industrial applications. Simultaneous source acquisition technology can reduce the computational cost of LSRTM by reducing the number of wavefield simulations. However, this technique also can cause high-wavenumber crosstalk artifacts in the migration results. To effectively remove the high-wavenumber artifacts caused by these issues, simultaneous source and deep learning are combined to speed up LSRTM as well as suppress high-wavenumber artifacts. A deep residual neural network (DR-Unet) is trained with synthetic samples, which are generated by adding field noise to synthesized noise-free migration images. Then, the trained DR-Unet is applied on the gradient of LSRTM to remove high-wavenumber artifacts in each iteration. Compared to directly applying DR-Unet denoising to LSRTM results, embedding DR-Unet denoising into the inversion process can better preserve weak reflectors and improve denoising effects. Finally, the proposed LSRTM method is tested on two synthetic data sets and a land data set. The tests demonstrate that the proposed method can effectively remove high-wavenumber artifacts, improve imaging results, and accelerate convergence speed.

Wasserstein distance-based full waveform inversion method for density reconstruction

Reliable density information is an essential factor in lithologic interpretation and reservoir evaluation. However, density reconstruction is hampered by a lack of long-wavelength information and the crosstalk between different parameters. The powerful nonlinearity in density inversion constrains the multi-parameter full waveform inversion application. This paper introduces the Wasserstein distance into the full waveform inversion for velocity and density based on the optimal transport theory. We construct an objective function with better convexity to avoid the cycle-skipping caused by the poor initial model. Furthermore, due to the sensitivity of the quadratic Wasserstein distance to low-frequency, we add the low-wavenumber component absent in the conventional density inversion. We acquire a long-wavelength density background using optimal transport inversion and then apply it as an initial model for least-squares inversion. Numerical examples show that our optimal transport inversion effectively builds a reasonable density background model for FWI. Density inversion can be improved by incorporating optimal transport and least-squares theory, leading to a reliable quantitative description for petroleum exploration and development.

An efficient approach for inverting rock exhumation from thermochronologic age–elevation relationship

Abstract. This study implements the least-squares inversion method for solving the exhumation history from the thermochronologic age–elevation relationship (AER) based on the linear equation among exhumation rate, age and total exhumation from the closure depth to the Earth surface. Modeling experiments suggest significant and systematic influence of initial geothermal model, the a priori exhumation rate and the time interval length on the a posteriori exhumation history. Lessons learned from the experiments include that (i) the modern geothermal gradient can be used for constraining the initial geothermal model, (ii) a relatively high a priori exhumation rate would lead to systematically lower a posteriori exhumation and vice versa, (iii) the variance of the a priori exhumation rate controls the variation in the inverted exhumation history, and (iv) the choice of time interval length should be optimized for resolving the potential temporal changes in exhumation. To mitigate the dependence of inverted erosion history on these initial parameters, we implemented a new stepwise inverse modeling method for optimizing the model parameters by comparing the observed and predicted thermochronologic data and modern geothermal gradients. Finally, method demonstration was performed using four synthetic datasets and three natural examples of different exhumation rates and histories. It is shown that the inverted rock exhumation histories from the synthetic datasets match the whole picture of the “truth”, although the temporal changes in the magnitude of exhumation are underestimated. Modeling of the datasets from natural samples produces geologically reasonable exhumation histories. The code and data used in this work are available on Zenodo (https://doi.org/10.5281/zenodo.10839275).

Ocean bottom dual-sensorQ-compensated elastic least-squares reverse time migration based on acoustic and separated-viscoelastic coupling equations

The ocean bottom dual-sensor (OBD) observation system places water detectors (pressure sensors) and land detectors on the irregular seabed interface to receive acoustic pressure fields and elastic wavefields, respectively. These data are usually applied to effectively remove ghost waves and ringing interference in the seawater layer, rather than being jointly used for migration. We propose an ocean bottom dual-sensor viscoacoustic and separated-viscoelastic coupled Q-compensated least-squares reverse time migration (OBD-VSV- QLSRTM) in curvilinear coordinates. In this method, to solve the Q-compensated elastic inverse problem, we jointly use the recorded acoustic pressure and elastic multicomponent seismic data from the OBD observation system. A new misfit function in the sense of least-squares inversion is constructed based on viscoacoustic and separated viscoelastic wavefields. Acoustic and separated viscoelastic equations are used to describe the acoustic wavefield in the acoustic medium and the Q-compensated P and S wavefields in the underlying viscoelastic medium, respectively. On the acoustic-viscoelastic interface, we implement a stable governing equation to ensure continuous and steady transmission of Q-compensated stresses in the subseabed and pressure in the seawater. To address the irregular seabed problem, we mesh the acoustic-viscoelastic models onto curvilinear grids and apply coordinate transformations to map the models and equations to a new curvilinear coordinate system. We derive viscoacoustic and separated-viscoelastic coupled adjoint and demigration operators in the curvilinear coordinates, enabling linear acoustic-viscoelastic modeling and stable receiver-side back-propagated wavefield continuation. Numerical examples conducted on two typical acoustic-viscoelastic models demonstrate that our proposed OBD-VSV- QLSRTM in curvilinear coordinates can produce highly accurate P- and S-wave images efficiently.

Image-domain seismic inversion by deblurring with invertible recurrent inference machines

In complex geologic settings and in the presence of sparse acquisition systems, seismic migration images manifest as nonstationary blurred versions of the unknown subsurface model. Thus, image-domain deblurring is an important step to produce interpretable and high-resolution models of the subsurface. Most deblurring methods focus on inverting seismic images for their underlying reflectivity by iterative least-squares inversion of a local Hessian approximation; this is obtained by either direct modeling of the so-called point-spread functions (PSFs) or by a migration-demigration process. In this work, we adopt a novel deep-learning (DL) framework, based on invertible recurrent inference machines (i-RIMs), which allows approaching any inverse problem as a supervised learning task informed by the known modeling operator (convolution with PSFs in our case): our algorithm can directly invert migrated images for impedance perturbation models, assisted with the prior information of a smooth velocity model and the modeling operator. Because i-RIMs are constrained by the forward operator, they implicitly learn to shape/regularize output models in a training-data-driven fashion. As such, the resulting deblurred images indicate great robustness to noise in the data and spectral deficiencies (e.g., due to limited acquisition). The key role played by the i-RIM network design and the inclusion of the forward operator in the training process is supported by several synthetic examples. Finally, using field data, we find that i-RIM-based deblurring has great potential in yielding robust, high-quality relative impedance estimates from migrated seismic images. Our approach could be of importance toward future DL-based quantitative reservoir characterization and monitoring.

Ocean Bottom Seismometer Clock Correction using Ambient Seismic Noise

Ocean-bottom seismometers (OBSs) are equipped with seismic sensors that record acoustic and seismic events at the seafloor, which makes them suitable for investigating tectonic structures capable of generating earthquakes offshore. One critical parameter to obtain accurate earthquake locations is the absolute time of the incoming seismic signals recorded by the OBSs. It is, however, not possible to synchronize the internal clocks of the OBSs with a known reference time, given that GNSS signals are unable to reach the instrument at the sea bottom. To address this issue, here we introduce a new method to synchronize the clocks of large-scale OBS deployments. Our approach relies on the theoretical time-symmetry of time-lapse (averaged) crosscorrelations of ambient seismic noise. Deviations from symmetry are attributed to clock errors. This implies that the recovered clock errors will be obscured by lapse crosscorrelations' deviations from symmetry that are not due to clock errors. Non-uniform surface wave illumination patterns are arguably the most notable source which breaks the time symmetry. Using field data, we demonstrate that the adverse effects of non-uniform illumination patterns on the recovered clock errors can be mitigated by means of a weighted least-squares inversion that is based on station-station distances. In addition, our methodology permits the recovery of timing errors at the time of deployment of the OBSs. This error can be attributed to either: i) a wrong initial time synchronization of the OBS or ii) a timing error induced by changing temperature and pressure conditions while the OBS is sunk to the ocean floor. The methodology is implemented in an open-source Python package named OCloC, and we applied it to the OBS recordings acquired in the context of the IMAGE project in and around Reykjanes, Iceland. As expected, most OBSs suffered from clock drift. Surprisingly, we found incurred timing errors at the time of deployment for most of the OBSs.

Denoising land-based controlled-source electromagnetic data based on a same-site noise reference channel

SUMMARY The applications of land-based controlled-source electromagnetic (CSEM) exploration are severely limited by strong noise interferences, particularly in mining areas. In this study, we introduce a novel denoising method for CSEM data using a same-site noise reference channel (NRC). While recording data through the normal survey channel (NSC), an additional set of the NRC was added at the same site. The NRC had a different surveying azimuth compared to the NSC and contained minimal or no useful signals. However, the noise characteristics in both the NRC and NSC were considerably similar due to their simultaneous acquisition at the same site. By establishing a set of overdetermined equations for the NSC based on quantified spectrogram characteristics of the NRC, the noise can be effectively eliminated from the NSC using least-squares inversion, resulting in enhanced signal-to-noise ratio data. The effectiveness of the proposed CSEM data-denoising method was validated through its application on real data, and the proposed method is applicable to other types of artificial source data.

Slip Deficit Rates on Southern Cascadia Faults Resolved with Viscoelastic Earthquake Cycle Modeling of Geodetic Deformation

ABSTRACT The fore-arc of the southern Cascadia subduction zone (CSZ), north of the Mendocino triple junction (MTJ), is home to a network of Quaternary-active crustal faults that accumulate strain due to the interaction of the North American, Juan de Fuca (Gorda), and Pacific plates. These faults, including the Little Salmon and Mad River fault (LSF and MRF) zones, are located near the most populated parts of California’s north coast and show paleoseismic evidence for three slip events of several-meter scale in the past 1700 yr. However, the geodetic slip rates of these faults are poorly constrained. In this work, we analyze a new compilation of interseismic geodetic velocities from Global Navigation Satellite Systems, leveling, and tide gauge data near the MTJ to constrain present-day slip deficit rates on upper-plate faults and coupling on the megathrust. We construct Green’s functions for interseismic slip deficit for discrete faults embedded in an elastic plate overlying a viscoelastic mantle. We then use a constrained least-squares inversion to determine best-fitting slip rates on the major faults and investigate slip rate trade-offs between faults. Results indicate that the LSF and MRF systems together accumulate 4–5 mm/yr of reverse-slip deficit, although their separate slip rates cannot be determined independently. Modeling of the horizontal and vertical velocities suggests that the southernmost CSZ is coupled interseismically to deeper than 25 km depth. We also find that 6–17 mm/yr of right-lateral slip deficit extends north of the MTJ and into the southern Cascadia fore-arc. These results reinforce the notion that both the southernmost Cascadia megathrust and the smaller fore-arc faults above it contribute to regional seismic hazard.

Seeing through the CO2plume: Joint inversion-segmentation of the Sleipner 4D seismic data set

Time-lapse (4D) seismic inversion is the leading method to quantitatively monitor fluid-flow dynamics in the subsurface, with applications ranging from enhanced oil recovery to subsurface CO2storage. The process of inverting 4D seismic data for reservoir properties is a notoriously ill-posed inverse problem due to the band-limited and noisy nature of seismic data and inaccuracies in the repeatability of 4D acquisition surveys. Consequently, ad-hoc regularization strategies are essential for the 4D seismic inverse problem to obtain geologically meaningful subsurface models and associated 4D changes. Motivated by recent advances in the field of convex optimization, we propose a joint inversion-segmentation algorithm for 4D seismic inversion that integrates total variation and segmentation priors as a way to counteract missing frequencies and present noise in 4D seismic data. The proposed inversion framework is designed for poststack seismic data and applied to a pair of seismic volumes from the open Sleipner 4D seismic data set. Our method has three main advantages over state-of-the-art least-squares inversion methods. First, it produces high-resolution baseline and monitor acoustic models. Second, it mitigates nonrepeatable noise and better highlights real 4D changes by leveraging similarities between multiple data. Finally, it provides a volumetric classification of the acoustic impedance 4D difference model (4D changes) based on user-defined classes (i.e., percentages of speedup or slowdown in the subsurface). Such advantages may enable more robust stratigraphic/structural and quantitative 4D seismic interpretation and provide more accurate inputs for dynamic reservoir simulations. Alongside presenting our novel inversion method, we introduce a streamlined data preprocessing sequence for the 4D Sleipner poststack seismic data set that includes time-shift estimation and well-to-seismic tie. Finally, we provide insights into the open-source framework for large-scale optimization that we used to implement the proposed algorithm in an efficient and scalable manner.

Thaw-Season InSAR Surface Displacements and Frost Susceptibility Mapping to Support Community-Scale Planning in Ilulissat, West Greenland

In permafrost regions, ground surface deformations induced by freezing and thawing threaten the integrity of the built environment. Mapping the frost susceptibility of the ground at a high spatial resolution is of practical importance for the construction and planning sectors. We processed Sentinel-1 Interferometric Synthetic Aperture Radar (InSAR) data from thawing seasons 2015 to 2019, acquired over the area of Ilulissat, West Greenland. We used a least-squares inversion scheme to retrieve the average seasonal displacement (S) and long-term deformation rate (R). We secondly investigated two different methods to extrapolate active layer thickness (ALT) measurements, based on their statistical relationship with remotely sensed surface characteristics. A generalized linear model (GLM) was first implemented, but the model was not able to fit the data and represent the ALT spatial variability over the entire study domain. ALT were alternatively averaged per vegetation class, using a land cover map derived by supervised classification of Sentinel-2 images. We finally estimated the active layer ice content and used it as a proxy to map the frost susceptibility of the ground at the community scale. Fine-grained sedimentary basins in Ilulissat were typically frost susceptible and subject to average seasonal downward displacements of 3 to 8 cm. Areas following a subsiding trend of up to 2.6 cm/yr were likely affected by permafrost degradation and melting of ground ice below the permafrost table. Our approach enabled us to identify frost-susceptible areas subject to severe seasonal deformations, to long-term subsidence induced by degrading permafrost, or to both. Used in combination with traditional site investigations, InSAR maps provide valuable information for risk management and community planning in the Arctic.

Strain-based forward modeling and inversion of seismic moment tensors using distributed acoustic sensing (DAS) observations

This study used a waveform inversion of distributed acoustic sensing (DAS) data, acquired in two horizontal monitoring wells, to estimate the moment tensor (MT) of two induced microearthquakes. An analytical forward model was developed to simulate far-field tangential strain generated by an MT source in a homogeneous and anisotropic medium, averaged over the gauge length along a fiber of arbitrary orientation. To prepare the data for inversion, secondary scattered waves were removed from the field observations, using f-k filtering and time-windowing. The modeled and observed primary arrivals were aligned using a cut-and-paste approach. The MT parameters were inverted via a least-squares approach, and their uncertainties were determined through bootstrap analysis. Using simulated data with additive noise derived from the field data and the same fiber configuration as the monitoring wells, the inversion method adequately resolved the MT. Despite the assumption of Gaussian noise, which underlies the least-squares inversion approach, the method was robust in the presence of heavy-tailed noise observed in field data. When the inversion was applied to field data, independent inversion results using P-waves, S-waves, and both waves together yielded results that were consistent between the two events and for different wave types. The agreement of the inversion results for two events resulting from the same stress field illustrated the reliability of the method. The uncertainties of the MT parameters were small enough to make the inversion method useful for geophysical interpretation. The variance reduction obtained from the data predicted for the most probable MT was satisfying, even though the polarity of the P-waves was not always correctly reproduced.

Nonlinear inversion of electrical resistivity sounding data for multi-layered 1-D earth model using global particle swarm optimization (GPSO)

Interpreting geophysical data requires solving nonlinear optimization problem(s) in inversion. Analytical methods such as least-square have some intrinsic limitations, which include slow convergence and dimensionality, making heuristic-based swarm intelligence a better alternative. Large-scale nonlinear optimization problems in inversion can be solved effectively using a technique within the swarm intelligence family called Particle Swarm Optimization (PSO). This study evaluates the inversion of geoelectrical resistivity data with global particle swarm optimization (GPSO). We attempted to invert field vertical electrical sounding data for a multi-layered 1-D earth model using the developed particle swarm optimization algorithm. The result of the PSO-interpreted VES data was compared with that of the least square inversion result from Winresist 1.0. According to the PSO-interpreted VES results, satisfactory solutions may be attained with a swarm of 200 or fewer particles, and convergence can be reached in fewer than 100 iterations. The GPSO inversion approach has a maximum capacity of 100 iterations, more than the least square inversion algorithm of the Winresist, which has a maximum capacity of 30 iterations. The misfit error of GPSO inversion is 6.14×10−7, much lower than that of the least square inversion of 4.0. The GPSO inversion model has lower and upper limit values of the geoelectric layer parameters model to fit the true model better. The limitations of the developed PSO inversion scheme include a slower execution time of the inversion procedures than the least-square inversion. There is a need for a priori knowledge of the number of layers from borehole reports in the study area. The PSO inversion scheme, however, estimates inverted models closer to the true solutions with greater accuracy than the least-square inversion scheme.

Chemometrics Assisted Spectrophotometric Method Development and Validation for Simultaneous Estimation of Abacavir, Lamivudine and Dolutegravir in Dosage Form

Abstract: Aim: Multivariate methods, particularly Classical Least Square, Inverse Least Square (ILS), Partial Least Square and Principal Component Regression are invented for the quantitation of the Abacavir sulphate (ABA), Lamivudine (LAM) and Dolutegravir sodium (DOL) in their combined tablet formulation. Materials and Methods: Chemometrics is the integration of statistical and mathematical approaches to analytical data in order to extract as much information as possible. The calibration and validation sets were built using fractional factorial design. 32 ternary mixtures of calibration sets and 16 mixtures of validation set were prepared. The absorbance data matrix was created by measuring absorbance in the range of 230 to 308 nm (Δλ = 3 nm) at 27 distinct wavelengths. The models were developed with the aid of MATLAB 2018a, Minitab 16.1.1 and MS Excel 2010. Results: The recovery values were close to 100% with low standard deviation (SD) justified the high accuracy of the proposed methods. For chemometrics approaches, the RMSECV, RMSEC, and RMSEP values produced show good accuracy and precision. The values of model diagnostic tools were lowest for ILS method. Conclusion: The ILS was shown to be the most appropriate method among produced chemometric models. The chemometric method is more accurate and precise than conventional methods as the total absorbance of the ternary mixture was measured and can be utilised in simultaneous estimation. With great recoveries and precision, the proposed approach was successfully used to the assay of formulation. Keywords: Abacavir sulphate, Lamivudine, Dolutegravir sodium, Chemometrics, Spectophotometric, Validation.