Inverse Parameter Research Articles

Vertical Slowness-Constrained Joint Anisotropic Parameters and Event-Location Inversion for Downhole Microseismic Monitoring

The construction of accurate anisotropic velocity models is essential for effective microseismic monitoring in hydraulic fracturing. Ignoring anisotropy can result in significant distortions in microseismic event locations and their interpretation. Although methods exist to simultaneously invert anisotropic parameters and event locations using microseismic arrival times, the results heavily depend on accurate initial models and sufficient ray coverage due to strong trade-offs among multiple parameters. Microseismic waveform inversion for anisotropic parameters remains challenging due to the low signal-to-noise ratio of the data and the high computational cost. To address these challenges, we propose a method for jointly inverting event locations and velocity updates based on arrival times and vertical slowness estimates, under the assumption of small horizontal velocity variations. Vertical slowness estimates, which are independent of source information and easily obtainable, provide an additional constraint that enhances inversion stability. We test the proposed method in four synthetic examples under various conditions. The results demonstrate that incorporating vertical slowness effectively constrains and stabilizes conventional travel-time inversion, especially in scenarios with poor raypath coverage. Additionally, we apply this method to a field case and find that it produces more reasonable event locations compared to inversions using arrival times alone. This joint inversion method can enhance the accuracy of anisotropic structures and event locations, which thus help with fracture characterization in tight and low-permeability reservoirs. It may serve as an effective downhole monitoring approach for hydrocarbon and geothermal energy production.

Application of machine learning and optimization-based mesoscopic parameter inversion in numerical models of cement-stabilized macadam

ABSTRACT Cement-stabilised macadam (CSM) is widely used in road engineering due to its high strength and durability. Constructing accurate numerical models is crucial for analysing failure mechanisms and improving the performance and service life of CSM. However, the accuracy of these models largely depends on the precision of mesoscopic parameter inversion. Existing inversion methods mainly rely on formula-based derivations and manual trial-and-error approaches, which are time-consuming and often limited in accuracy, typically below 70%. To address these limitations, this study employs machine learning to enhance both the efficiency and precision of inversion. A semi-circular bending model of CSM was established using the discrete element method (DEM) to generate a dataset of macroscopic and mesoscopic parameters. Six machine learning models were evaluated, with the backpropagation neural network (BPNN) yielding the best performance. BPNN was further integrated with a particle swarm optimisation (PSO) algorithm to perform mesoscopic parameter inversion. Validation against laboratory tests showed that the PSO-integrated BPNN method reduced simulation errors to less than 5%, significantly improving inversion accuracy. Additionally, SHAP analysis identified the key factors influencing macroscopic mechanical properties. This study proposes an efficient mesoscopic parameter inversion method, providing valuable insights for optimising CSM materials in engineering applications.

A deep learning-based parametric inversion for forecasting water-filled bodies position using electromagnetic method

A deep learning-based parametric inversion for forecasting water-filled bodies position using electromagnetic method

Application of Karhunen-Loève Transform Algorithms in Hydrogeological Parameter Compression: A Comparative Study

ABSTRACT This paper proposes a parameter compression method using the Karhunen-Loève Transform (K-L) to reduce the computational burden of parameter inversion in groundwater models. Two spatial distributions of hydraulic conductivity (K) were generated using Kriging interpolation and Sequential Gaussian Simulation (SGS), and the K-L transform was applied to reduce their dimensionality. The method’s generality was assessed by varying model boundaries, extreme values of K, and simulation periods. The results showed that sequentially adding different boundary conditions resulted in high accuracy in model output. The model was most accurate when K values were within the range of 50-100 m/d, and its performance decreased as the range of K expanded. The model also exhibited high accuracy across various time periods within a single stress period. Dimensionality reduction through Kriging-KL and SGS- KL resulted in high accuracy of model-simulated heads, with R2 values exceeding 0.80 and 0.98 respectively. Overall, the K-L transform efficiently reduces parameter dimensions without compromising model performance. SGS-KL showed greater robustness under varying parameters, indicating its suitability for complex groundwater systems. This study contributes to efficient groundwater model inversion and provides valuable insights into the characteristics of groundwater systems.

Inverse Problem of Parameter Estimation in Natural Convection of Iron Oxide – Distilled Water Nanofluids

Abstract Nanofluids have been used to facilitate the transport of nanoparticles to tumor regions for different purposes, such as drug delivery, promotion of antioxidant effects, and selective absorption of energy from external sources for thermal treatments. The characterization of nanofluids by solving an inverse parameter estimation model was the main objective of this work. A nanofluid of Fe2O3 nanoparticles dissolved in distilled water was heated by a diode-laser, causing natural convection currents during the experiment. The parameter estimation problem was solved within the Bayesian framework of statistics by applying the Metropolis-Hastings algorithm of the Markov Chain Monte Carlo method, thus demanding large computational times associated with stochastic simulations of a natural convection problem. A multivariate linear regression model was then trained with the high-fidelity natural convection model, in order to speed up calculations during the solution of the inverse problem. It is shown that the multivariate linear regression low-fidelity model can be used as an accurate representation of the temperatures at the heated surface of the nanofluid, thus resulting in estimated parameters with small uncertainties.

Bayesian Fourier coefficient inversion for gravity-induced stress parameters in tilted transversely isotropic gas-bearing reservoirs

Field observations and core data reveal that natural fractures may not be perfectly vertical but are commonly inclined, yielding an effective tilted transversely isotropic (TTI) medium. Neglecting TTI symmetry can lead to erroneous stress prediction results, which are important for hydrocarbon exploration and development. We have developed a Bayesian Fourier coefficient (FC) inversion approach to estimate gravity-induced stress parameters in TTI media, specifically horizontal stress and the differential horizontal stress ratio (DHSR). The gas-bearing reservoir with dipping fractures is modeled as a linearly elastic, homogeneous TTI material. Under the assumption of no lateral strain, we combine fracture-effective medium models with the generalized Hook’s law to establish the relationship between gravity-induced stress parameters and TTI elastic and fracture parameters. Based on seismic scatter theory, we derive a linearized PP-wave reflection coefficient and corresponding FC expressions parameterized by P- and S-wave moduli, density, fracture density, and fracture dip in TTI media. Furthermore, we present a Bayesian FC inversion constrained by a joint multivariable Cauchy prior model to estimate these model parameters, which are then used to calculate gravity-induced stress parameters. A synthetic example demonstrates that Bayesian FC inversion under the TTI model assumption produces more reliable estimates of gravity-induced stress parameters compared to those obtained under the horizontal transversely isotropic (HTI) model assumption. Additionally, a real data set from a gas-bearing reservoir is employed to demonstrate the feasibility of our method. Results indicate that our method yields reasonable estimates of gravity-induced stress parameters with good lateral continuity. The proposed method could aid in identifying optimal zones for hydraulic fracturing of a subterranean formation with TTI symmetry.

Frequency-dependent nonlinear amplitude-variation-with-offset inversion for fluid mobility in viscoelastic media

Reservoir fluid mobility is defined as the ratio of rock permeability to fluid viscosity, which is an important attribute to guide the prediction of high-quality oil and gas reservoirs. Frequency-dependent amplitude-variation-with-offset (AVO) inversion, based on viscoelastic theory, is a useful tool for fluid identification. In conventional prestack inversion, linear approximations are usually used to calculate the reflection coefficients, whereas nonlinear inversions are only occasionally carried out. However, the nonlinear equation for the reflection coefficient, derived from the exact Zoeppritz equation, has higher accuracy and fewer assumptions than the linear approximations. Therefore, we derive a nonlinear frequency-dependent reflection coefficient equation of the PP wave in terms of P-wave velocity reflectivity, S-wave velocity reflectivity, and fluid mobility, based on the relationship among fluid mobility, incident angle, and seismic wave frequency. We consider viscoelastic media and frequency-dependent responses to improve the authenticity of the reflection coefficients. In addition, we develop a split-step inversion method for fluid mobility based on the artificial neural network inversion algorithm. Synthetic and field data examples demonstrate that our split-step inversion method outperforms traditional inversion methods that rely on approximate equations for predicting underground reservoirs, improving the stability of fluid mobility parameter inversion.

Half logistic exponentiated inverse Rayleigh distribution: Properties and application to life time data.

This paper presents a novel extension of the exponentiated inverse Rayleigh distribution called the half-logistic exponentiated inverse Rayleigh distribution. This extension improves the flexibility of the distribution for modeling lifetime data for both monotonic and non-monotonic hazard rates. The statistical properties of the half-logistic exponentiated inverse Rayleigh distribution, such as the quantiles, moments, reliability, and hazard function, are examined. In particular, we provide several techniques to estimate the half-logistic exponentiated inverse Rayleigh distribution parameters: weighted least squares, Cramér-Von Mises, maximum likelihood, maximum product spacings and ordinary least squares methods. Moreover, numerical simulations were performed to evaluate these estimation methods for both small and large samples through Monte Carlo simulations, and the finding reveals that the maximum likelihood estimation was the best among all estimation methods since it comprises small mean square error compared to other estimation methods. We employ real-world lifetime data to demonstrate the performance of the newly generated distribution compared to other distributions through practical application. The results show that the half-logistic exponentiated inverse Rayleigh distribution performs better than alternative versions of the Rayleigh distributions.

Irregular seeds DEM parameters prediction based on 3D point cloud and GA-BP-GA optimization

Due to the small and irregular shapes of vegetable seeds, modeling them is challenging, and the imprecision of physical parameters hinders the performance of vegetable seeders, impeding simulation development. In this study, seeds of cucumber, pepper, and tomato were seen as examples. A 3D point cloud reconstruction method based on Structure-from-Motion Multi-View Stereo (SfM-MVS) was employed to accurately extract 3D models of small and irregularly shaped seeds. Corresponding discrete element models were established. Combining physical and simulation experiments on seed angle of repose(AOR), significant parameters influencing seed AOR and their ranges were identified through Plackett–Burman Design (PBD) and steepest ascent test. Within this range, the GA-BP-GA algorithm was used to accurately inverse the optimal parameter combination. The results indicate that the SfM-MVS 3D point cloud reconstruction method can extract more detailed shape information of small and irregularly shaped seeds. The GA-BP-GA algorithm achieved an inversion of physical parameters with the smallest relative error of cucumber, pepper, and tomato seeds being 0.26%, 0.98%, and 0.51%, respectively. Through experimental comparative analysis, the feasibility and accuracy of this method in calibrating discrete element parameters for small and irregularly shaped seeds were validated. The established seed models and calibrated parameters in this study can be implemented to the simulation optimization design of vegetable seeders, enhancing development efficiency and operational performance.

Investigating small-strain site response using inverse soil dynamic parameters from downhole arrays

Previous research on site response has primarily focused on reproducing and predicting ground motions recorded by vertical seismic arrays. This study evaluated the ability to reproduce and predict small-strain site response at the Treasure Island Downhole Array and Delaney Park Downhole Array using inverse soil dynamic parameters. First, parameters such as seismic wave velocity profiles and Rayleigh damping ratios were obtained through seismic interferometry and spectral ratio methods based on the earthquake records. Subsequently, the validity and reliability of these inverse soil dynamic parameters were evaluated by comparing the simulated and observed ground responses. Finally, the inverse method was compared with other methods considering spatial variability in one-dimensional site response analysis. Quantitative comparisons show that the inverse method effectively predicts and reproduces site response and outperforms the traditional method relying on the single borehole shear wave velocity profile and damping ratio from empirical model. Moreover, the inverse method better captures spatial variability at the Delaney Park Downhole Array.

Microstructural Analysis of Inversion Degree in Sol-Gel Synthesized Spinel MnCo2O4 Particles

Spinel-type compounds exhibit versatile structural and functional properties, which stems from the unique cation distribution that spans a spectrum from partial to total cell inversion degrees.In this study, we investigated the preparation of MnCo₂O₄ particles synthesized via a modified sol-gel method. The synthesized particles were thoroughly characterized using X-ray diffraction, scanning electron microscopy, Raman spectroscopy, and Rietveld refinements to assess their microstructural properties. The impact of different annealing temperatures (1000, 1100, and 1200 °C) and durations (1 and 8 hours) on the crystal evolution of the synthesized particles was systematically investigated to assess the structural adaptability of the MnCo₂O₄ spinel under these synthesis conditions. The degree of inversion and oxygen positional parameters within the crystalline systems were quantified using the Bertaut method to obtain the specific arrangement of manganese and cobalt ions for inversion degrees from approximately 0.85 (random) to 1.00 (inversion) with the presence of a secondary phase of Co3O4 (20 wt%). The lattice parameter was determined from Rietveld analysis to be 8.2720 and 8.2927 Å for the normal and inverted spinel, respectively. Finally, the I(220)/I(400) and I(400)/I(422) intensity ratios were identified as reliable indicators of inversion degree, with these intensities ratios significantly influenced by the oxygen positional parameter.

Feedforward neural network-assisted parameter identification and tuning for uniaxial superelastic shape memory alloy models under dynamic loads

In this study, we introduce a machine learning-based method to predict the modeling parameters of superelastic shape memory alloys (SMAs). Our goal is to simultaneously determine and fine-tune all internal and material-related parameters, including thermodynamic ones, for a specific constitutive model using only cyclic tensile tests. We employ feedforward neural networks (FNNs) for their versatile structure. First, we sample the searched parameters within a predefined parameter space using the Latin hypercube sampling method. Then, using the constitutive model with the sampled parameters and representative strain loading, we generate the corresponding stress responses and finally train the FNN. To address the ill-posed nature of this inverse parameter identification problem and ensure a unique parameter set, during training, we use a dual network architecture with an additional FNN-based surrogate of the constitutive model. We also utilize transfer learning to accelerate the training process through knowledge transfer and handle multiple load cases simultaneously, ensuring consistent parameter identification across different scenarios. We validate the method by comparing the numerical results with the experimental data and demonstrate the importance of accurately identified parameter sets by numerical investigations on a SMA-retrofitted frame structure.

Adaptive Surrogate Model Assisted Swarm Intelligence for Parameter Inversion of complex hydrological models

Adaptive Surrogate Model Assisted Swarm Intelligence for Parameter Inversion of complex hydrological models

Simulation of Load–Sinkage Relationship and Parameter Inversion of Snow Based on Coupled Eulerian–Lagrangian Method

The accurate calibration of snow parameters is necessary to establish an accurate simulation model of snow, which is generally used to study tire–snow interaction. In this paper, an innovative parameter inversion method based on in situ test results is proposed to calibrate the snow parameters, which avoids the damage to the mechanical properties of snow when making test samples using traditional test methods. A coupled Eulerian–Lagrangian (CEL) model of plate loading in snow was established; the sensitivity of snow parameters to the macroscopic load–sinkage relationship was studied; a plate-loading experiment was carried out; and the parameters of snow at the experimental site were inverted. The parameter inversion results from the snow model were verified by the experimental test results of different snow depths and different plate sizes. The results show the following: (1) The material cohesive, angle of friction, and hardening law of snow have great influence on the load–sinkage relationship of snow, the elastic modulus has a great influence on the unloading/reloading stiffness of snow, and the influence of density and Poisson’s ratio on the load–sinkage relationship can be ignored. (2) The correlation coefficient between the inversion result and the matching test data is 0.979, which is 0.304 higher than that of the initial inversion curve. (3) The load–sinkage relationship of snow with different snow depths and plate diameters was simulated by using the model parameter of inversion, and the results were compared with the experimental results. The minimum correlation coefficient was 0.87, indicating that the snow parameter inversion method in this paper can calibrate the snow parameters of the test site accurately.

Multi-Band Scattering Characteristics of Miniature Masson Pine Canopy Based on Microwave Anechoic Chamber Measurement

Using microwave remote sensing to invert forest parameters requires clear canopy scattering characteristics, which can be intuitively investigated through scattering measurements. However, there are very few ground-based measurements on forest branches, needles, and canopies. In this study, a quantitative analysis of the canopy branches, needles, and ground contribution of Masson pine scenes in C-, X-, and Ku-bands was conducted based on a microwave anechoic chamber measurement platform. Four canopy scenes with different densities by defoliation in the vertical direction were constructed, and the backscattering data for each scene were collected in the C-, X-, and Ku-bands across eight incidence angles and eight azimuth angles, respectively. The results show that in the vertical observation direction, the backscattering energy of the C- and X-bands was predominantly contributed by the ground, whereas the Ku-band signal exhibited higher sensitivity to the canopy structure. The backscattering energy of the scene was influenced by the incident angle, particularly in the cross-polarization, where backscattering energy increased with larger incident angles. The scene’s backscattering energy was influenced by the scattering and extinction of canopy branches and needles, as well as by ground scattering, resulting in a complex relationship with canopy density. In addition, applying orientation correction to the polarization scattering matrix can mitigate the impact of the incident angle and reduce the decomposition energy errors in the Freeman–Durden model. In order to ensure the reliability of forest parameter inversion based on SAR data, a greater emphasis should be placed on physical models that account for signal scattering and the extinction process, rather than relying on empirical models.

Optimization of Grassland Carrying Capacity with Grass Quality Indicators Through GF5B Hyperspectral Images

The accurate estimation of grassland carrying capacity (GCC) in the alpine grasslands of the Changjiang River source region is crucial for managing livestock loads and ensuring ecological security on the Qinghai-Tibetan Plateau. Previous remote sensing methods have predominantly focused on yield indicators, often neglecting quality indicators, which hampers precise GCC estimation. Here, we collected 25 samples from the Dangqu basin, analyzing various grass parameters including yield, crude protein (CP), neutral detergent fiber (NDF), and acid detergent fiber (ADF). Then, we developed models to optimize GCC using quality indicators derived from GF5B images, assessing performance through Pearson correlation coefficient (R2), root mean square error (RMSE), and relative root mean square error (rRMSE). Results were found to show an average yield of 61.26 g/m2, with CP, ADF, and NDF ranging from 5.81% to 18.75%, 45.47% to 58.80%, and 27.50% to 31.81%, respectively. Spectra in the near-infrared range, such as 1918 nm, and spectral indices improved the accuracy of the hyperspectral inversion of grass parameters. The GCC increased from 0.51 SU·hm−2 to 0.63 SU·hm−2 post-optimization, showing an increasing trend from northwest to southeast. This study enhances GCC estimation accuracy, aiding in reasonable livestock management and effective ecological preservation.

Towards Real-Time Detection of Wakes for Various Sea States with Lightweight Deep Learning Model in Synthetic Aperture Radar Images

Synthetic aperture radar (SAR) is an essential tool for monitoring and managing maritime traffic and ensuring safety. It is particularly valuable because it can provide surveillance in all weather conditions. Ship wake detection has attracted considerable attention in offshore management as it has potential for widespread use in ship positioning and motion parameter inversion, surpassing conventional ship detection methods. Traditional wake detection methods depend on linear feature extraction through image transformation processing techniques, which are often ineffective and time-consuming when applied to large-scale SAR data. Conversely, deep learning (DL) algorithms have been infrequently utilized in wake detection and encounter significant challenges due to the complex ocean background and the effect of the sea state. In this study, we propose a lightweight rotating target detection network designed for detecting ship wakes under various sea states. For this purpose, we initially analyzed the features of wake samples across various frequency domains. In the framework, a YOLO structure-based deep learning is implemented to achieve wake detection. Our network design enhances the YOLOv8’s structure by incorporating advanced techniques such as deep separation convolution and combined frequency domain–spatial feature extraction modules. These modules are used to replace the usual convolutional layer. Furthermore, it integrates an attention technique to extract diverse features. By conducting experiments on the OpenSARWake dataset, our network exhibited outstanding performance, achieving a wake detection accuracy of 66.3% while maintaining a compact model size of 51.5 MB and time of 14 ms. This model size is notably less than the existing techniques employed for rotating target detection and wake detection. Additionally, the algorithm exhibits excellent generalization ability across different sea states, addressing to a certain extent the challenge of wake detection being easily influenced by varying sea states.

Instability Hazard Effect of Mined-out Areas Near the Mining Site by Fusion InSAR and PSO-BP Rock Mechanical Parameter Inversion

Exploring the impact characteristics of near the mining activities on goaf and clarifying the disaster effects of instability in the mined-out area are critical research endeavors essential for effectively managing major risk hazards inherent to underground mining operations. This study integrates SBAS-InSAR and PSO-BP methodologies for inversely analyzing rock mechanical parameters in a lead-zinc deposit and applies the inversion results through the FLAC3D simulation method to the mining site adjacent to the null zone to study destabilizing disaster effects in the mined-out area under the influence of mining disturbance. The simulation aims to analyze the evolution process of surrounding rock destruction and instability in empty areas, identify the primary causes of disaster effects, develop a risk assessment and judgment model, and prevent accidents from occurring. The results of the study show that the integration of SBAS-InSAR and PSO-BP techniques for inverting rock mechanical parameters has yielded favorable outcomes in analyzing the destabilizing effect of the gob area near the mining site, and more accurately, it obtained the displacement and stress characteristics of the roof and pillars in the goaf under the mining disturbance as the mining near the empty area progresses. The simulation results demonstrate that influenced by mining disturbance, the maximum principal stress of the ore column in the void area significantly increases, primarily appearing as compressive stress. The distribution of the plastic zone indicates notably that the process of plastic deformation of the ore column leading to damage is primarily due to maximum shear stress. Evidently, the primary reason for the destabilization of the ore column is the concentration of stress resulting from mining disturbance, leading to compression and shear damage.FLAC3D simulation analysis has conclusively determined that pressure shear damage to the ore column resulting from undermining disturbance is the main cause of airspace destabilization in mining. The research methodology and analysis results provide vital theoretical support for the prevention and control measures against destabilization disasters in empty zones near mining sites, holding significant theoretical and practical value.

Parallel Bayesian Optimization of Thermophysical Properties of Low Thermal Conductivity Materials Using the Transient Plane Source Method in the Body-Fitted Coordinate.

The transient plane source (TPS) method heat transfer model was established. A body-fitted coordinate system is proposed to transform the unstructured grid structure to improve the speed of solving the heat transfer direct problem of the winding probe. A parallel Bayesian optimization algorithm based on a multi-objective hybrid strategy (MHS) is proposed based on an inverse problem. The efficiency of the thermophysical properties inversion was improved. The results show that the meshing method of 30° is the best. The transformation of body-fitted mesh is related to the orthogonality and density of the mesh. Compared with parameter inversion the computational fluid dynamics (CFD) software, the absolute values of the relative deviations of different materials are less than 0.03%. The calculation speeds of the body-fitted grid program are more than 36% and 91% higher than those of the CFD and self-developed unstructured mesh programs, respectively. The application of body-fitted coordinate system effectively improves the calculation speed of the TPS method. The MHS is more competitive than other algorithms in parallel mode, both in terms of accuracy and speed. The accuracy of the inversion is less affected by the number of initial samples, time range, and parallel points. The number of parallel points increased from 2 to 6, reducing the computation time by 66.6%. Adding parallel points effectively accelerates the convergence of algorithms.

Inversion of Fracture Weakness Parameters Based on the 3CVSP Data—Part II: ORT Media Composed of A Single Fracture Set in the VTI Background Media

The inversion of fracture parameters from seismic data is a key issue in predicting fractured reservoirs. When a set of vertical fractures developed in a background medium of laminated shales or thin interbedded sandstone and mudstone with VTI (transversely isotropic media with a vertical symmetry axis) characteristics, this medium is a typical ORT (orthotropic) medium. In such a medium, due to the presence of fractures, the PS wave in the original VTI medium splits into two types of waves: PS1 and PS2 waves (fast and slow shear waves). To use the travel times of these two waveforms to invert the fracture weakness parameters, we derive approximate formulas for the travel times of PS1 and PS2 waves recorded in a Vertical Seismic Profile (VSP) for horizontally layered media. These approximate formulas are obtained using rational form approximation methods for short offsets with respect to the shot position. This approximation transforms the calculation of travel time from the complex phase velocity domain (the function of the two horizontal slownesses) to the group velocity domain (the function of shot point coordinates). The results from numerical errors analysis indicate that even with a near offset assumption, the approximated formula has high accuracy for offsets close to the depth of the target layer. By utilizing the travel times of PS1 and PS2 waves picked up by velocity under isotropic conditions, combined with undetermined anisotropic parameters and rational form approximations, we establish an objective function for inversion. The inversion results from different azimuths indicate that the accuracy of the inverted anisotropic parameters has different azimuthal sensitivities. The inversion method is applied to field multi-directional 3CVSP data and the results confirm the effectiveness of the method.