Forward Model Research Articles

Retrieval of snow and soil properties for forward radiative transfer modeling of airborne Ku-band SAR to estimate snow water equivalent: the Trail Valley Creek 2018/19 snow experiment

Abstract. Accurate snow information at high spatial and temporal resolution is needed to support climate services, water resource management, and environmental prediction services. However, snow remains the only element of the water cycle without a dedicated Earth observation mission. The snow scientific community has shown that Ku-band radar measurements provide quality snow information with its sensitivity to snow water equivalent and the wet/dry state of snow. With recent developments of tools like the snow micropenetrometer (SMP) to retrieve snow microstructure data in the field and radiative transfer models like the Snow Microwave Radiative Transfer (SMRT) model, it becomes possible to properly characterize the snow and how it translates into radar backscatter measurements. An experiment at Trail Valley Creek (TVC), Northwest Territories, Canada, was conducted during the winter of 2018/19 in order to characterize the impacts of varying snow geophysical properties on Ku-band radar backscatter at a 100 m scale. Airborne Ku-band data were acquired using the University of Massachusetts radar instrument. This study shows that it is possible to calibrate SMP data to retrieve statistical information on snow geophysical properties and properly characterize a representative snowpack at the experiment scale. The tundra snowpack measured during the campaign can be characterize by two layers corresponding to a rounded snow grain layer and a depth hoar layer. Using RADARSAT-2 and TerraSAR-X data, soil background roughness properties were retrieved (msssoil=0.010±0.002), and it was shown that a single value could be used for the entire domain. Microwave snow grain size polydispersity values of 0.74 and 1.11 for rounded and depth hoar snow grains, respectively, were retrieved. Using the geometrical optics surface backscatter model, the retrieved effective soil permittivity increased from C-band (εsoil=2.47) to X-band (εsoil=2.61) and to Ku-band (εsoil=2.77) for the TVC domain. Using the SMRT and the retrieved soil and snow parameterizations, an RMSE of 2.6 dB was obtained between the measured and simulated Ku-band backscatter values when using a global set of parameters for all measured sites. When using a distributed set of soil and snow parameters, the RMSE drops to 0.9 dB. This study thus shows that it is possible to link Ku-band radar backscatter measurements to snow conditions on the ground using a priori knowledge of the snow conditions to retrieve snow water equivalent (SWE) at the 100 m scale.

Diagenesis and reservoir quality evolution of estuarine sandstones: Insights from the Cenomanian-Turonian Yolde Formation, northern Benue Trough, NE Nigeria

Estuarine sandstones often exhibit complex diagenetic pathways due to the interaction of fluvial and shallow marine processes, resulting in significant reservoir heterogeneities. The Yolde Formation is an important petroleum reservoir in the Northern Benue Trough, NE Nigeria. However, diagenetic and reservoir quality evolution of the formation are still poorly understood. This study utilizes thin-section petrography, XRD, SEM, and fluid inclusion microthermometry to analyse the composition, diagenesis, and reservoir quality of the sandstones. Results show that the sandstones are mainly arkose and subarkose in composition; they are generally well-sorted and vary in grain size from very fine-to coarse-grained. Three diagenetic stages are identified: early, middle, and late. The early stage includes feldspar dissolution, formation of kaolinite, development of clay coating, and mechanical compaction. The middle stage comprises the formation of authigenic chlorite and Fe-oxide cements. The late-stage diagenesis involves illitization of kaolinite, formation of dickite, albitization of K-feldspar, and precipitation of quartz overgrowths. The diagenetic evolution of the sandstones was strongly controlled by their compositional makeup. The feldspathic nature of the sandstones resulted in the formation of kaolinite, illite, and quartz overgrowths, through feldspar dissolution and silica supply. The inner and middle estuarine facies have inhibited the development of quartz overgrowths due to well-developed clay coatings, whereas the outer estuarine facies were well-cemented by quartz overgrowths due to lack of clay coatings. Illitic clay coatings were found to be effective in preventing quartz cementation. Fluid inclusion analysis reveals that the formation temperatures of the quartz overgrowths range from 98 °C to 135.5 °C, corresponding to burial depths ranging between 2.3 and 3.5 km. These findings would provide useful insights that would reduce the risks of exploration of the sandstones and also supplies potential input data for forward diagenetic modelling of their subsurface equivalents in similar depositional settings elsewhere.

Technical note: Posterior uncertainty estimation via a Monte Carlo procedure specialized for 4D-Var data assimilation

Abstract. Through the Bayesian lens of four-dimensional variational (4D-Var) data assimilation, uncertainty in model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive forward models, posterior covariance knowledge must be relaxed to deterministic or stochastic approximations. In the carbon flux inversion literature, (Chevallier et al., 2007) proposed a stochastic method capable of approximating posterior variances of linear functionals of the model parameters that is particularly well suited for large-scale Earth-system 4D-Var data assimilation tasks. This note formalizes this algorithm and clarifies its properties. We provide a formal statement of the algorithm, demonstrate why it converges to the desired posterior variance quantity of interest, and provide additional uncertainty quantification allowing incorporation of the Monte Carlo sampling uncertainty into the method's Bayesian credible intervals. The methodology is demonstrated using toy simulations and a realistic carbon flux inversion observing system simulation experiment.

Delineation of deep-seated crustal structures from magnetic data in the southeastern part of the Niger Delta basin, Nigeria

Regional magnetic data in the southeastern segment of the Nigerian Niger Delta were evaluated with the aim of mapping deep-seated tectonic elements. Enhanced filtering operations and 3D forward modelling were applied on the magnetic data. These geologic features triggered the formation of rollover anticlines and faults that serve as structural traps in the study area. The filtered residual magnetic data revealed geologic structures characterized with NE - SW, N - S, and E - W orientations. The 3-D models detected the faulted crustal blocks, gradient zones, and intra-basement compositional magnetic variations. Furthermore, some prominent horst and graben structures as well as related normal faults characterized with distinct magnetic signatures were observed. Faults of base magnetic (of various compositions) were observed to be the fabricating mechanisms of the magnetic anomalies. Collectively, these structures influenced the patterns of magnetic anomalies with direct effects on the hydrocarbon trapping systems, as well as the pathways and accumulation zones for hydrothermal minerals. On the whole, the interpreted results revealed that the basement surface is rippling. Additionally, the depth result showed sedimentary thicknesses that ranged from 4–10 km. Again, the estimated crustal thickness varied from 14 to 19 km. This study has displayed the capabilities of the magnetic method in mapping the depth and configuration of basement rocks, which are crucial in controlling the formation of structural traps. Identifying these basement structures early helps in understanding the overall geological framework and potential hydrocarbon systems.

Sensitivity analysis-based quality optimization strategy for multi-correlation parameters in spinning process

To address the problem of quality optimization of multi-correlation parameters in the spinning process, this paper proposes a new method based on a sparrow search algorithm (SSA). Firstly, a generalized regression neural network (GRNN) is used to investigate the impact of the spinning process parameters on yarn quality, and quality forward modeling in the spinning process is established. And based on the coupling and correlation characteristics of spinning process parameters, sensitivity analysis is used to analyze the influence of each spinning process parameter on yarn quality, the correlation spinning process parameters for further analysis. Then a model of quality optimization with spinning process parameters is established, and SSA is used to solve the model of quality optimization with multi-correlation parameters in the spinning process. Finally, the effectiveness of the proposed method was validated through an instance. The results show that the optimal spinning process parameters combination generation of [32.159 5.2 0.8 14.8 24.540 8588.677 21.708] occurs in a configuration with a fitness value of 0.0003. The proposed sensitivity analysis-based quality optimization strategy reveals good performances in terms of both convergence speed and optimization accuracy, which will provide guidance for improving yarn quality.

A probabilistic machine learning framework for stiffness tensor estimation of carbon composite laminate

The potential uses of carbon composite material are vast, particularly in the civil, mechanical and aero-structures. Nonetheless, the practical utilization of carbon composite faces challenges due to complex experimental methods and imprecise algorithms for inverting material properties. Characterization of full set of stiffness tensor for an anisotropic material in particular orthotropic material can be considered as a complex non-linear inversion problem. The inversion process requires a robust optimization algorithm and forward models. The complexity of this inversion process impedes the practical utility in large-scale automation and in real-time structural health monitoring (SHM) application. To cater this, in this work an advanced probabilistic machine learning framework based on multi-output Gaussian process regression (moGPR) is proposed as an inversion algorithm. The inversion algorithm proposed is based on probabilistic framework that utilises the dispersion of Lamb waves as an input for optimal estimation of stiffness tensor. Experimental measurements of full wavefield data of propagating waves are conducted by scanning laser Doppler vibrometer. Further, an optimal training dataset is generated by employing a forward model based on stiffness matrix method (SMM). In the presence of measurement uncertainties, the effectiveness of the optimal prediction algorithm is showcased through a comparison between the estimated parameter and its ground truth. This comparison reveals that the proposed inversion algorithm is both efficient and robust, delivering satisfactory performance even in the presence of substantial measurement uncertainties.

Coupled hydrogeophysical inversion through ensemble smoother with multiple data assimilation and convolutional neural network for contaminant plume reconstruction

In the field of groundwater, accurate delineation of contaminant plumes is critical for designing effective remediation strategies. Typically, this identification poses a challenge as it involves solving an inverse problem with limited concentration data available. To improve the understanding of contaminant behavior within aquifers, hydrogeophysics emerges as a powerful tool by enabling the combination of non-invasive geophysical techniques (i.e., electrical resistivity tomography—ERT) and hydrological variables. This paper investigates the potential of the Ensemble Smoother with Multiple Data Assimilation method to address the inverse problem at hand by simultaneously assimilating observed ERT data and scattered concentration values from monitoring wells. A novelty aspect is the integration of a Convolutional Neural Network (CNN) to replace and expedite the expensive geophysical forward model. The proposed approach is applied to a synthetic case study, simulating a tracer test in an unconfined aquifer. Five scenarios are compared, allowing to explore the effects of combining multiple data sources and their abundance. The outcomes highlight the efficacy of the proposed approach in estimating the spatial distribution of a concentration plume. Notably, the scenario integrating apparent resistivity with concentration values emerges as the most promising, as long as there are enough concentration data. This underlines the importance of adopting a comprehensive approach to tracer plume mapping by leveraging different types of information. Additionally, a comparison was conducted between the inverse procedure solved using the full geophysical forward model and the CNN model, showcasing comparable performance in terms of results, but with a significant acceleration in computational time.

Implementation of the Gauss-Kronrod Quadrature Method (G7, K15) on 2D Gravity Anomaly Modeling in Basins with a Polynomial Variation of Density Distribution with Depth

Forward modeling of 2D gravity anomalies, considering density contrasts that vary polynomially with depth, was performed to examine basin structures. This process involved two main stages: deriving analytical formulas and executing numerical integration. The Gauss-Kronrod Quadrature Method, utilizing 7 Gauss points and 15 Kronrod points, was employed to precisely compute these integrals. Initial modeling applied to theoretical basement scenarios with fixed density contrasts showed gravity anomalies that accurately reflected the curvature of the basement. To validate the approach, it was then applied to real-world cases including the Sebastian Vizcaino Basin, San Jacinto Graben, and Sayula Basin. By incorporating suitable density contrasts, modeling lengths, and basement curvature shapes, the results revealed that both fixed-density and depth-variable density models produced gravity anomalies with patterns consistent with the actual basement curvature. These findings validate the modeling technique’s effectiveness in representing real geological features accurately. The study confirms that the Gauss-Kronrod Quadrature Method (G7, K15) is robust for analyzing 2D gravity anomalies, providing a reliable tool for understanding the influence of varying density contrasts on gravity responses.

Calculation of Porosity and CO2 Content in CO2-Bearing Gas Formations Based on Density and Neutron Logging Forward and Inverse Methods.

When the gas reservoir contains CO2, the logging response tends to be complex. When calculating porosity with neutron and density curves, the accuracy of porosity calculation is reduced due to the uncertainty of fluid parameters, which in turn affects the evaluation of CO2 content. It increases the uncertainty of reserve evaluation. In this paper, a forward modeling model of density logging is established based on the equivalent volume model, and the method of neutron logging is formed by putting forward the nonlinear formula of the reciprocal of the comprehensive deceleration length. The key parameters and their variation rules of neutron logging and density logging forward modeling under different temperature and pressure conditions are obtained by experimental means and Monte Carlo method, respectively. The variation law of the influence of different CO2 content on neutron logging and density logging curves is simulated. The research shows that with the increase of CO2 content, the neutron logging value of gas reservoir decreases, while the density logging value increases, and the greater the porosity of gas reservoir, the more obvious this change trend is. Compared with CH4, CO2 has a more significant impact on the excavation effect of neutron logging. On this basis, combined with the conductivity model of the study area, the porosity and CO2 content of CO2 bearing gas reservoir are solved by the least-square method. The practice shows that the relative error of porosity calculation is within ±4% and the error of CO2 content calculation is within ±10%, which proves the reliability of this method.

Accurate heat flux estimation in continuous casting Molds via MH-MCMC Bayesian Inverse Method

The present work focuses on accurately estimating heat flux variations on the hot faces of the billet and slab molds during continuous casting using the Metropolis Hastings–Markov Chain Monte Carlo (MH-MCMC) Bayesian inverse method and experimental data. Accurate estimation of heat flux variation is crucial for operational efficiency and ensuring high-quality steel products. The variation in the hot face heat flux (qn(y)) of the billet mold is estimated using the proposed MH-MCMC Bayesian inverse method and experimental data for various casting speeds. The study extends this methodology to the slab mold for estimating the variations in the heat fluxes (qnr(y), qw(x,y)) on the hot narrow and wide faces of the slab mold. The estimated heat fluxes for both molds are used in respective forward models to obtain temperatures. The temperatures obtained excellently match experimental temperatures and show superior accuracy in estimating the heat fluxes. From the present methodology, the errors between these simulated and experimental temperatures are much less compared with the literature. The predicted heat flux variations on the hot faces of the billet and slab molds are also compared with the heat flux obtained from the literature.This study provides valuable insights into accurately estimating heat fluxes in continuous casting molds (billet and slab) using the MH-MCMC Bayesian inverse method. The accurately estimated heat fluxes of the molds are essential for ensuring the quality, efficiency, and innovation of continuous casting processes.

Forward modeling of single-sided magnetic resonance and evaluation of [formula omitted] fitting error based on geometric analytical method

Single-sided magnetic resonance (SSMR) offers advantages of portability and noninvasive measurement for water detection, with significant potential applications in groundwater exploration, petroleum well logging, and soil moisture monitoring. However, the inherent highly inhomogeneous static magnetic field and radiofrequency (RF) field in SSMR necessitate the utilization of the Carr–Purcell–Meiboom–Gill (CPMG) sequence measurement scheme. To accelerate forward modeling during pulse excitation, we introduce a Geometric Analysis Method (GAM) and assess T2 error using its primary parameters. The GAM involves applying spatial geometric rotations on the magnetization vector, leading to an analytical solution to the Bloch equation that disregards relaxation effects. Compared with the rotation matrix (RM) method, the GAM demonstrates high accuracy and reduces computational time by approximately 20.9%. By analyzing the primary parameters governing the magnetization vector in the analytical formula, we evaluated their impact on the transverse relaxation time (T2) obtained through fitting the SE signal. Ultimately, the forward modeling results of the CPMG sequence within the region of interest (ROI) of a single-sided Halbach magnet array are validated. The T2 fitting error increases as the primary parameters deviate from the ideal values, highlighting their significant role in the T2 fitting results. This study provides a theoretical foundation for optimizing the design of SSMR magnets and RF coils.

Three-dimensional unstructured adaptive finite element forward modeling simulation of magnetotellurics based on magnetic vector potential-electric scalar potential

Three-dimensional unstructured adaptive finite element forward modeling simulation of magnetotellurics based on magnetic vector potential-electric scalar potential

A hp-adaptive finite element approach for 3D controlled source electromagnetic forward modeling

Accurate and efficient 3D controlled-source electromagnetic (CSEM) forward modeling is crucial for deciphering CSEM responses in complex geological contexts and for assessing the efficacy of survey designs. It also serves as the foundation for 3D inversion, a critical technique for interpreting CSEM data. We present a novel hp-adaptive finite element method for 3D CSEM forward modeling. This method enhances the traditional h-adaptive approach, which only refines the mesh while keeping the polynomial degree of the basis functions constant, by enabling simultaneous refining mesh and increasing polynomial degree of basis functions. High-order elements yield superior approximations when the solution exhibits sufficient smoothness, while mesh refinement enhances accuracy in regions with less smooth solutions. The adaptive refinement process is guided by a goal-oriented error estimator that relies on the residual of the governing equation and the continuity of electromagnetic fields. The hp-adaptive strategy, which determines whether to refine elements or increase their polynomial degree, is based on the refinement levels of the elements. Constraints are applied to hanging nodes, introduced during the refinement process, to ensure the continuity of the finite element space. We validate the accuracy, efficiency, and convergence of the hp-adaptive method through tests on two layered models. Further simulations on a topographic model and a realistic model corroborate its effectiveness. Our findings indicate that the hp-adaptive method outperforms the traditional h-adaptive method in terms of accuracy, convergence rate and computational cost, making it a promising technique for 3D CSEM forward modeling.

Pareto Optimization and Tuning of a Laser Wakefield Accelerator.

Optimization of accelerator performance parameters is limited by numerous trade-offs, and finding the appropriate balance between optimization goals for an unknown system is challenging to achieve. Here, we show that multiobjective Bayesian optimization can map the solution space of a laser wakefield accelerator (LWFA) in a very sample-efficient way. We observe that there exists a wide range of Pareto-optimal solutions that trade beam energy versus charge at similar laser-to-beam efficiency. Moreover, many applications such as light sources require particle beams at certain target energies. We demonstrate accurate energy tuning of the LWFA from 150 to 400MeV via the simultaneous adjustment of eight parameters. To further advance this use case, we propose an inverse model that allows a user to specify desired beam parameters. Trained on the forward Gaussian process model, the inverse model generates input parameter value ranges within which the desired setting is likely to be reached. The method reveals different strategies for accelerator tuning and is expected to drastically facilitate the operation of LWFAs in the near future.

Intensified carbonate weathering during storm events in a highly-erosion river catchment

Carbonate weathering is sensitive to tectonic and climatic settings due to its rapid dissolution kinetics, playing an important role in the carbon cycle at short time scales (102 to 104 years). Under global warming, extreme weather and hydrological events have become more frequent worldwide. How carbonate weathering and its associated carbon budget respond to these extreme events remains unclear. Here, high-temporal-resolution (weekly) riverine chemistry during 2010 was investigated in the upper Min Jiang, a highly-erosion river catchment on the eastern Tibetan Plateau. River water chemistry during the monsoon season fluctuated with six storm events (9 days in total) that were characterized by 7–14 times higher water discharge and 10–40 times higher erosion than those of the non-monsoon seasons. Based on a forward model, riverine chemistry was dominated by carbonate dissolution in the upper Min Jiang. Compared to the non-monsoon seasons, the storm events triggered 270% and 264% increases in the average fluxes of carbonate weathering and associated CO2 consumption, respectively. Furthermore, an incongruent carbonate dissolution (ICD) model as a possible mechanism was employed to reveal the preferential leaching of Mg2+ and Sr2+ relative to Ca2+ during carbonate weathering under extremely-high erosion at basin scale. Accompanying the ICD, the storm-derived carbonates were likely carried downstream as suspended particles for further weathering. This study demonstrates the intensification of carbonate weathering and a carbon sink by storm events, with incongruent carbonate dissolution under storm-induced high erosion.

Advances in forward modelling and inversion of geophysical electromagnetic data

Advances in forward modelling and inversion of geophysical electromagnetic data

RLSynC: Offline-Online Reinforcement Learning for Synthon Completion.

Retrosynthesis is the process of determining the set of reactant molecules that can react to form a desired product. Semitemplate-based retrosynthesis methods, which imitate the reverse logic of synthesis reactions, first predict the reaction centers in the products and then complete the resulting synthons back into reactants. We develop a new offline-online reinforcement learning method RLSynC for synthon completion in semitemplate-based methods. RLSynC assigns one agent to each synthon, all of which complete the synthons by conducting actions step by step in a synchronized fashion. RLSynC learns the policy from both offline training episodes and online interactions, which allows RLSynC to explore new reaction spaces. RLSynC uses a standalone forward synthesis model to evaluate the likelihood of the predicted reactants in synthesizing a product and thus guides the action search. Our results demonstrate that RLSynC can outperform state-of-the-art synthon completion methods with improvements as high as 14.9%, highlighting its potential in synthesis planning.

A probabilistic full waveform inversion of surface waves

AbstractOver the past decades, surface wave methods have been routinely employed to retrieve the physical characteristics of the first tens of meters of the subsurface, particularly the shear wave velocity profiles. Traditional methods rely on the application of the multichannel analysis of surface waves to invert the fundamental and higher modes of Rayleigh waves. However, the limitations affecting this approach, such as the 1D model assumption and the high degree of subjectivity when extracting the dispersion curve, motivate us to apply the elastic full‐waveform inversion, which, despite its higher computational cost, enables leveraging the complete information embedded in the recorded seismograms. Standard approaches solve the full‐waveform inversion using gradient‐based algorithms minimizing an error function, commonly measuring the misfit between observed and predicted waveforms. However, these deterministic approaches lack proper uncertainty quantification and are susceptible to get trapped in some local minima of the error function. An alternative lies in a probabilistic framework, but, in this case, we need to deal with the huge computational effort characterizing the Bayesian approach when applied to non‐linear problems associated with expensive forward modelling and large model spaces. In this work, we present a gradient‐based Markov chain Monte Carlo full‐waveform inversion where we accelerate the sampling of the posterior distribution by compressing data and model spaces through the discrete cosine transform. Additionally, a proposal is defined as a local, Gaussian approximation of the target density, constructed using the local Hessian and gradient information of the log posterior. We first validate our method through a synthetic test where the velocity model features lateral and vertical velocity variations. Then we invert a real dataset from the InterPACIFIC project. The obtained results prove the efficiency of our proposed algorithm, which demonstrates to be robust against cycle‐skipping issues and able to provide reasonable uncertainty evaluations with an affordable computational cost.

Average‐derivative optimized 21‐point and improved 25‐point forward modelling and full waveform inversion in frequency domain

Average‐derivative optimized 21‐point and improved 25‐point forward modelling and full waveform inversion in frequency domain

Bayesian inference of the spatial distribution of steel corrosion in reinforced concrete structures using corrosion-induced crack width

Observations of corrosion-induced crack widths offer crucial information about the corrosion states of steel reinforcements in reinforced concrete (RC) structures, enabling a cost-effective method for inferring corrosion states through inverse analysis. However, the uncertainty associated with the relationship between corrosion-induced cracking and steel weight loss necessitates a probabilistic inference method, especially when considering the spatial distributions of steel weight loss, which provides important information to estimate the load-bearing capacity loss of corroded RC structures. This paper proposes a Bayesian framework to infer the steel weight loss distribution in RC structures based on the observed corrosion-induced crack width. To reduce the dimensions of the Bayesian inference, a Karhunen-Loève transform is applied to extract the principal distribution features of the steel weight loss. The forward model of the Bayesian inference adopts a data-driven sequence-to-sequence transduction approach to predict corrosion-induced crack width from steel weight loss. This model incorporates a novel nonlinear convolution kernel for input encoding and a sparse polynomial chaos expansion for decoding, which proves more accurate and efficient than finite element simulations. The Hamiltonian Markov chain Monte Carlo (HMCMC) sampler is used to efficiently sample from the posterior distribution of the Bayesian inference. The case study of the proposed method demonstrated that Bayesian inference provides robust range estimation for the steel weight loss distribution, with its 95% confidence interval encompassing most observations. Additionally, the method efficiently inferred high-dimensional steel weight loss sequences up to 61 dimensions, taking advantage of the dimension reduction technique and the gradient-informed HMCMC sampler.