A Review of Geophysical Modeling Based on Particle Swarm Optimization

This paper reviews the application of the algorithm particle swarm optimization (PSO) to perform stochastic inverse modeling of geophysical data. The main features of PSO are summarized, and the most important contributions in several geophysical felds are analyzed. The aim is to indicate the fundamental steps of the evolution of PSO methodologies that have been adopted to model the Earth’s subsurface and then to undertake a critical evaluation of their benefts and limitations. Original works have been selected from the existing geophysical literature to illustrate successful PSO applied to the interpretation of electromagnetic (magnetotelluric and time-domain) data, gravimetric and magnetic data, self-potential, direct current and seismic data. These case studies are critically described and compared. In addition, joint optimization of multiple geophysical data sets by means of multi-objective PSO is presented to highlight the advantage of using a single solver that deploys Pareto optimality to handle diferent data sets without conficting solutions. Finally, we propose best practices for the implementation of a customized algorithm from scratch to perform stochastic inverse modeling of any kind of geophysical data sets for the beneft of PSO practitioners or inexperienced researchers

A local global pattern matching method for subsurface stochastic inverse modeling

Inverse modeling is an essential step for reliable modeling of subsurface flow and transport, which is important for groundwater resource management and aquifer remediation. Multiple-point statistics (MPS) based reservoir modeling algorithms, beyond traditional two-point statistics-based methods, offer an alternative to simulate complex geological features and patterns, conditioning to observed conductivity data. Parameter estimation, within the framework of MPS, for the characterization of conductivity fields using measured dynamic data such as piezometric head data, remains one of the most challenging tasks in geologic modeling. We propose a new local global pattern matching method to integrate dynamic data into geological models. The local pattern is composed of conductivity and head values that are sampled from joint training images comprising of geological models and the corresponding simulated piezometric heads. Subsequently, a global constraint is enforced on the simulated geologic models in order to match the measured head data. The method is sequential in time, and as new piezometric head become available, the training images are updated for the purpose of reducing the computational cost of pattern matching. As a result, the final suite of models preserve the geologic features as well as match the dynamic data. This local global pattern matching method is demonstrated for simulating a two-dimensional, bimodally-distributed heterogeneous conductivity field. The results indicate that the characterization of conductivity as well as flow and transport predictions are improved when the piezometric head data are integrated into the geological modeling. (C) 2015 Elsevier Ltd. All rights reserved.The authors gratefully acknowledge the financial support by DOE through projects DE-FE0004962 and DE-SC0001114. The last author acknowledges the support of the Spanish Ministry of Economy and Competitiveness through project CGL2011-23295. We greatly thank the three anonymous reviewers for their comments, which substantially improved the manuscript.Li ., L.; Srinivasan, S.; Zhou, H.; Gómez Hernández, JJ. (2015). A local global pattern matching method for subsurface stochastic inverse modeling. Environmental Modelling and Software. 70:55-64. https://doi.org/10.1016/j.envsoft.2015.04.008S55647

Stochastic inverse modeling of transient laboratory-scale three-dimensional two-phase core flooding scenarios

We develop a comprehensive and efficient workflow for a stochastic assessment of key parameters governing two-phase flow conditions associated with core-scale experiments. We rely on original and detailed datasets collected on a Berea sandstone sample. These capture the temporal evolution of pressure drop across the core and three-dimensional maps of phase saturations (determined via X-ray CT) in oil- and brine-displacement flooding scenarios characterized by diverse brine/oil viscosity contrasts. Such experiments are used as a test-bed for the proposed stochastic model calibration strategy. The latter is structured across three main steps: (i) a preliminary calibration, aimed at identifying a behavioral region of the model parameter space; (ii) a Global Sensitivity Analysis (GSA), geared towards identification of the relative importance of model parameters on observed model outputs and assessment of non-influential parameters to reduce dimensionality of the parameter space; and (iii) a stochastic inverse modeling procedure. The latter is based on a differential-evolution genetic algorithm to efficiently explore the reduced parameter space stemming from the GSA. It enables one to obtain a probabilistic description of the relevant model parameters through their frequency distributions conditional on the detailed type of information collected. Coupling GSA with a stochastic parameter estimation approach based on a genetic algorithm of the type we consider enables streamlining the procedure and effectively cope with the considerable computational efforts linked to the two-phase scenario considered. Results show a remarkable agreement with experimental data and imbue us with confidence on the potential of the approach to embed the type of rich datasets considered towards model parameter estimation fully including uncertainty

Probabilistic assessment of equivalent fracture aperture constrained on quasi-real-time drilling mud loss data

We provide a rigorous workflow to quantify the effects of key sources of uncertainty associated with equivalent fracture aperture estimates w constrained through mud loss information acquired while drilling a well in a reservoir. A stochastic inverse modeling framework is employed to estimate the probability distribution of w. This choice is consistent with the quantity and quality of available data. The approach allows assessing the probability that values of w inferred from mud loss events exceed a given threshold. We rely on a streamlined analytical solution to model mud losses while drilling. We explicitly consider uncertainties associated with model parameters and forcing terms, including drilling fluid rheological properties and flow rates, pore fluid pressure, and dynamic drilling fluid pressure. A synthetic scenario is considered to provide a transparent reference setting against which our stochastic inverse modeling workflow can be appraised. The approach is then applied to a real-case scenario. The latter is associated with data monitored on a rig site. A direct comparison of the impact of data collected through two common techniques (respectively, relying on flow meter sensors or pump strokes) on the ensuing probability of w is provided. A detailed analysis of the uncertainty related to the level of data corruption is also performed, considering various levels of measurement errors. Results associated with the field setting suggest that the proposed workflow yields probability distribution of w that are compatible with interpretations relying on traditional analyses of image logs. Results stemming from direct and indirect flow data display similar shapes. This suggests the viability of the probabilistic inversion methodology to assist quasi-real-time identification of equivalent fracture apertures on the basis of routinely acquired information during drilling

Low salinity waterflooding for Enhanced Oil Recovery - stochastic model calibration and uncertainty quantification

We focus on key aspects related to the quantification of the uncertainty associated with modeling of Enhanced Oil Recovery (EOR) through Low Salinity (LS) water injection in a reservoir. Low salinity waterflooding is an emerging EOR technique in which the salinity of the injected water is controlled to improve oil recovery, as opposed to conventional waterflooding where brine is usually used. Several mechanisms have been proposed to underpin the processes leading to additional oil mobility, but none of them has been conclusively identified as the key driving cause. Literature results suggest that LS water causes an alteration of the wettability of the porous medium, leading to more favorable conditions for oil recovery. In this context, simulation models that represent the process using salinity-dependent relative permeabilities have been developed. Here, we consider a tertiary coreflood experiment performed at Eni laboratory facilities through LS water injection, following sea water flooding. Oil and water relative permeability curves are parameterized through the Corey model. Model parameters and their uncertainties are estimated within a stochastic inverse modeling approach, upon relying on a classical reservoir simulator to simulate the measured oil recovery. The likelihood function is maximized through a joint use of the Latin hypercube sampling and the Metropolis Hastings algorithm, while the process model is coupled with a universal Kriging technique. The posterior sample of model parameters is then employed to quantify uncertainty propagation to a sector model of a selected North-East African sandstone reservoir. This enables us to quantify the impact of parameter uncertainty on the expected oil production resulting from a field scale application of the technique under study. The reservoir simulation reveals the potential of the LS water injection technique to improve the recovery in the considered field

Inverse problems in engineering

[EN] An inverse problem in engineering is the process of obtaining from a set of observations the causal factors that produce those data. Contrary to forward problems, an inverse problem starts with the results and subsequently calculates the causes. They are widely applied in many engineering fields since they allows obtaining parameters that cannot be directly observed. Additionally, they play a major role in uncertainty, reliability and risk assessment. This paper discusses an uncertainty assessment about the environmental impacts of future scenarios of sustainable groundwater pumping strategies on the quantitative status of an aquifer.Llopis Albert, C.; Palacios Marqués, D. (2016). Inverse problems in engineering. International Journal on Advances in Education Research. 3(2):61-67. http://hdl.handle.net/10251/108475S61673

Structure Adaptation in Stochastic Inverse Methods for Integrating Information

[EN] The use of inverse modeling techniques has greatly increased during the past several years because the advances in numerical modeling and increased computing power. Most of these methods require an a priori definition of the stochastic structure of conductivity (K) fields that is inferred only from K measurements. Therefore, the additional conditioning data, that implicitly integrate information not captured by K data, might lead to changes in the a priori model. Different inverse methods allow different degrees of structure adaptation to the whole set of data during the conditioning procedure. This paper illustrates the application of a powerful stochastic inverse method, the Gradual Conditioning (GC) method, to two different sets of data, both non-multiGaussian. One is based on a 2D synthetic aquifer and another on a real-complex case study, the Macrodispersion Experiment (MADE-2), site on Columbus Air Force Base in Mississippi (USA). We have analyzed how additional data change the a priori model on account of the perturbations performed when constraining stochastic simulations to data. Results show how the GC method tends to honour the a priori model in the synthetic case, showing fluctuations around it for the different simulated fields. However, in the 3D real case study, it is shown how the a priori structure is slightly modified not obeying just to fluctuations but possibly to the effect of the additional information on K, implicit in piezometric and concentration data. We conclude that implementing inversion methods able to yield a posteriori structure that incorporate more data might be of great importance in real cases in order to reduce uncertainty and to deal with risk assessment projects.Llopis Albert, C.; Merigó, JM.; Palacios Marqués, D. (2015). Structure Adaptation in Stochastic Inverse Methods for Integrating Information. Water Resources Management. 29(1):95-107. doi:10.1007/s11269-014-0829-2S95107291Abolverdi J, Khalili D (2010) Development of regional rainfall annual maxima for Southwestern Iran by LMoments. Water Resour Manag 24(11):2501–2526Adams EE, Gelhar LW (1992) Field study of dispersion in a heterogeneous aquifer 2. Spatial moments analysis. Water Resour Res 28(12):3293–3307Boggs JM, Adams EE (1992) Field study of dispersion in a heterogeneous aquifer. 4. Investigation of adsorption and sampling bias. Water Resour Res 28(12):3325–3336Boggs JM, Young SC, Beard LM (1992) Field study of dispersion in a heterogeneous aquifer. 1. Overview and site description. Water Resour Res 28(12):3281–3291Caers J (2007) Comparing the gradual deformation with the probability perturbation method for solving inverse problems. Math Geol 39(1). doi:10.1007/s11004-006-9064-6Capilla JE, Llopis-Albert C (2009) Gradual conditioning of non-Gaussian transmissivity fields to flow and mass transport data: 1. Theory. J Hydrol 371:66–74Carrera J, Alcolea A, Medina A, Hidalgo J, Slooten LJ (2005) Inverse problem in hydrogeology. J Hydrogeol 13:206–222Charalambous J, Rahman A, Carroll D (2013) Application of Monte Carlo simulation technique to design flood estimation: a case study for North Johnstone River in Queensland, Australia. Water Resour Manag 27:4099–4111. doi: 10.1007/s11269-013-0398-9De Marsily G, Delhomme JP, Coudrain-Ribstein A, Lavenue AM (2000) Four decades of inverse problems in hydrogeology. Geol Soc Am (Special Paper 348)Doherty J (1994) PEST: Corinda, Australia. Watermark Computing, 122 pGómez-Hernández JJ, Srivastava RM (1990) ISIM3D: An ANSI-C three dimensional multiple indicator conditional simulation program. Comput Geosci 16(4):395–440Gómez-Hernández JJ, Wen XH (1998) To be or not to be multiGaussian? A reflection on stochastic hydrogeology. Adv Water Resour 21(1):47–61Gómez-Hernández JJ, Sahuquillo A, Capilla JE (1997) Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data. 1. Theory. J Hydrol 203:162–174Hu LY (2000) Gradual deformation and iterative calibration of gaussian-related stochastic models. Math Geol 32(1):87–108Llopis-Albert C, Capilla JE (2009a) Gradual conditioning of non-gaussian transmissivity fields to flow and mass transport Data: 3. Application to the Macrodispersion experiment (MADE-2) site, on Columbus air force base in Mississippi (USA). J Hydrol 371:75–84Llopis-Albert C, Capilla JE (2009b) Gradual conditioning of non-Gaussian transmissivity fields to flow and mass transport data: 2. Demonstration on a synthetic aquifer. J Hydrol 371:53–65Llopis-Albert C, Capilla JE (2010a) Stochastic inverse modeling of hydraulic conductivity fields taking into account independent stochastic structures: a 3D case study. J Hydrol 391:277–288Llopis-Albert C, Capilla JE (2010b) Stochastic simulation of non-Gaussian 3D conductivity fields in a fractured medium with multiple statistical populations: a case study. J Hydrol Eng 15(7):554–566Llopis-Albert C., Capilla JE (2011) Change of the a priori stochastic structure in the conditional simulation of transmissivity fields. P.M. Atkinson and C.D. Lloyd (eds.), geoENV VII – Geostatistics for Environmental Applications, Quant Geol Geostat 16. Springer. ISBN: 9048123216Llopis-Albert C, Palacios-Marqués D, Merigó JM (2014) A coupled stochastic inverse-management framework for dealing with nonpoint agriculture pollution under groundwater parameter uncertainty. J Hydrol 511:10–16. doi: 10.1016/j.jhydrol.2014.01.021McLaughlin D, Townley LR (1996) A reassessment of the groundwater inverse problem. Water Resour Res 32(5):1131–1161Mylopoulos YA, Theodosiou N, Mylopoulos NA (1999) A stochastic optimization approach in the design of an aquifer remediation under Hydrogeologic uncertainty. Water Resour Manag 13(5):335–351Neupauer RM, Wilson JL (1999) Adjoint method for obtaining backward-in-time location and travel time probabilities of a conservative groundwater contaminant. Water Resour Res 35(11):3389–3398Oliver DS, Chen Y (2010) Recent progress on reservoir history matching: a review. Comput Geosci 15(1):185–221Poeter EP, Hill MC (1998) Documentation of UCODE, a computer code for universal inverse modeling. US Geol Surv Water Resour Investig Rep 98–4080:116Rehfeldt KR, Boggs JM, Gelhar LW (1992) Field study of dispersion in a heterogeneous aquifer 3. Geostatistical analysis of hydraulic conductivity. Water Resour Res 28(12):3309–3324Salamon P, Fernández-Garcia D, Gómez-Hernández JJ (2007) Modeling tracer transport at the MADE site: the importance of heterogeneity. Water Resour Res 43:W08404. doi: 10.1029/2006WR005522Vázquez RF, Beven K, Feyen J (2009) GLUE based assessment on the overall predictions of a MIKE SHE application. Water Resour Manag 23:1325–1349. doi: 10.1007/s11269-008-9329-6Yeh WWG (1986) Review of parameter identification procedures in groundwater hydrology: the inverse problem. Water Resour Res 22(2):95–108Zakaria ZA, Shabri A, Ahmad UN (2012) Regional frequency analysis of extreme rainfalls in the West Coast of Peninsular Malaysia using partial L-Moments. Water Resour Manag 26(15):4417–4433Zheng C, Bianchi M, Gorelick SM (2011) Lessons learned from 25 years of research at the MADE Site. Groundw 49(5):649–662Zhou H, Gómez-Hernández JJ, Li L (2014) Inverse methods in hydrogeology: evolution and recent trends. Adv Water Resour 63:22–37. doi: 10.1016/j.advwatres.2013.10.014Zimmerman DA et al (1998) A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow. Water Resour Res 34(6):1373–141

Inverse sequential simulation: Performance and implementation details

For good groundwater flow and solute transport numerical modeling, it is important to characterize the formation properties. In this paper, we analyze the performance and important implementation details of a new approach for stochastic inverse modeling called inverse sequential simulation (iSS). This approach is capable of characterizing conductivity fields with heterogeneity patterns difficult to capture by standard multiGaussian-based inverse approaches. The method is based on the multivariate sequential simulation principle, but the covariances and cross-covariances used to compute the local conditional probability distributions are computed by simple co-kriging which are derived from an ensemble of conductivity and piezometric head fields, in a similar manner as the experimental covariances are computed in an ensemble Kalman filtering. A sensitivity analysis is performed on a synthetic aquifer regarding the number of members of the ensemble of realizations, the number of conditioning data, the number of piezometers at which piezometric heads are observed, and the number of nodes retained within the search neighborhood at the moment of computing the local conditional probabilities. The results show the importance of having a sufficiently large number of all of the mentioned parameters for the algorithm to characterize properly hydraulic conductivity fields with clear non-multiGaussian features. © 2015 Elsevier Ltd. All rights reserved.The first author acknowledgs the financial support from the China Scholarship Council (CSC [2010]3010). Financial support to carry out this work was also received from the Spanish Ministry of Economy and Competitiveness through Project CGL2014-59841-P. We thank the three reviewers for their thorough review and their insightful comments, which have helped to improve the final manuscript.Xu, T.; Gómez-Hernández, JJ. (2015). Inverse sequential simulation: Performance and implementation details. Advances in Water Resources. 86B:311-326. https://doi.org/10.1016/j.advwatres.2015.04.015S31132686

Ensemble random forest filter: An alternative to the ensemble Kalman filter for inverse modeling

[EN] The ensemble random forest filter (ERFF) is presented as an alternative to the ensemble Kalman filter (EnKF) for inverse modeling. The EnKF is a data assimilation approach that forecasts and updates parameter estimates sequentially in time as observations are collected. The updating step is based on the experimental covariances computed from an ensemble of realizations, and the updates are given as linear combinations of the differences between observations and forecasted system state values. The ERFF replaces the linear combination in the update step with a non-linear function represented by a random forest. This way, the non-linear relationships between the parameters to be updated and the observations can be captured, and a better update produced. The ERFF is demonstrated for log-conductivity identification from piezometric head observations in several scenarios with varying degrees of heterogeneity (log-conductivity variances going from 1 up to 6.25 (ln m/d)2), number of realizations in the ensemble (50 or 100), and number of piezometric head observations (18 or 36). In all scenarios, the ERFF works well, reconstructing the log-conductivity spatial heterogeneity while matching the observed piezometric heads at selected control points. For benchmarking purposes, the ERFF is compared to the restart EnKF to find that the ERFF is superior to the EnKF for the number of ensemble realizations used (small in typical EnKF applications). Only when the number of realizations grows to 500 the restart EnKF can match the performance of the ERFF, albeit at more than double the computational cost.The authors acknowledge grant PID2019-109131RB-I00 funded by MCIN/AEI/10.13039/501100011033 and project InTheMED, which is part of the PRIMA Programme supported by the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreement No 1923.A. Godoy, V.; Napa-García, GF.; Gómez-Hernández, JJ. (2022). Ensemble random forest filter: An alternative to the ensemble Kalman filter for inverse modeling. Journal of Hydrology. 615:1-13. https://doi.org/10.1016/j.jhydrol.2022.12864211361