Geostatistical Simulation Approach Research Articles

Geostatistical Simulation of Daily Rainfall Fields—Performance Assessment for Extremes in West Africa

Abstract The spatial description of high-resolution extreme daily rainfall fields is challenging because of the high spatial and temporal variability of rainfall, particularly in tropical regions due to the stochastic nature of convective rainfall. Geostatistical simulations offer a solution to this problem. In this study, a stochastic geostatistical simulation technique based on the spectral turning bands method is presented for modeling daily rainfall extremes in the data-scarce tropical Ouémé River basin (Benin). This technique uses meta-Gaussian frameworks built on Gaussian random fields, which are transformed into realistic rainfall fields using statistical transfer functions. The simulation framework can be conditioned on point observations and is computationally efficient in generating multiple ensembles of extreme rainfall fields. The results of tests and evaluations for multiple extremes demonstrate the effectiveness of the simulation framework in modeling more realistic rainfall fields and capturing their variability. It successfully reproduces the empirical cumulative distribution function of the observation samples and outperforms classical interpolation techniques like ordinary kriging in terms of spatial continuity and rainfall variability. The study also addresses the challenge of dealing with uncertainty in data-poor areas and proposes a novel approach for determining the spatial correlation structure even with low station density, resulting in a performance boost of 9.5% compared to traditional techniques. Additionally, we present a low-skill reference simulation method to facilitate a comprehensive comparison of the geostatistical simulation approaches. The simulations generated have the potential to provide valuable inputs for hydrological modeling.

Evaluating the Effectiveness of Nanotechnology in Environmental Remediation of a Highly Metal-Contaminated Area—Minas Gerais, Brazil

A column experiment at a laboratory level was carried out to assess the effect of the application of nanotechnology in the decontamination of soils and alluvial deposits with high levels of potentially toxic elements (PTEs). A suspension of zero-valent iron nanoparticles (nZVI) was injected at three different concentrations in selected samples (two sediments, one soil). For most of the elements, the retention by nZVI was proportional to the concentration of the suspension and the trend was similar. Metals were immobilized by adsorption on the surface layer of the nanoparticles and/or by complexation, co-precipitation, and chemical reduction. By day 60 following injection, the nZVI lost reactivity and the retained species were desorbed and back into the soluble phase. The definition of spatial patterns for PTEs’ distribution allowed for the construction of contamination risk maps using a geostatistical simulation approach. The analysis obtained from the extractable contents of five target elements (Zn, Cu, Cd, Pb, As) was cross-checked with the estimated map network to assess their retention efficiency. Data from the analysis of these elements, in the extractable phase and in the porewater of the sediments/soils, indicate the nZVI injection as a suitable technique for reducing the risk level of PTEs in contaminated Fe-rich tropical environments.

Single-step probabilistic inversion of 3D seismic data of a carbonate reservoir in Southwest Iran

We use a sampling-based Markov chain Monte Carlo method to invert seismic data directly for porosity and to quantify its uncertainty distribution in a hard-rock carbonate reservoir in southwest Iran. The noise that remains in seismic data after the processing flow is correlated with the bandwidth in the range of the seismic wavelet. Hence, to account for the inherent correlated nature of the band-limited seismic noise in the probabilistic inversion of real seismic data, we assume the estimated seismic wavelet as a suitable proxy for capturing the coupling of noise samples. In contrast to the common approach of inserting a delta function on the main diagonal of the covariance matrix, we insert the seismic wavelet on its main diagonal. We also calibrate an empirical and a semiempirical inclusion-based rock-physics model (RPM) to characterize the rock-frame elastic moduli via a lithology-constrained fitting of the parameters of these models, i.e., the critical porosity and the pore aspect ratio. These calibrated RPMs are embedded in the inversion procedure to link petrophysical and elastic properties. In addition, we obtain the pointwise critical porosity and pore aspect ratio, which can potentially facilitate the interpretation of the reservoir for further studies. The inversion results are evaluated by comparing with porosity logs and an existing geologic model (porosity model) constructed through a geostatistical simulation approach. We assess the consistency of the geologic model through a geomodel-to-seismic modeling approach. The results confirm the performance of the probabilistic inversion in resolving some thin layers and reconstructing the observed seismic data. We have evaluated the applicability of our sampling-based approach to invert 3D seismic data for estimating the porosity distribution and its associated uncertainty for four subzones of the reservoir. The porosity time maps and the facies probabilities obtained via porosity cutoffs indicate the relative quality of the reservoir’s subzones.

A hybrid approach to model the dykes in Sungun porphyry copper deposit using Dempster–Shafer theory

Modeling geological units such as dykes is a powerful tool in mineral exploration studies. The most significant issue in modeling of uncertainty in the mineral exploration studies is the identification of the geological domains that consist of the zones with significant exploratory factor located in the area under study. The sequential indicator simulation (SIS) algorithm has the ability to model lithological facies. Although the two-point geostatistical simulation approaches are simple, they have some substantial drawbacks. For instance, they do not take into account the complex and nonlinear continuities in geological units like a swarm of the dyke. Therefore, if the area under study has complex geological units, it is necessary to improve the SIS algorithm considering the spatial patterns of complex and nonlinear structures. The pattern recognition method is an effective approach that can improve the two-point geostatistical simulation algorithm. It is based on the informative complex geological spatial patterns that contain the connectivity and nonlinear structures. This paper proposes a hybrid approach (PR-SIS) for simulation of geological units in the presence of several nonlinear structures. To perform hybrid approach, the SIS and pattern recognition methods were used in a combined form. To this end, the results of two methods were combined by the Dempster–Shafer theory (DST) approach. The main purpose of this paper is to investigate the impact of the proposed hybrid approach for modeling the dykes of the Sungun porphyry copper deposit (Iran). To this end, two evidences have been used including the sequential indicator simulation (SIS) method and the pattern recognition approach. These evidences were then applied for using the DST to obtain the final accuracy of the model. Final modeling of this approach shows the continuity of dykes in each location and optimal check with respect to the DST approach based on the geological map. The overall accuracy (OA) and the kappa index (KI) in different dimensions of the search windows showed that the dykes modeling using the hybrid approach by the DST provide a better accuracy. In this regard, the values of OA and KI were 0.889 and 0.792 and 0.901 and 0.805, as well as 0.982 and 0.891 for the SIS method, the pattern recognition method using 2.5 × 2.5 search window, and the proposed hybrid approach by the DST, respectively.

How many sampling points are needed to estimate the mean nitrate-N content of agricultural fields? A geostatistical simulation approach with uncertain variograms

Knowledge of how many sampling points are needed to estimate the mean content of soil nutrients in agricultural fields, given a precision requirement on the estimated mean, is limited. This paper describes a versatile geostatistical simulation approach for predicting the variance of the mean nitrate-N (NO3-N) content within an agricultural field estimated by random sampling. In fall of 2016 sixteen agricultural fields were sampled on a square grid to model the spatial variation of NO3-N. On twelve out of sixteen fields NO3-N showed a lognormal distribution rather than a normal distribution. Variograms for (log-transformed) NO3-N are estimated using a Bayesian approach, resulting in 100 vectors with possible variogram parameters per field, obtained by MCMC sampling from the posterior distribution. Each of these variograms is used to simulate 100 maps of NO3-N, resulting in 100 × 100 maps of NO3-N per field. Each map is used to compute the variance of the estimated mean with stratified simple random sampling of 5,10,…,50 points, with one point per compact geographical stratum. For each sample size (number of sampling points) the mean, median and P90 of the uncertainty distribution are computed. Based on the medians, the sample size required for a maximum expanded measurement uncertainty of 50% varies from <5 to >50. This large variation in required sample size shows the large variation among the sixteen fields in variance of NO3-N within a field.

Iterative algorithms for non-conditional and conditional simulation of Gaussian random vectors

The conditional simulation of Gaussian random vectors is widely used in geostatistical applications to quantify uncertainty in regionalized phenomena that have been observed at finitely many sampling locations. Two iterative algorithms are presented to deal with such a simulation. The first one is a variation of the propagative version of the Gibbs sampler aimed at simulating the random vector without any conditioning data. The novelty of the presented algorithm stems from the introduction of a relaxation parameter that, if adequately chosen, allows quickening the rates of convergence and mixing of the sampler. The second algorithm is meant to convert the non-conditional simulation into a conditional one, based on the successive over-relaxation method. Again, a relaxation parameter allows quickening the convergence in distribution to the desired conditional random vector. Both algorithms are applicable in a very general setting and avoid the pivoting, inversion, square rooting or decomposition of the variance-covariance matrix of the vector to be simulated, thus reduce the computation costs and memory requirements with respect to other discrete geostatistical simulation approaches.

Heuristic search strategy based on probabilistic and geostatistical simulation approach for simultaneous identification of groundwater contaminant source and simulation model parameters

In this study, a heuristic search strategy based on probabilistic and geostatistical simulation approach is developed for simultaneous identification of groundwater contaminant source and simulation model parameters. The numerical simulation model, which is repeatedly invoked to evaluate the likelihood in Bayesian formula, can be substituted by the surrogate system to reduce the huge computational load. To improve the approximation accuracy of the surrogate system to the simulation model, we employ Entropy Weight method as a novel method to establish a combined surrogate system by combining Gaussian process, support vector regression, and kernel extreme learning machine. A state evaluation (heuristic) function based on Bayesian formula and the surrogate system is introduced to quantify the approximation degree of variables in current state to true values for contaminant sources and simulation model parameters. Thereafter, a heuristic search iterative process related to artificial intelligence is designed for simultaneous identification, which takes full advantage of the guidance and correction role of actual field monitoring data. A multi-vector and variable-step size random walk method is proposed to select the candidate point. A Metropolis formula based on the state evaluation function is constructed, and the result is used as the judging criterion for the state transition. Finally, simultaneous identification results are obtained when the iteration reaches the convergence criteria. The proposed approaches are tested with a numerical case study. The results indicate that the heuristic search strategy can assist in identifying groundwater contaminant source and simulation model parameters simultaneously with high accuracy and efficiency.

An Optimum Selection of Simulated Geological Models by Multi-Point Geostatistics and Multi-Criteria Decision-Making Approaches; a Case Study in Sungun Porphyry-Cu deposit, Iran

An accurate modeling of sophisticated geological units has a substantial impact on designing a mine extraction plan. Geostatistical simulation approaches, via defining a variogram model or incorporating a training image (TI), can tackle the construction of various geological units when a sparse pattern of drilling is available. The variogram-based techniques (derived from two-point geostatistics) usually suffer from reproducing complex and non-linear geological units as dyke. However, multipoint geostatistics (MPS) resolves this issue by incorporating a training image from a prior geological information. This work deals with the multi-step Single Normal Equation Simulation (SNESIM) algorithm of dyke structures in the Sungun Porphyry-Cu system, NW Iran. In order to perform a multi-step SNESIM algorithm, the multi-criteria decision-making and MPS approaches are used in a combined form. To this end, two TIs are considered, one for simulating dyke structures in the shallow depth, and two for simulating dyke structures in a deeper depth. In the first step, a TI is produced using geological map, which has been mined out during the previous exploration operations. After producing TI, the 35 realizations are simulated for the shallow depth of deposit in the area under study. To select the best realization (as a TI for the next step) of the simulation results, several statistical criteria are used and the results obtained are compared. To this end, a hybrid multi-criteria decision-making is designed on the basis of a group of statistical criteria. In the next step, the dyke structures in the deeper depth are also simulated by the new TI.

County-level indoor radon concentration mapping and uncertainty assessment in South Korea using geostatistical simulation and environmental factors

This paper presents a geostatistical simulation approach to not only map the county-level indoor radon concentration (IRC) distributions in South Korea, but also quantify the uncertainty that can be used as decision-supporting information. For county-level IRC mapping in South Korea, environmental factors including geology, radium concentration in surface soil, gravel content in subsoil, and fault line density, which are known to be associated with the source and migration of radon gas, were incorporated into IRC measurements using multi-Gaussian kriging with local means. These four environmental factors could account for about 36% of the variability of noise-filtered IRCs, implying that regional variations of IRCs were affected by these factors. Sequential Gaussian simulation was then applied to generate alternative realizations of county-level IRC distributions. By summarizing the multiple simulation results, we identified some counties that lay on the great limestone series showed elevated IRCs. In addition, there were some counties in which the proportion of grids exceeding the recommended level was high but the uncertainty was also large according to the analysis of several uncertainty measures, which indicates that additional sampling is required for these counties. From the local cluster analysis in conjunction with simulation results, we found that the counties with higher levels of IRC belonged to the statistically significant clusters of high values, and these counties should be the prime targets for radon management and in-depth survey. The geographical distributions of IRC and uncertainty measures presented in this study provide guidance for effective radon management if they are consistently combined with both future IRC measurements and a geogenic radon potential map.

Bayesian kriging for reproducing reservoir heterogeneity in a tidal depositional environment of a sandstone formation

Spatial permeability modeling is an important step in reservoir characterization as it controls spatial continuity, heterogeneity, and fluid flow modeling. The conventional kriging algorithms, such as simple, ordinary, and universal kriging, have been used for spatial petrophysical property distribution. However, all are unbiased estimators that disregard the impact of uncertainty in the covariance structure, which is first estimated, and then adopted for interpolation. To prevail over the restrictions of unbiased prediction in conventional approaches, Bayesian Kriging has been recently presented to take into account the uncertainty about variogram parameters on subsequent predictions. Bayesian Kriging incorporates prior knowledge about observations, such as expert grasp and outcome from neighboring data, to be incorporated as a qualified guess in the spatial estimation. The uncertainty about model parameters in Bayesian Kriging is then represented in a form of posterior probability distribution to attain optimal unbiased linear interpolation, which then leads to avoid unrealistic small regions within the reservoir. The efficiency of Bayesian Kriging was justified through simulating the reservoir heterogeneity in terms of spatial permeability continuity in a tidal depositional environment of heterogeneous sandstone reservoir in South Rumaila oil field. The Bayesian kriging simulation was implemented in extensive comparison with other conventional geostatistical algorithms, such as simple, ordinary and universal kriging. It was illustrated that Bayesian Kriging algorithm is an efficient geostatistical simulation approach for reproducing reservoir heterogeneity by attaining less estimation variance. Multiple equiprobable stochastic reservoir images (realizations) were created by Bayesian kriging and ranked to select the three quantiles P10, P50, and P90. The entire work was implemented through R, the powerful open-source statistical computing language, and R codes can be used as fast vehicles to conduct the geostatistical simulation in various formations.

Surficial and Deep Earth Material Prediction from Geochemical Compositions

Prediction of true classes of surficial and deep earth materials using multivariate spatial data is a common challenge for geoscience modelers. Most geological processes leave a footprint that can be explored by geochemical data analysis. These footprints are normally complex statistical and spatial patterns buried deep in the high-dimensional compositional space. This paper proposes a spatial predictive model for classification of surficial and deep earth materials derived from the geochemical composition of surface regolith. The model is based on a combination of geostatistical simulation and machine learning approaches. A random forest predictive model is trained, and features are ranked based on their contribution to the predictive model. To generate potential and uncertainty maps, compositional data are simulated at unsampled locations via a chain of transformations (isometric log-ratio transformation followed by the flow anamorphosis) and geostatistical simulation. The simulated results are subsequently back-transformed to the original compositional space. The trained predictive model is used to estimate the probability of classes for simulated compositions. The proposed approach is illustrated through two case studies. In the first case study, the major crustal blocks of the Australian continent are predicted from the surface regolith geochemistry of the National Geochemical Survey of Australia project. The aim of the second case study is to discover the superficial deposits (peat) from the regional-scale soil geochemical data of the Tellus Project. The accuracy of the results in these two case studies confirms the usefulness of the proposed method for geological class prediction and geological process discovery.

Agricultural practices and geostatistical evaluation of nitrate pollution of groundwater in the Júcar River Basin District, Spain

Groundwater pollution by nitrates induced by intensive agriculture and overexploitation of water in the Jucar River Basin District is a major concern. This work is a contribution to understanding the spatial and temporal distribution of nitrates in groundwater and the possible relationships between the presence of nitrates and contextual variables, such as rainfall, seepage and lithology. A space-time table of groundwater measurements of nitrate levels between 1969 and 2012 (41 hydrological years) in 6381 monitoring locations is used. First, a statistical analysis was performed to find correlations between nitrate concentrations and the contextual variables of yearly rainfall and recharge amounts evaluated by the PATRICAL model. A geostatistical simulation approach was then used to build a space-time model of nitrate concentrations, including calculation of experimental variograms and fitting of a theoretical model. The results of the variograms were used to infer the maximum spatial correlation distance and the maximum time range of temporal correlation for the same location. Sequential Gaussian simulation was selected instead of kriging for the purpose of declustering of data locations. Finally, yearly maps of average nitrate concentrations were generated.The results show that nitrate concentrations have increased steadily from the early 1970s and have stabilized since 2005. Contamination by nitrates occurs predominantly in agricultural areas, such as the plateau of La Mancha and the coastal plain.

Preliminary analysis of spatial development of karst using a geostatistical simulation approach

Earth science phenomena are primarily spatially dependent with variations occurring on varying scales. Geostatistics is a well-known approach for the assessment of spatial models of regionalized variables, such as porosity. In this study, we used the results of 953 Lugeon tests (402 tests in exploratory wells and 550 tests in grouting wells) to assess effective porosity and karst development at the Tangab Dam site, Iran. Lugeon values were first normalized, following which the variogram method (i.e., range, sill, and nugget effect) was used to identify the spatial variability of Lugeon values. A high correlation range of 200 m was obtained along the grout curtain galleries, while the range was about 40 m in the vertical direction. The simple kriging method with Gaussian variograms was determined to be the best method for estimating the Lugeon values in the study area using cross validation-criteria (e.g., RMSE = 0.835 and ρ = 0.914). Spatial variation of Lugeon values was mapped using a simulated annealing approach. The analysis revealed: (1) a higher potential for karst development on the left abutment of the Tangab Dam site, (2) the average of simulated Lugeon values decreased from values of about 180 close to the ground surface at 1,440 m a.s.l. to lower values of about 50 at 1,260 m a.s.l., and (3) high Lugeon values in the abutments of the dam site approximately followed the 15° bedrock dip, which confirms the potential development of karst features in the Asmari limestone. A schematic model for development of karst at the Tangab Dam site is proposed based on hydrogeological data and results of simulated Lugeon values around the dam site.

Characterization of ambient air pollution measurement error in a time-series health study using a geostatistical simulation approach

In recent years, geostatistical modeling has been used to inform air pollution health studies. In this study, distributions of daily ambient concentrations were modeled over space and time for 12 air pollutants. Simulated pollutant fields were produced for a 6-year time period over the 20-county metropolitan Atlanta area using the Stanford Geostatistical Modeling Software (SGeMS). These simulations incorporate the temporal and spatial autocorrelation structure of ambient pollutants, as well as season and day-of-week temporal and spatial trends; these fields were considered to be the true ambient pollutant fields for the purposes of the simulations that followed. Simulated monitor data at the locations of actual monitors were then generated that contain error representative of instrument imprecision. From the simulated monitor data, four exposure metrics were calculated: central monitor and unweighted, population-weighted, and area-weighted averages. For each metric, the amount and type of error relative to the simulated pollutant fields are characterized and the impact of error on an epidemiologic time-series analysis is predicted. The amount of error, as indicated by a lack of spatial autocorrelation, is greater for primary pollutants than for secondary pollutants and is only moderately reduced by averaging across monitors; more error will result in less statistical power in the epidemiologic analysis. The type of error, as indicated by the correlations of error with the monitor data and with the true ambient concentration, varies with exposure metric, with error in the central monitor metric more of the classical type (i.e., independent of the monitor data) and error in the spatial average metrics more of the Berkson type (i.e., independent of the true ambient concentration). Error type will affect the bias in the health risk estimate, with bias toward the null and away from the null predicted depending on the exposure metric; population-weighting yielded the least bias.

Sparse data integration for the interpolation of concentration measurements using kriging in natural coordinates

Summary Groundwater contaminant plumes often display a curvilinear anisotropy which conventional kriging and geostatistical simulation approaches generally fail to reproduce. In this paper, we use a physically relevant coordinate transformation in order to improve the kriging of contaminant plumes in 2D. The proposed coordinate transformation maps the Cartesian grid into the natural coordinates of flow: the hydraulic head and the stream function. This simplifies the specification of a nonlinear anisotropy by modifying the spatial relationships between grid points. The computation of the natural coordinates, however, requires the availability of a flow model, which often needs to be defined using limited data. For this reason, a data integration procedure is included in the methodology to support the use of the natural coordinate transformation in real cases. The performance of the approach is tested on two synthetic test cases where it produces concentration maps that are more accurate than those obtained with Cartesian coordinates kriging. These test cases also highlight some limitations of the approach. Whereas the transformation enables kriging to account for advection, results show the need to consider dispersion as well. Further work is also required to generalize the approach to 3D cases and to groundwater flow including wells and sources.

Homogenization of Climate Data: Review and New Perspectives Using Geostatistics

The homogenization of climate data is of major importance because non-climatic factors make data unrepresentative of the actual climate variation, and thus the conclusions of climatic and hydrological studies are potentially biased. A great deal of effort has been made in the last two decades to develop procedures to identify and remove non-climatic inhomogeneities. This paper reviews the characteristics of several widely used procedures and discusses the potential advantages of geostatistical techniques. In a case study, the geostatistical simulation approach is applied to precipitation data from 66 monitoring stations located in the southern region of Portugal (1980–2001). The results from this procedure are then compared with those from three well established statistical tests: the Standard normal homogeneity test (SNHT) for a single break, the Buishand range test, and the Pettit test. Promising results from the case study open new research perspectives on the homogenization of climate time series.

An intrinsic model of coregionalization that solves variance inflation in collocated cokriging

Sequential Gaussian simulation (SGS) is a widely used geostatistical simulation approach for continuous variables. A variant of SGS that employs collocated cokriging under a Markov model is commonly applied to integrate seismic data and to cosimulate multiple variables. This approach is popular because it is simple; the correlation coefficient between the primary variable being modeled and secondary data is the sole additional statistic required to integrate the secondary data. Collocated cokriging, however, has a longstanding problem with variance inflation that leads to a systematic bias in the mean and variance of the simulated realizations. An alternative approach is presented here that is equally simple, with no additional parameters needed. An intrinsic model of coregionalization is adopted for cokriging using secondary data at the location being considered and at the locations of the primary data. The resulting technique can be referred to as intrinsic collocated cokriging (ICCK). The resulting estimates are checked carefully and no variance inflation is observed. This implementation should systematically replace all versions of the Markov model and collocated cokriging.

Using chance constrained binary integer programming in optimising long term production scheduling for open pit mine design

The present paper attempts to model long term production scheduling problems by chance constrained binary integer programming in a stochastic environment. This stochastic model is set up to account for ore block grade uncertainty. The probability distribution function of grade in each block is used as a stochastic input to the optimisation model. This distribution function in each block should be determined using geostatistical simulation approach. The deterministic equivalent of proposed chance constrained model is then achieved which is the form of non-linear quadratic in binary variables. A confidence level at which it is desire that the uncertain constraints holds, is specified in each scheduling period. Rather than previous risk based model, this formulation will yield schedules with high chance of achieving planned production targets while maximises the expectation of net present value and minimises the variance function simultaneously. Using this method the grade uncertainty is integrated explicitly into the optimisation process.

A Geostatistical Simulation Approach to a Pollution Case in Northeastern Italy

The study zone is located in the city of Padova (the Veneto region, NE Italy). The industrial activities present in this area since 1950 have produced very high concentrations of Pb, Zn, Cu, Pcb and oils until a depth of 7 m. The unsaturated and the saturated zones are both polluted. Because of the abundance of Pb values it was decided to analyze the lead distribution in the studied zone. In many studies of the polluted sites, the geometry of the investigated volume is highly anisotropic. Generally we have an extension of some hectares in the horizontal plane and of a few meters in depth. It is likely that different horizontal spatial continuity structures in pollution distribution are found at different depths both for the layered nature of the medium and for the transition between unsaturated and saturated conditions. In such conditions the decision to divide a 3D problem into 1D and 2D problems can be useful. Initially the studied volume was divided into seven layers up to 5 m in depth; the study was then approached in two phases. First, the Pb values in the vertical direction were analyzed, considering a derive along z, and estimating the values using the Kriging with Trend (KT) method. Thus it was possible to increase the data in the z direction, especially in the deeper layers. Second, 500 realizations of the Pb distribution for each of the seven layers were simulated using the simulated annealing procedure. Finally, results were presented and discussed for each layer in terms of median and probability maps.

Quantitative integration of hydrogeophysical data: Conditional geostatistical simulation for characterizing heterogeneous alluvial aquifers

High-resolution geophysical parameter information, as it can be provided, for example, by crosshole georadar and seismic tomography, has proven to provide useful spatial information to complement traditional hydrological methods such as core analyses, logging techniques, and tracer or pumping tests. Quantitative integration of these diverse database components is one of the major challenges in the field of high-resolution hydrogeophysics because of their different scales of measurement and the usually weak petrophysical relations among the measurements. In this study, we systematically explore the usefulness of a conditional stochastic simulation approach based on simulated annealing for this purpose. First, we generate a realistic model of an alluvial aquifer consisting of a 2D scale-invariant porosity field. On the basis of this model, we generate synthetic neutron porosity logs and crosshole georadar tomographic surveys. We then use the proposed geostatistical simulation approach to integrate this hydrogeophysical database. The effectiveness of this approach to characterize the detailed porosity distribution in heterogeneous alluvial aquifers is assessed by comparing the results for a variety of simulated porosity fields that differ fundamentally in terms of their conditioning information. Our results indicate this approach has the potential to allow for a realistic hydrogeophysical characterization in the submeter range of the porosity distribution in heterogeneous alluvial aquifers.