Probability Perturbation Method Research Articles

A Practical probabilistic history matching framework for characterizing fracture network parameters of shale gas reservoirs

Simulating fluid flow in complex fracture systems encountered in subsurface systems, such as those encountered in tight or shale gas reservoirs, presents considerable challenges. Sophisticated numerical techniques and characterization approaches are required to integrate static and dynamic data from multiple sources to account for the intricate interplay between fractures and the surrounding rock matrix. A novel workflow using an indicator-based probability perturbation method (PPM) is applied to characterize uncertain discrete fracture network parameters. The posterior probability distributions of primary and secondary fracture transmissivity, aperture, length, height, and intensity of the secondary fracture are estimated according to the production (flow) histories. A case study based on the Horn River shale gas reservoir is presented. A pilot point scheme is formulated to update the distributions of P32L. The forward modelling entails upscaling each fracture model into a dual-porosity dual-permeability model and performing multiphase flow simulation. This approach produces an ensemble of history-matched discrete fracture and upscaled models by incorporating static and dynamic data. The results demonstrate the utility of the developed method for estimating secondary fracture parameters, which are not inferrable from other static information alone. The inference of both primary and secondary fractures offers a more comprehensive characterization of the fracture networks in tight or shale gas reservoirs. Integrating a pilot point parameterization technique and a sequential simulation approach into the PPM framework presents significant novelties in contributing to a comprehensive and effective method of simulating fluid flow in complex fracture systems, addressing the challenges associated with non-linear relationships between fracture model parameters and the corresponding flow response.

A geostatistical implicit modeling framework for uncertainty quantification of 3D geo-domain boundaries: Application to lithological domains from a porphyry copper deposit

The spatial modeling of geo-domains has become ubiquitous in many geoscientific fields. However, geo-domains’ spatial modeling poses real challenges, including the uncertainty assessment of geo-domain boundaries. Geo-domain models are subject to uncertainties due mainly to the inherent lack of knowledge in areas with little or no data. Because they are often used for impactful decision-making, they must accurately estimate the geo-domain boundaries’ uncertainty. This paper presents a geostatistical implicit modeling method to assess the uncertainty of 3D geo-domain boundaries. The basic concept of the method is to represent the underlying implicit function associated with each geo-domain as a sum of a random implicit trend function and a residual random function. The conditional simulation of geo-domains is performed through a step-by-step approach. First, implicit trend function realizations and optimal covariance parameters associated with the residual random function are generated through the probability perturbation method. Then, residual function realizations are generated through classical geostatistical unconditional simulation methods and added to implicit trend function realizations to obtain unconditional implicit function realizations. Next, the conditioning of unconditional implicit function realizations to hard data is performed via principal component analysis and randomized quadratic programming. Finally, conditional implicit function simulations are transformed to conditional geo-domain simulations by applying a truncation rule. The proposed method is constructed to honor hard data and stated rules of how geo-domains interact spatially. It is applied to a lithological dataset from a porphyry copper deposit. A comparison with the classical sequential indicator simulation (SIS) method is carried out. The results indicate that the proposed approach can provide a more reliable and realistic uncertainty assessment of 3D geo-domain boundaries than the traditional sequential indicator simulation (SIS) approach.

Probabilistic history matching of multi-scale fractured reservoirs: Integration of a novel localization scheme based on rate transient analysis

In this paper, a new assisted history-matching workflow is presented, where rate transient analysis (RTA) results are used to constrain not only the initial discrete fracture network (DFN) models, the interpreted flow regimes are also used to formulate a localization scheme for more efficient updating of the pertinent DFN model parameters. The outcome is an ensemble of DFN realizations that are calibrated to both geologic and dynamic production data.RTA interpretations and other pertinent geological data are used to infer the prior probability distributions of the unknown fracture parameters, from which an ensemble of initial DFN models is sampled. The DFN models are subjected to numerical multiphase flow simulation. The fracture parameters are adjusted following an indicator-based probability perturbation method, which is capable of minimizing the objective function and reducing the uncertainties in the unknown fracture parameters simultaneously. A key feature is that the flow regimes identified from RTA are used to formulate a localization strategy, where individual segments of the production data are used to tune only a specified subset of the unknown model parameters.In a case study, the method is applied to characterize the probability distributions of four parameters in a multifractured shale gas well: primary fracture transmissivity, aperture of the secondary fracture, transmissivity of the secondary induced fracture, and global fracture intensity. Their probability distributions are updated following the proposed approach to match the production history. Multiple realizations of the DFN model are sampled.A key novelty is that the proposed probabilistic approach facilitates the representation of uncertainties in fracture parameters via multiple equally-probable DFN models and their corresponding upscaled flow-simulation models. A more comprehensive and robust approach is presented for integrating specific RTA interpretations and estimations into various steps of the history-matching process.

Reservoir lithofacies modeling using well logs and seismic data based on Sequential Indicator Simulations and Probability Perturbation Method in a Bayesian framework

In this paper, an inverse framework based on Bayes’ theorem is suggested for integrating well logs and seismic data into reservoir lithofacies modeling process. The proposed method is based on combination of the Sequential Indicator Simulation (SIS), and a stochastic optimization method (i.e. Probability Perturbation Method (PPM)). SIS is used to calculate the conditional probability of presence/absence of lithofacies indicators in each grid-block, and PPM is applied to update (perturb) the conditional probability used in SIS. A notable innovation presented in this study is using the Genetic algorithm’ crossover operator to increase the PPM exploitation capability. To demonstrate the efficiency of our proposed approach, the results of its application on a 3D test model is compared with outcomes of two commonly-used constraining approaches on SIS. Qualitative and quantitative analysis of the obtained results on 3D test model reveals a (23.8)% and (16.98)% (on average) improvement in consistency of lithofacies models generated using the proposed approach with the reference lithofacies model over the employed Vertical Probability Trend and Seismic Probability Trend constraining approaches on SIS, respectively. Besides, the obtained results show that implementing crossover operator leads to a 4.56% improvement in matching of the constructed lithofacies models with the reference model.

Inference of Hydraulically Fractured Reservoir Properties from Production Data Using the Indicator-Based Probability Perturbation Assisted History-Matching Method

Hydraulically fractured horizontal wells are widely adopted for the development of tight or shale gas reservoirs. The presence of highly heterogeneous, multi-scale, fracture systems often renders any detailed characterization of the fracture properties challenging. Discrete fracture network (DFN) model offers a viable alternative for explicit representation of multiple fractures in the domain, where the comprising fracture properties are defined in accordance to specific probability distributions. However, even with the successful modelling of a DFN, the relationship between a set of fracture parameters and the corresponding production performance is highly nonlinear, implying that a robust history-matching workflow capable of updating the pertinent DFN model parameters is required for calibrating stochastic reservoir models to both geologic and dynamic production data.This paper proposes an integrated approach for the history matching of hydraulically fractured reservoirs. First, multiple realizations of the DFN model are constructed conditioning to available geological information such as seismic data and well logs, which are useful for inferring the prior probability distributions of relevant fracture parameters. Next, the models are upscaled into equivalent continuum dual-permeability models and subjected to numerical multiphase flow simulation. The predicted production performance is compared with the actual recorded responses. Finally, the DFN-model parameters are adjusted following an indicator-based probability perturbation method. Although the probability perturbation technique has been applied to update facies distributions in the past, its application in modeling DFN distributions is limited. To account for the non-Gaussian nature of the DFN parameters, an indicator formulation is proposed. The algorithm aims at minimizing the objective function, while reducing the uncertainties in the unknown fracture parameters.The method is applied to estimate the posterior probability distributions of the transmissivity of the primary fracture (Tpf), transmissivity of the secondary induced fracture (Tsf) and global fracture intensity (Psf32G) in a multifractured shale gas well in the Horn River Basin. An initial realization of the DFN model is sampled from the prior probability distributions using the Monte Carlo simulation. These probability distributions are updated to match the production history, and multiple equi-probable realizations of the DFN models are sampled from the updated (posterior) distributions accordingly. The final sampled realizations of the DFN model are consistent with both static geological information and dynamic production history.

Stochastic inversion of facies and reservoir properties based on multi-point geostatistics

A stochastic inversion method that can provide reservoir models of facies and reservoir properties is proposed for seismic reservoir characterization. It is an iterative optimization process achieved by the probability perturbation method on the basis of conditional simulation with multi-point geostatistics, and it also incorporates a quantum annealing algorithm to improve the accuracy of inverted reservoir properties. The usual practice of stochastic inversion based on multi-point geostatistics is time-consuming and only generates the inverted facies. The probability perturbation method can help to reduce the number of simulations and speed up the inversion process. An inverted model of facies is generated, and a volume of pseudo reservoir properties met with a fixed error is also produced in this stage. However, the continuity of this volume is poor because random sampling is used when transforming facies models into reservoir property volumes. Moreover, the characteristics of reservoir properties in the same facies cannot be reflected well. We extract the volume of pseudo reservoir properties as an initial model for optimization to improve the inversion accuracy of reservoir properties. A quantum annealing algorithm is utilized for its fast convergence rate and ability to avoid falling into a local minimum. The presented method can produce fine-scaled reservoir models of facies, and produce reservoir properties in a reasonable amount of computation time. Tests on model data demonstrate the feasibility and reliability of this technique. Facies and porosity inversion results with relatively higher accuracy are acquired, which verifies the advantages and feasibility of the proposed method. Successful application to field data further validates the effectiveness of this method.

A new approach with multiple realizations for image perturbation using co-simulation and probability perturbation method

History matching is an inverse problem with multiple possible answers. The petrophysical properties of a reservoir are highly uncertain because data points are scarce and widely scattered. Some methods reduce uncertainty in petrophysical characterization; however, they commonly use a single matched model as a reference, which may excessively reduce uncertainty. Choosing a single image may cause the model to converge to a local minimum, yielding less reliable history matching. This work improves on the history matching presented by Oliveira et al. ((2017a) J. Petrol. Sci. Eng. 153, 111–122) using a benchmark model (UNISIM-I-H based on the Namorado field in Brazil). We use a new approach for a Probability Perturbation Method and image perturbation using Co-Simulation. Instead of using a single image as the reference, a set of best images is used to increase variability in the properties of the reservoir model while matching production data with history data. This approach mitigates the risk of the potentially excessive reduction of uncertainties that can happen when using a single model. Our methodology also introduces a new objective function for water breakthrough, improving model quality because of the importance of matching the water breakthrough in the process. Our proposed methodology for image perturbation uses the UNISIM-I-H, which comprises 25 wells and has 11 years of history data. Our methodology made the process of calibration more effective than the history matching by Oliveira et al. ((2017a) J. Petrol. Sci. Eng. 153, 111–122). Cross-influence was minimized, making the history matching more objective and efficient, and consequently, the production forecasts more reliable.

Analysis of antiwear for hydraulic relief valve under different surface treatment processes

Wear between valve core and valve seat is one of the main failure modes of the hydraulic valve. The surface treatment process for valve core and valve seat has a great influence on their service life, so the reliability research of the hydraulic valve should focus on analysis of wear failure problem. Techniques from the probability statistical theory, wear theory, hydraulic technique and probability perturbation method are employed to present the practical and effective method for the wear failure analysis for the hydraulic valve under different surface treatment processes in this paper. The problem for the reliability analysis design of the hydraulic valve system is solved practicably and effectively. The respective programme can be used to obtain the reliability information of the hydraulic valve accurately and quickly.

Research on the hydraulic turbine vertical vibration power flow in the head cover system

On the basis of the prior models about the vertical vibration of the hydraulic vibration source, this research introduced a sub-system—head cover. Head cover is one of the main paths when vibration is transferred from the water vibration source to the stable structure. This essay aims to analyze the hydraulic turbine vertical vibration power flow in the head cover system. The research is based on the power flow theory and the probability perturbation method; meanwhile, it considered on the reciprocal coupling effect of the water machine parts and power house structure, etc. Therefore, the results of can clearly provide the random power flow of the vibration transfer path system, which including the head cover system, in frequency domain by given of some uncertain factors in one project. In conclusions, the research provide an overall analysis on the hydropower station vertical vibration transfer path; and it suggest some simplified and efficient solutions in the analysis on the vibration path with some random parameters.

Stochastic inversion of facies from seismic data based on sequential simulations and probability perturbation method

We presented a new methodology for seismic reservoir characterization that combined advanced geostatistical methods with traditional geophysical models to provide fine-scale reservoir models of facies and reservoir properties, such as porosity and net-to-gross. The methodology we proposed was a stochastic inversion where we simultaneously obtained earth models of facies, rock properties, and elastic attributes. It is based on an iterative process where we generated a set of models of reservoir properties by using sequential simulations, calculated the corresponding elastic attributes through rock-physics relations, computed synthetic seismograms and, finally, compared these synthetic results with the real seismic amplitudes. The optimization is a stochastic technique, the probability perturbation method, that perturbs the probability distribution of the initial realization and allows obtaining a facies model consistent with all available data through a relatively small number of iterations. The probability perturbation approach uses the Tau model probabillistic method, which provides an analytical representation to combine single probabilistic information into a joint conditional probability. The advantages of probability perturbation method are that it transforms a 3D multiparameter optimization problem into a set of 1D optimization problems and it allowed us to include several probabilistic information through the Tau model. The method was tested on a synthetic case where we generated a set of pseudologs and the corresponding synthetic seismograms. We then applied the method to a real well profile, and finally extended it to a 2D seismic section. The application to the real reservoir study included data from three wells and partially stacked near and far seismic sections, and provided as a main result the set of optimized models of facies, and of the relevant petrophysical properties, to be the initial static reservoir models for fluid flow reservoir simulations.

An Algorithm for 3D Pore Space Reconstruction from a 2D Image Using Sequential Simulation and Gradual Deformation with the Probability Perturbation Sampler

The construction of a faithful 3D pore space model of a porous medium that could reproduce the macroscopic behavior of that medium is of great interest in various fields including medicine, material science, hydrology and petroleum engineering. A computationally efficient algorithm is developed that uses the probability perturbation method and sequential multiple-point statistics simulations to generate 3D stochastic and equiprobable representations of random porous media when only a 2D thin section image is available. By employing the probability perturbation method as a gradual deformation technique, the pore patterns of a single 2D image are deformed to generate a series of 2D stochastically simulated images. The 3D pore structure is then generated by simply stacking the 2D-simulated images. The quality of the 3D reconstruction is critically dependent on the rate of deformation and a simple general procedure for choosing this parameter is presented. Various criteria such as porosity, two-point auto-correlation function, multiple-point connectivity function, local percolation probability, absolute permeability obtained by lattice-Boltzmann method (LBM), formation factor and two-phase relative permeability calculations are used to validate the results. The method is tested on two random porous solids; Berea Sandstone and synthetic Silica, for which directly measured 3D micro-CT images are available. The stochastically reconstructed 3D pore space preserves the low- and high-order spatial statistics, the macroscopic flow properties and the microstructure of the 3D micro-CT images.

Fatigue Reliability Sensitivity Analysis of Complex Mechanical Components under Random Excitation

Fatigue failure is the typical failure mode of mechanical components subjected to random load‐time history. It is important to ensure that the mechanical components have an expected life with a high reliability. However, it is difficult to reduce the influence of factors that affect the fatigue reliability and thus a reliability sensitivity analysis is necessary. An approach of fatigue reliability sensitivity analysis of complex mechanical components under random excitation is presented. Firstly, load spectra are derived using a theoretical method. A design of experiment (DOE) is performed to study the stresses of dangerous points according to the change of design parameters of the mechanical component. By utilizing a Back‐Propagation (BP) algorithm, the explicit function relation between stresses and design parameters is formulated and thus solves the problem of implicit limit state function. Based on the damage accumulation (DA) approach, the probability perturbation method, the fourth‐moment method, the Edgeworth expansion is adopted to calculate the fatigue reliability and reliability‐based sensitivity. The fatigue reliability sensitivity analysis of a train wheel is performed as an example. The results of reliability are compared with that obtained using Monte Carlo simulation. The reliability sensitivity of design parameters in the train wheel is analyzed.

Multiple‐point geostatistics for modeling subsurface heterogeneity: A comprehensive review

For more than half a century, geostatistics has been developed and has increasingly been used for modeling subsurface heterogeneity. Traditionally, geostatistical simulations are based on a random function model defined according to the specificities of the geological formation under investigation. Unlike traditional geostatistics, multiple‐point (MP) geostatistics avoids the explicit definition of a random function but directly infers the necessary multivariate distributions from training images. This confers on MP geostatistics a potential applicability to any geological environment, provided that there is a training image representative of the geological heterogeneity and that the essential features of this training image can be characterized by statistics defined on a limited point configuration. This paper presents a comprehensive review of MP geostatistics. If the principle of MP geostatistics is straightforward and attractive, its industrial applicability largely depends on the implementation methods. The use of a search tree for storing MP statistics is a great step that made MP geostatistics actually applicable in industry. In the meantime, other methods such as multiple grids and image postprocessing are introduced and allow enhancing the reproduction of patterns observed in training images. Because of the sequential procedure, MP simulations can easily honor local hard data. There are methods available for constraining MP simulations to target global statistics (facies proportions) and also for integrating spatial auxiliary constraints that can tremendously improve the spatial features of MP simulations. Furthermore, both the gradual deformation method and the probability perturbation method are compatible with MP geostatistics and allow integrating hydrodynamic data into MP simulations. More recent developments of MP geostatistics include sequentially simulating patterns instead of points and using different geological scenarios (training images) for dynamic data inversion.

Extended Probability Perturbation Method for Calibrating Stochastic Reservoir Models

Calibrating a stochastic reservoir model on large, fine-grid to hydrodynamic data requires consistent methods to modify the petrophysical properties of the model. Several methods have been developed to address this problem. Recent methods include the Gradual Deformation Method (GDM) and the Probability Perturbation Method (PPM). The GDM has been applied to pixel-based models of continuous and categorical variables, as well as object-based models. Initially, the PPM has been applied to pixel-based models of categorical variables generated by sequential simulation. In addition, the PPM relies on an analytical formula (known as the tau-model) to approximate conditional probabilities. In this paper, an extension of the PPM to any type of probability distributions (discrete, continuous, or mixed) is presented. This extension is still constrained by the approximation using the tau-model. However, when applying the method to white noises, this approximation is no longer necessary. The result is an entirely new and rigorous method for perturbing any type of stochastic models, a modified PPM employed in similar manner to the GDM.

Correlation failure analysis of an uncertain hysteretic vibration system

In this paper, a numerical method for correlation sensitivity analysis of a nonlinear random vibration system is presented. Based on the first passage failure model, the probability perturbation method is employed to determine the statistical characteristics of failure modes and the correlation between them. The sensitivity of correlation between failure modes with respect to random parameters characterizing the uncertainty of the hysteretic loop is discussed. In a numerical example, a two-DOF shear structure with uncertain hysteretic restoring force is considered. The statistical characteristics of response, failure modes and the sensitivity of random hysteretic loop parameters are provided, and also compared with a Monte Carlo simulation.

Solving spatial inverse problems using the probability perturbation method: An S-GEMS implementation

The probability perturbation method (PPM) is introduced as a flexible and efficient sampling technique for generating inverse solutions under a given prior geological constraint (prior model). In this paper, we present a methodology for producing software code that runs PPM within a public domain geostatistical software called the Stanford Geostatistical Earth Modeling Software (S-GEMS). The challenge in creating such code lies in the great diversity of forward models as well as prior models that can be handled by the PPM. Therefore, our software solution must be highly flexible and extensible such that it can be tailored to the various applications at hand. Our implementation has two main objectives: (1) to create an integrated working environment which provides users easy access to functionalities of the PPM through a general user interface as well as visualize results; (2) allow the users to plug-in their application specific code into the PPM algorithm workflow. We provide a two-part solution. The first part, which is hard-coded in S-GEMS as a plug-in module, runs the Dekker-Brent optimization algorithm to control the parameter perturbation needed for the inversion. It generates the PPM user interface and allows visualization of the spatial domain of interest using S-GEMS graphics capability. The second part is coded in object-oriented Python scripts and is used to control the PPM execution in S-GEMS. Users can program their particular needs in scripts and load them into S-GEMS as part of the PPM workflow. The same mechanism can be used to extend the capabilities of PPM itself by implementing new PPM variants in Python and making them a part of the base class hierarchy. Case studies are used to demonstrate the flexibility of our code. This approach requires the user to adapt only a small amount of python code, without modifying, or re-compiling the core S-GEMS code.

Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems

Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems

Hybridization of the probability perturbation method with gradient information

Geostatistically based history-matching methods make it possible to devise history-matching strategies that will honor geologic knowledge about the reservoir. However, the performance of these methods is known to be impeded by slow convergence rates resulting from the stochastic nature of the algorithm. It is the purpose of this paper to introduce a method that integrates qualitative gradient information into the probability perturbation method to improve convergence. The potential of the proposed method is demonstrated on a synthetic history-matching example. The results indicate that inclusion of qualitative gradient information improves the performance of the probability perturbation method.

History Matching of Naturally Fractured Reservoirs Using Elastic Stress Simulation and Probability Perturbation Method

Summary The application of elastic stress simulation for fracture modeling provides a more realistic description of fracture distribution than conventional statistical and geostatistical techniques, allowing the integration of geomechanical data and models into reservoir characterization. The geomechanical prediction of the fracture distribution accounts for the propagation of fracture caused by stress perturbation associated with faults. However, the challenge lies in estimating the past remote stress conditions which induced structural deformation and fracturing, the limited applicability of the elasticity assumption, and the latent uncertainty in the structural geometry of faults. The integration of historical production data and well-test permeability into geomechanical fracture modeling is a practical way to reduce such uncertainty. We propose to combine geostatistical algorithms for history matching with geomechanical elastic simulation models for developing an integrated yet efficient fracture modeling tool. This paper presents an integrated approach to history matching of naturally fractured reservoirs which includes (1) fracture trend prediction through elastic stress simulation; (2) geostatistical population of fracture density based on a fracture trend model; (3) fracture permeability modeling integrating fracture density, matrix permeability and well-test permeability; and (4) numerical flow simulation and history matching. All of these implementations are incorporated into a single forward modeling process and iterated in the automatic history-matching scheme. To obtain a history match on a reservoir model, we jointly perturb the large-scale fracture trend and local-scale geostatistical fluctuations of fracture densities rather than perturbing permeability calibrated from fractures. This strategy enables us to preserve the geological/geomechanical consistency throughout the history-matching process. The geomechanically simulated fracture trend model is calibrated to both production data and the reservoir geological structure (faults and horizons) by searching for the optimum remote stress condition for elastic stress-field simulation. The latter is achieved by matching the actually observed structural deformation with the simulated one. The smaller-scale fluctuation of fracture density is simultaneously history matched through the probability perturbation method of Caers (Caers 2003; Hoffman and Caers 2005; Caers 2007). The methodology is presented on a synthetic reservoir application. Introduction The modeling of the density and pattern of fracture distributions can take different approaches depending on the origin and the type of fracture sets and on the ultimate reservoir engineering questions raised. In this paper, we focus on the modeling of shear fractures which are generated by structural deformation accompanied with fault slip. Recently, an application of the elastic stress simulation has been proposed for predicting the pattern of shear/tensile fractures or the pattern of secondary faults and shown promising results (Bourne and Willemse 2001; Maerten et al. 2002; Bourne et al. 2001). The elastic simulation numerically simulates the structural deformation of the reservoir by solving linear elasticity equations under given boundary conditions, and simultaneously calculates the corresponding stress/strain tensor fields (Bourne and Willemse 2001; Maerten et al. 2002; Bourne et al. 2001; Daly and Mueller 2004; Roxar FracPerm Reference Manual 2005). The boundary conditions consist of (1) location/geometry of fault surface, (2) stress conditions or displacement conditions on the fault surfaces, and (3) the remote loads applied to the structure at the time of structural deformation accompanied with fault slippage. First, satisfying boundary conditions and by minimizing strain energy, the linear elastic equations are solved to obtain a structural deformation field which is expressed by the displacement vector. Next, strain field is computed from the displacement gradient based on the definition of strain. Finally, under the assumption of elasticity, stress is calculated from strain by means of Hook's law.

Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems

Inverse problems are ubiquitous in the Earth Sciences. Many such problems are ill-posed in the sense that multiple solutions can be found that match the data to be inverted. To impose restrictions on these solutions, a prior distribution of the model parameters is required. In a spatial context this prior model can be as simple as a Multi-Gaussian law with prior covariance matrix, or could come in the form of a complex training image describing the prior statistics of the model parameters. In this paper, two methods for generating inverse solutions constrained to such prior model are compared. The gradual deformation method treats the problem of finding inverse solution as an optimization problem. Using a perturbation mechanism, the gradual deformation method searches (optimizes) in the prior model space for those solutions that match the data to be inverted. The perturbation mechanism guarantees that the prior model statistics are honored. However, it is shown with a simple example that this perturbation method does not necessarily draw accurately samples from a given posterior distribution when the inverse problem is framed within a Bayesian context. On the other hand, the probability perturbation method approaches the inverse problem as a data integration problem. This method explicitly deals with the problem of combining prior probabilities with pre-posterior probabilities derived from the data. It is shown that the sampling properties of the probability perturbation method approach the accuracy of well-known Markov chain Monte Carlo samplers such as the rejection sampler. The paper uses simple examples to illustrate the clear differences between these two methods