Bayesian Stochastic Inversion Research Articles

Nonstationary Prestack Linear Bayesian Stochastic Inversion

Nonstationary Prestack Linear Bayesian Stochastic Inversion

Bayesian stochastic inversion with petro-elastic relation to quantify thin gas sands of Khadro Formation, Zamzama gas field

Bayesian stochastic inversion with petro-elastic relation to quantify thin gas sands of Khadro Formation, Zamzama gas field

Gas Saturated Sandstone Reservoir Modeling Using Bayesian Stochastic Seismic Inversion

This study has been done to map the distribution of gas saturated sandstone reservoir by using stochastic seismic inversion in the “X” field, Bonaparte basin. Bayesian stochastic inversion seismic method is an inversion method that utilizes the principle of geostatistics so that later it will get a better subsurface picture with high resolution. The stages in conducting this stochastic inversion technique are as follows, (i) sensitivity analysis, (ii) well to seismic tie, (iii) picking horizon, (iv) picking fault, (v) fault modeling, (vi) pillar gridding, ( vii) making time structure maps, (viii) scale up well logs, (ix) trend modeling, (x) variogram analysis, (xi) stochastic seismic inversion (SSI). In the process of well to seismic tie, statistical wavelets are used because they can produce good correlation values. Then, the stochastic seismic inversion results show that the reservoir in the study area is a reservoir with tight sandstone lithology which has a low porosity value and a value of High acoustic impedance ranging from 30,000 to 40,000 ft /s*g/cc.

Bayesian Stochastic Inversion (A case study from an Iranian oil field)

We have implemented an estimation procedure whereby wireline data can be extrapolated away from existing well using geostatistical inversion of post-stack 3D seismic data. This procedure works directly in a fine-scale stratigraphic grid, and is conditioned by well and seismic data. It uses a Bayesian framework and a linearized, weak contrast approximation of the Zoeppritz equation to construct a joint log-Gaussian posterior distribution for Pwave impedances. Variograms are also estimated from well-log, seismic data and acoustic inversion results that define the expected degree of lateral smoothness away from the well. A sequential Gaussian Simulation algorithm is applied to sample the posterior PDF and generates multiple, high-resolution realizations of the acoustic impedance which can be utilized to generate stochastic realizations of petrophysical variables that not only honor the well-log data, but most importantly, that fully honor the 3D seismic. Sensitivity analysis was also performed to find the optimum values for S/N ratio, Variogram ranges and prior standard deviation. We had just one well in the area and preferred to keep it to perform quality control of the inversion results. Without constraining with well, geostatistical inversion still can be used to estimate acceptable static reservoir model for the subsequent simulation and planning of in-fill drilling and/or enhanced-oil-recovery operations.

Detailed seismic lithofluid distribution using Bayesian stochastic inversion for a thinly bedded reservoir: A case study over Huntington UK Central North Sea

A geostatistical inversion scheme was designed and performed for reservoir characterization of the UK Central North Sea (CNS) Huntington Oil field, with the goal of increasing the resolution of the seismic inversion and derived attributes, and to provide statistical measures of the uncertainties involved in the seismic facies prediction. The aim of the study was to fully understand lithology and pore-fluid rock properties in the Forties sandstone reservoir, Late Paleocene Sele Formation fan system of the UK CNS. In the Forties, multiple sand beds are separated by thin layers of silt and shale. Reprocessed prestack seismic volumes and considerable well-log data were input to an advanced stochastic simultaneous inversion method. This method combines the strengths of geostatistical inversion with sequential Gaussian simulation and Bayesian inversion. The approach allowed the inversion to be built on a fine-scale stratigraphic grid at a reservoir scale rather than at a seismic scale, and it enabled a detailed description of facies distribution and associated uncertainty. A sufficiently large number of stochastic solutions (100 realizations) enabled probabilistic models of lithofluid distribution to be generated. Facies geobody connectivity can also be derived, but this was not part of this work. As a consequence of our study, a sidetrack water injector well location was evaluated, and a potential undrilled hydrocarbon accumulation was identified, which could extend the field life of the Huntington asset.

Joint Bayesian Stochastic Inversion of Well Logs and Seismic Data for Volumetric Uncertainty Analysis

Here in, an application of a new seismic inversion algorithm in one of Iran’s oilfields is described. Stochastic (geostatistical) seismic inversion, as a complementary method to deterministic inversion, is perceived as contribution combination of geostatistics and seismic inversion algorithm. This method integrates information from different data sources with different scales, as prior information in Bayesian statistics. Data integration leads to a probability density function (named as a posteriori probability) that can yield a model of subsurface. The Markov Chain Monte Carlo (MCMC) method is used to sample the posterior probability distribution, and the subsurface model characteristics can be extracted by analyzing a set of the samples. In this study, the theory of stochastic seismic inversion in a Bayesian framework was described and applied to infer P-impedance and porosity models. The comparison between the stochastic seismic inversion and the deterministic model based seismic inversion indicates that the stochastic seismic inversion can provide more detailed information of subsurface character. Since multiple realizations are extracted by this method, an estimation of pore volume and uncertainty in the estimation were analyzed.

A box model test of the freshwater forcing hypothesis of abrupt climate change and the physics governing ocean stability

[1] Observations and an ocean box model are combined in order to test the adequacy of the freshwater forcing hypothesis to explain abrupt climate change given the uncertainties in the parameterization of vertical buoyancy transport in the ocean. The combination is carried out using Bayesian stochastic inversion, which allows us to infer changes in the mass balance of Northern Hemisphere (NH) ice sheets and in the meridional transports of mass and heat in the Atlantic Ocean that would be required to explain Dansgaard-Oeschger Interstadials (DOIs) from 30 to 39 kyr B.P. The mean sea level changes implied by changes in NH ice sheet mass balance agree in amplitude and timing with reconstructions from the geologic record, which gives some support to the freshwater forcing hypothesis. The inversion suggests that the duration of the DOIs should be directly related to the growth of land ice. Our results are unaffected by uncertainties in the representation of vertical buoyancy transport in the ocean. However, the solutions are sensitive to assumptions about physical processes at polar latitudes.

Bayesian Stochastic Inversion (A case study from an Iranian oil field)

SummaryWe have implemented an estimation procedure whereby wireline data can be extrapolated away from existing well using geostatistical inversion of post-stack 3D seismic data. This procedure works directly in a fine-scale stratigraphic grid, and is conditioned by well and seismic data. It uses a Bayesian framework and a linearized, weak contrast approximation of the Zoeppritz equation to construct a joint log-Gaussian posterior distribution for Pwave impedances. Variograms are also estimated from well-log, seismic data and acoustic inversion results that define the expected degree of lateral smoothness away from the well. A sequential Gaussian Simulation algorithm is applied to sample the posterior PDF and generates multiple, high-resolution realizations of the acoustic impedance which can be utilized to generate stochastic realizations of petrophysical variables that not only honor the well-log data, but most importantly, that fully honor the 3D seismic.Sensitivity analysis was also performed to find the optimum values for S/N ratio, Variogram ranges and prior standard deviation. We had just one well in the area and preferred to keep it to perform quality control of the inversion results. Without constraining with well, geostatistical inversion still can be used to estimate acceptable static reservoir model for the subsequent simulation and planning of in-fill drilling and/or enhanced-oil-recovery operations.

Optimization and uncertainty estimates of WMO regression models for the systematic bias adjustment of NLDAS precipitation in the United States

World Meteorological Organization (WMO) regression models for precipitation gauge bias developed by Goodison et al. (1998) were optimized using the very fast simulated annealing algorithm. The regression model uncertainties were estimated by use of a Bayesian stochastic inversion (BSI) algorithm. Legates and Willmott's (1990) precipitation correction factors database (applicable to average monthly conditions) were used to constrain model parameters. Daily wind speed, air temperature, and precipitation from the North American Land Data Assimilation System (NLDAS) were used as input for the WMO regression models in the United States. The results show that the optimal regression model is reasonably bounded by the WMO Alter‐shielded and unshielded models for both rain and snow. The optimized regression model, aside from reproducing reasonably well the Legates‐Willmott average monthly adjustment factors, also describes daily and interannual variation of precipitation correction factors. The relations among model parameters and model uncertainties, including regression parameter uncertainty and input data uncertainty, are examined. The results show strong relations between regression model uncertainties and uncertain NLDAS wind speed. Uncertainty of NLDAS data has little effect on optimization of the WMO regression model. However, it has significant effects on uncertainty of the regression model parameters and the precipitation correction factors.

Optimal parameter and uncertainty estimation of a land surface model: Sensitivity to parameter ranges and model complexities

Most previous land-surface model calibration studies have defined global ranges for their parameters to search for optimal parameter sets. Little work has been conducted to study the impacts of realistic versus global ranges as well as model complexities on the calibration and uncertainty estimates. The primary purpose of this paper is to investigate these impacts by employing Bayesian Stochastic Inversion (BSI) to the Chameleon Surface Model (CHASM). The CHASM was designed to explore the general aspects of land-surface energy balance representation within a common modeling framework that can be run from a simple energy balance formulation to a complex mosaic type structure. The BSI is an uncertainty estimation technique based on Bayes theorem, importance sampling, and very fast simulated annealing. The model forcing data and surface flux data were collected at seven sites representing a wide range of climate and vegetation conditions. For each site, four experiments were performed with simple and complex CHASM formulations as well as realistic and global parameter ranges. Twenty eight experiments were conducted and 50 000 parameter sets were used for each run. The results show that the use of global and realistic ranges gives similar simulations for both modes for most sites, but the global ranges tend to produce some unreasonable optimal parameter values. Comparison of simple and complex modes shows that the simple mode has more parameters with unreasonable optimal values. Use of parameter ranges and model complexities have significant impacts on frequency distribution of parameters, marginal posterior probability density functions, and estimates of uncertainty of simulated sensible and latent heat fluxes. Comparison between model complexity and parameter ranges shows that the former has more significant impacts on parameter and uncertainty estimations.

Multidataset Study of Optimal Parameter and Uncertainty Estimation of a Land Surface Model with Bayesian Stochastic Inversion and Multicriteria Method

Abstract This study evaluates the ability of Bayesian stochastic inversion (BSI) and multicriteria (MC) methods to search for the optimal parameter sets of the Chameleon Surface Model (CHASM) using prescribed forcing to simulate observed sensible and latent heat fluxes from seven measurement sites representative of six biomes including temperate coniferous forests, tropical forests, temperate and tropical grasslands, temperate crops, and semiarid grasslands. Calibration results with the BSI and MC show that estimated optimal values are very similar for the important parameters that are specific to the CHASM model. The model simulations based on estimated optimal parameter sets perform much better than the default parameter sets. Cross-validations for two tropical forest sites show that the calibrated parameters for one site can be transferred to another site within the same biome. The uncertainties of optimal parameters are obtained through BSI, which estimates a multidimensional posterior probability density function (PPD). Marginal PPD analyses show that nonoptimal choices of stomatal resistance would contribute most to model simulation errors at all sites, followed by ground and vegetation roughness length at six of seven sites. The impact of initial root-zone soil moisture and nonmosaic approach on estimation of optimal parameters and their uncertainties is discussed.

An Efficient Stochastic Bayesian Approach to Optimal Parameter and Uncertainty Estimation for Climate Model Predictions

Abstract One source of uncertainty for climate model predictions arises from the fact that climate models have been optimized to reproduce observational means. To quantify the uncertainty resulting from a realistic range of model configurations, it is necessary to estimate a multidimensional probability distribution that quantifies how likely different model parameter combinations are, given knowledge of the uncertainties in the observations. The computational cost of mapping a multidimensional probability distribution for a climate model using traditional means (e.g., Monte Carlo or Metropolis/Gibbs sampling) is impractical, requiring 104–106 model evaluations for problems involving less than 10 parameters. This paper examines whether such a calculation is more feasible using a particularly efficient but approximate algorithm called Bayesian stochastic inversion, based on multiple very fast simulated annealing (VFSA). Investigated here is how the number of model parameters, natural variability, and the d...

Impacts of data length on optimal parameter and uncertainty estimation of a land surface model

The optimal parameters and uncertainty estimation of land surface models require that appropriate length of forcing and calibration data be selected for computing error functions. Most of the previous studies used less than two years of data to optimize land surface models. In this study, 18‐year hydrometeorological data at Valdai, Russia, were used to run the Chameleon Surface Model (CHASM). The optimal parameters were obtained by employing a global optimization technique called very fast simulated annealing. The uncertainties of model parameters were estimated by the Bayesian stochastic inversion technique. Forty‐four experiments were conducted by using different lengths of data from the 18‐year record, and a total of about 3 million parameter sets were produced. This study found that different calibration variables require different lengths of data to obtain optimal parameters and uncertainty estimates which are insensitive to the period selected. In the case of optimal parameters, monthly root‐zone soil moisture, runoff, and evapotranspiration require 8, 3, and 1 years of data, respectively. In the case of uncertainty estimates, monthly root‐zone soil moisture, runoff, and evapotranspiration require 8, 8, and 3 years of data, respectively. Spin‐up has little impact on the selection of optimal parameters and uncertainty estimates when evapotranspiration and runoff were calibrated. However, spin‐up affects the selection of optimal parameters when soil moisture was calibrated.

Optimal parameter and uncertainty estimation of a land surface model: A case study using data from Cabauw, Netherlands

Land surface models involve a large number of interdependent parameters that affect the physics of how surface energy fluxes are partitioned between latent heat, sensible heat, net radiative, and ground heat fluxes. The goal of an optimal parameter and uncertainty analysis of a land surface model is to identify a range of parameter sets that enable model predictions to be bounded within observational uncertainties. Here we apply Bayesian stochastic inversion (BSI) using very fast simulated annealing (VFSA) to identify parameter sets of the Chameleon surface model (CHASM) land surface model that are consistent with the uncertainty limits ascribed to a high‐quality data set collected from Cabauw, Netherlands. These results are compared to the parameter sets obtained through the multicriteria (MC) approach. All analyses evaluate model performance against daily and monthly mean observations of sensible, latent, and ground heat fluxes. BSI and MC identify similar “best fit” model parameter sets that improve CHASM performance over default parameter settings. The three most important CHASM parameters at Cabauw are minimum stomatal resistance, vegetation roughness length, and vegetation fraction cover. BSI is based on a Bayesian inference model such that that it expresses uncertainty in terms of a posterior probability density function, different moments of which provide information about parameter means and covariances. Although MC gives a range of possible optimal parameters through the concept of a Pareto set, we found that these ranges did not provide a consistent or representative view of the uncertainty within the observational data. The BSI algorithm in the current study is particularly efficient in that it only requires about double the number of model evaluations than the MC algorithm. This is a substantial saving over other more accurate methods to evaluate uncertainty such as the Metropolis/Gibbs' sampler that requires at least 40 times more computations than the BSI algorithm to obtain similar results.