Joint interpretation and uncertainty analysis of petrophysical properties in unconventional shale reservoirs

2015 ◽  
Vol 3 (1) ◽  
pp. SA33-SA49 ◽  
Author(s):  
Qinshan Yang ◽  
Carlos Torres-Verdín
Keyword(s):  
Joint Inversion ◽  
A Priori ◽  
Estimation Method ◽  
Monte Carlo Algorithm ◽  
Posteriori Probability ◽  
Inversion Method ◽  
A Posteriori ◽  
A Priori Information ◽  
Core Data ◽  
Priori Information

Interpretation of hydrocarbon-bearing shale is subject to great uncertainty because of pervasive heterogeneity, thin beds, and incomplete and uncertain knowledge of saturation-porosity-resistivity models. We developed a stochastic joint-inversion method specifically developed to address the quantitative petrophysical interpretation of hydrocarbon-bearing shale. The method was based on the rapid and interactive numerical simulation of resistivity and nuclear logs. Instead of property values themselves, the estimation method delivered the a posteriori probability of each property. The Markov-chain Monte Carlo algorithm was used to sample the model space to quantify the a posteriori distribution of formation properties. Additionally, the new interpretation method allows the use of fit-for-purpose statistical correlations between water saturation, salt concentration, porosity, and electrical resistivity to implement uncertain, non-Archie resistivity models derived from core data, including those affected by total organic carbon (TOC). In the case of underdetermined estimation problems, i.e., when the number of measurements was lower than the number of unknowns, the use of a priori information enabled plausible results within prespecified petrophysical and compositional bounds. The developed stochastic interpretation technique was successfully verified with data acquired in the Barnett and Haynesville Shales. Core data (including X-ray diffraction data) were combined into a priori information for interpretation of nuclear and resistivity logs. Results consisted of mineral concentrations, TOC, and porosity together with their uncertainty. Eighty percent of the core data was located within the 95% credible interval of estimated mineral/fluid concentrations.

scholarly journals Statistical Ranging of Orbits for Trans-Neptunian Objects

2002 ◽  
Vol 12 ◽  
pp. 255-256 ◽  
Author(s):  
J. Virtanen ◽  
K. Muinonen ◽  
E. Bowell
Keyword(s):  
Phase Space ◽  
A Priori ◽  
Posteriori Probability ◽  
A Posteriori ◽  
A Priori Information ◽  
A Posteriori Probability ◽  
Uncertainty Prediction ◽  
Absolute Magnitudes ◽  
Priori Information

AbstractWe consider initial determination of orbits for trans-neptunian objects (TNOs), a topical theme because of the rapidly growing TNO population and the challenges in recovering lost TNOs. We apply the method of initial phase-space ranging of orbits to the poorly observed TNOs. The rigorous a posteriori probability density of the TNO orbital elements is examined using a Monte Carlo technique by varying the TNO topocentric ranges corresponding to the observation dates. We can optionally adopt a Bayesian approach to select the region of phase space containing the most plausible orbits. This is accomplished by incorporating semimajor axes, eccentricities, inclinations, and absolute magnitudes of multi-apparition TNOs as a priori information. The resulting a posteriori distributions permit ephemeris and ephemeris uncertainty prediction for TNO recovery observations.

scholarly journals Ozone profile smoothness as a priori information in the inversion of limb measurements

2004 ◽  
Vol 22 (10) ◽  
pp. 3411-3420 ◽  
Author(s):  
V. F. Sofieva ◽  
J. Tamminen ◽  
H. Haario ◽  
E. Kyrölä ◽  
M. Lehtinen
Keyword(s):  
A Priori ◽  
Optimal Estimation ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
A Priori Information ◽  
Ozone Profile ◽  
Stellar Occultation ◽  
Atmospheric Profiles ◽  
Priori Information ◽  
Typical Measurement

Abstract. In this work we discuss inclusion of a priori information about the smoothness of atmospheric profiles in inversion algorithms. The smoothness requirement can be formulated in the form of Tikhonov-type regularization, where the smoothness of atmospheric profiles is considered as a constraint or in the form of Bayesian optimal estimation (maximum a posteriori method, MAP), where the smoothness of profiles can be included as a priori information. We develop further two recently proposed retrieval methods. One of them - Tikhonov-type regularization according to the target resolution - develops the classical Tikhonov regularization. The second method - maximum a posteriori method with smoothness a priori - effectively combines the ideas of the classical MAP method and Tikhonov-type regularization. We discuss a grid-independent formulation for the proposed inversion methods, thus isolating the choice of calculation grid from the question of how strong the smoothing should be. The discussed approaches are applied to the problem of ozone profile retrieval from stellar occultation measurements by the GOMOS instrument on board the Envisat satellite. Realistic simulations for the typical measurement conditions with smoothness a priori information created from 10-years analysis of ozone sounding at Sodankylä and analysis of the total retrieval error illustrate the advantages of the proposed methods. The proposed methods are equally applicable to other profile retrieval problems from remote sensing measurements.

scholarly journals A practical information-centered technique to remove a priori information from lidar optimal-estimation-method retrievals

2019 ◽  
Vol 12 (7) ◽  
pp. 3943-3961 ◽  
Author(s):  
Ali Jalali ◽  
Shannon Hicks-Jalali ◽  
Robert J. Sica ◽  
Alexander Haefele ◽  
Thomas von Clarmann
Keyword(s):  
Water Vapor ◽  
A Priori ◽  
Estimation Method ◽  
Optimal Estimation ◽  
Mixing Ratio ◽  
A Priori Information ◽  
Fine Grid ◽  
Large Power ◽  
Priori Information ◽  
Water Vapor Mixing Ratio

Abstract. Lidar retrievals of atmospheric temperature and water vapor mixing ratio profiles using the optimal estimation method (OEM) typically use a retrieval grid with a number of points larger than the number of pieces of independent information obtainable from the measurements. Consequently, retrieved geophysical quantities contain some information from their respective a priori values or profiles, which can affect the results in the higher altitudes of the temperature and water vapor profiles due to decreasing signal-to-noise ratios. The extent of this influence can be estimated using the retrieval's averaging kernels. The removal of formal a priori information from the retrieved profiles in the regions of prevailing a priori effects is desirable, particularly when these greatest heights are of interest for scientific studies. We demonstrate here that removal of a priori information from OEM retrievals is possible by repeating the retrieval on a coarser grid where the retrieval is stable even without the use of formal prior information. The averaging kernels of the fine-grid OEM retrieval are used to optimize the coarse retrieval grid. We demonstrate the adequacy of this method for the case of a large power-aperture Rayleigh scatter lidar nighttime temperature retrieval and for a Raman scatter lidar water vapor mixing ratio retrieval during both day and night.

Three‐dimensional gravity inversion using simulated annealing: Constraints on the diapiric roots of allochthonous salt structures

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1438-1449 ◽  
Author(s):  
Seiichi Nagihara ◽  
Stuart A. Hall
Keyword(s):  
Simulated Annealing ◽  
Gulf Of Mexico ◽  
Gravity Data ◽  
A Priori ◽  
Gravity Inversion ◽  
Inversion Method ◽  
A Priori Information ◽  
Final Density ◽  
Smoothing Effects ◽  
Priori Information

In the northern continental slope of the Gulf of Mexico, large oil and gas reservoirs are often found beneath sheetlike, allochthonous salt structures that are laterally extensive. Some of these salt structures retain their diapiric feeders or roots beneath them. These hidden roots are difficult to image seismically. In this study, we develop a method to locate and constrain the geometry of such roots through 3‐D inverse modeling of the gravity anomalies observed over the salt structures. This inversion method utilizes a priori information such as the upper surface topography of the salt, which can be delineated by a limited coverage of 2‐D seismic data; the sediment compaction curve in the region; and the continuity of the salt body. The inversion computation is based on the simulated annealing (SA) global optimization algorithm. The SA‐based gravity inversion has some advantages over the approach based on damped least‐squares inversion. It is computationally efficient, can solve underdetermined inverse problems, can more easily implement complex a priori information, and does not introduce smoothing effects in the final density structure model. We test this inversion method using synthetic gravity data for a type of salt geometry that is common among the allochthonous salt structures in the Gulf of Mexico and show that it is highly effective in constraining the diapiric root. We also show that carrying out multiple inversion runs helps reduce the uncertainty in the final density model.

scholarly journals Effects of <i>a priori</i> profile shape assumptions oncomparisons between satellite NO<sub>2</sub> columns and model simulations

2020 ◽  
Author(s):  
Matthew J. Cooper ◽  
Randall V. Martin ◽  
Daven K. Henze ◽  
Dylan B. A. Jones
Keyword(s):  
Shape Factor ◽  
A Priori ◽  
Trace Gas ◽  
A Posteriori ◽  
A Priori Information ◽  
Profile Shape ◽  
Satellite Retrievals ◽  
Mass Factor ◽  
The Difference ◽  
Priori Information

Abstract. A critical step in satellite retrievals of trace gas columns is the calculation of the air mass factor (AMF) used to convert observed slant columns to vertical columns. This calculation requires a priori information on the shape of the vertical profile. As a result, comparisons between satellite-retrieved and model-simulated column abundances are influenced by the a priori profile shape. We examine how differences between the shape of the simulated and a priori profile can impact the interpretation of satellite retrievals by performing an adjoint-based 4D-Var assimilation of synthetic NO2 observations for constraining NOx emissions. We use the GEOS-Chem Adjoint model to perform assimilations using a variety of AMFs to examine how a posteriori emission estimates are affected if the AMF is calculated using an a priori shape factor that is inconsistent with the simulated profile. In these tests, an inconsistent a priori shape factor increased errors in a posteriori emissions estimates by up to 80 % over polluted regions. As the difference between the simulated profile shape and the a priori profile shape increases, so do the corresponding assimilated emission errors. This reveals the importance of using simulated profile information for AMF calculations when comparing that simulated output to satellite retrieved columns.

scholarly journals Detection of Jumps Parameters in Economic Processes(the Case of Modelling Profitability)

2018 ◽  
Vol 7 (4.3) ◽  
pp. 488 ◽  
Author(s):  
O. V. Poliarus ◽  
Y. O. Poliakov ◽  
I. L. Nazarenko ◽  
Y. T. Borovyk ◽  
M. V. Kondratiuk
Keyword(s):  
A Priori ◽  
Machine Building ◽  
Building Industry ◽  
A Posteriori ◽  
A Priori Information ◽  
Parameter Change ◽  
Economic Process ◽  
Intense Noise ◽  
Priori Information ◽  
Economic Nature

A new method of parameters jumps detection in economic processes is presented. A jump of the economic process parameter must be understood as a rapid parameter change for a time that does not exceed the period of process registration.  A system of stochastic differential equations for a posteriori density probability of a jump is synthesized. The solution of the system is the probability of a parameter jump, the estimation and variance of the jump in the presence of a priori information under conditions of noise influence. The simulation results are conducted for profitability of machine building industry of Kharkiv region, Ukraine. The system provides detection of jump parameters, even in conditions of intense noise of economic nature. To increase the probability of finding jumps it is necessary to have a priori information.  

scholarly journals Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. H19-H31 ◽  
Author(s):  
Knud Skou Cordua ◽  
Thomas Mejer Hansen ◽  
Klaus Mosegaard
Keyword(s):  
Inverse Problem ◽  
Monte Carlo ◽  
A Priori ◽  
Waveform Inversion ◽  
Multiple Point ◽  
Full Waveform Inversion ◽  
A Posteriori ◽  
A Priori Information ◽  
Full Waveform ◽  
Priori Information

We present a general Monte Carlo full-waveform inversion strategy that integrates a priori information described by geostatistical algorithms with Bayesian inverse problem theory. The extended Metropolis algorithm can be used to sample the a posteriori probability density of highly nonlinear inverse problems, such as full-waveform inversion. Sequential Gibbs sampling is a method that allows efficient sampling of a priori probability densities described by geostatistical algorithms based on either two-point (e.g., Gaussian) or multiple-point statistics. We outline the theoretical framework for a full-waveform inversion strategy that integrates the extended Metropolis algorithm with sequential Gibbs sampling such that arbitrary complex geostatistically defined a priori information can be included. At the same time we show how temporally and/or spatiallycorrelated data uncertainties can be taken into account during the inversion. The suggested inversion strategy is tested on synthetic tomographic crosshole ground-penetrating radar full-waveform data using multiple-point-based a priori information. This is, to our knowledge, the first example of obtaining a posteriori realizations of a full-waveform inverse problem. Benefits of the proposed methodology compared with deterministic inversion approaches include: (1) The a posteriori model variability reflects the states of information provided by the data uncertainties and a priori information, which provides a means of obtaining resolution analysis. (2) Based on a posteriori realizations, complicated statistical questions can be answered, such as the probability of connectivity across a layer. (3) Complex a priori information can be included through geostatistical algorithms. These benefits, however, require more computing resources than traditional methods do. Moreover, an adequate knowledge of data uncertainties and a priori information is required to obtain meaningful uncertainty estimates. The latter may be a key challenge when considering field experiments, which will not be addressed here.

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