Bayesian Monte Carlo method for seismic predrill prospect assessment

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. O9-O19 ◽  
Author(s):  
Heidi Kjønsberg ◽  
Ragnar Hauge ◽  
Odd Kolbjørnsen ◽  
Arild Buland

Predrill assessment of the probability that a potential drilling spot holds hydrocarbons (HC) is of vital importance to any oil company. Of equally great value is the assessment of hydrocarbon volumes and distributions. We have developed a methodology that uses seismic data to find the probability that a vertical earth profile contains hydrocarbons and the probability distribution of hydrocarbon volumes. The method combines linearized amplitude variation with offset (AVO) inversion and stochastic rock models and predicts the joint probability distribution of the combined lithology and fluid for the entire profile. We use a Bayesian approach and find the solution of the inverse problem by Markov chain Monte Carlo simulation. The stochastic simulation benefits from a new and tailored simulation algorithm. The computational cost of finding the full joint probability distribution is relatively high and implies that the method is best suited to the investigation of a few potential drilling spots. We applied the method to a case with well control and to two locations in a prospect: one in the center and one at the outskirts. At the well location, we identify the two reservoir zones and obtain volumes that fit the log data. At the prospect, we obtain significant increases in HC probability and volume in the center, whereas there are decreases at the outskirts. Despite the large noise components in the data, the risked volumes in the center changed by a factor of three. We have designed an algorithm for computing the joint distribution of lithology, fluid, and elastic parameters for a full vertical profile. As opposed to what can be done with pointwise approaches, this allows us to calculate success probability and HC volumes.

1990 ◽  
Vol 112 (1) ◽  
pp. 96-101
Author(s):  
A. B. Dunwoody

The risk of impact by a particular ice feature in the vicinity of an offshore structure or stationary vessel is of concern during operations. A general method is presented for calculating the risk of an impact in terms of the joint probability distribution of the forecast positions and velocities of the ice feature. A simple stochastic model of the motion of an ice feature is introduced for which the joint probability distribution of ice feature position and velocity can be determined as a function of time. The risk of an impact is presented for this model of the motion of an ice feature. Predictions of the distributions of the time until impact and the drift speed upon impact are also presented and discussed. Predictions are compared against results of a Monte Carlo simulation.


2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Huilin Huang

We consider an inhomogeneous growing network with two types of vertices. The degree sequences of two different types of vertices are investigated, respectively. We not only prove that the asymptotical degree distribution of typesfor this process is power law with exponent2+1+δqs+β1-qs/αqs, but also give the strong law of large numbers for degree sequences of two different types of vertices by using a different method instead of Azuma’s inequality. Then we determine asymptotically the joint probability distribution of degree for pairs of adjacent vertices with the same type and with different types, respectively.


Author(s):  
Reza Seifi Majdar ◽  
Hassan Ghassemian

Unlabeled samples and transformation matrix are two main parts of unsupervised and semi-supervised feature extraction (FE) algorithms. In this manuscript, a semi-supervised FE method, locality preserving projection in the probabilistic framework (LPPPF), to find a sufficient number of reliable and unmixed unlabeled samples from all classes and constructing an optimal projection matrix is proposed. The LPPPF has two main steps. In the first step, a number of reliable unlabeled samples are selected based on the training samples, spectral features, and spatial information in the probabilistic framework. In this way, the spectral and spatial probability distribution function is calculated for each unlabeled sample. Therefore, the spectral features and spatial information are integrated together with a joint probability distribution function. Finally, a sufficient number of unlabeled samples with the highest joint probability distribution are selected. In the second step, the selected unlabeled samples are applied to construct the transformation matrix based on the spectral and spatial information of the unlabeled samples. The adjacency graph is improved by using new weights based on spectral and spatial information. This method is evaluated on three data sets: Indian Pines, Pavia University, and Kennedy Space Center (KSC) and compared with some recent and well-known supervised, semi-supervised, and unsupervised FE methods. Various experiments demonstrate the efficiency of the LPPPF in comparison with the other FE methods. LPPPF has also considerable performance with limited training samples.


In this chapter, a fuzzy goal programming (FGP) model is employed for solving multi-objective linear programming (MOLP) problem under fuzzy stochastic uncertain environment in which the probabilistic constraints involves fuzzy random variables (FRVs) following joint probability distribution. In the preceding chapters, the authors explain about linear, fractional, quadratic programming models with multiple conflicting objectives under fuzzy stochastic environment. But the chance constraints in these chapters are considered independently. However, in practical situations, the decision makers (DMs) face various uncertainties where the chance constraints occur jointly. By considering the above fact, the authors presented a solution methodology for fuzzy stochastic MOLP (FSMOLP) with joint probabilistic constraint following some continuous probability distributions. Like the other chapters, chance constrained programming (CCP) methodology is adopted for handling probabilistic constraints. But the difference is that in the earlier chapters chance constraints are considered independently, whereas in this chapter all the chance constraints are taken jointly. Then the transformed problem involving possibilistic uncertainty is converted into a comparable deterministic problem by using the method of defuzzification of the fuzzy numbers (FNs). Objectives are now solved independently under the set of modified system constraints to obtain the best solution of each objective. Then the membership function for each objective is constructed, and finally, a fuzzy goal programming (FGP) model is developed for the achievement of the highest membership goals to the extent possible by minimizing group regrets in the decision-making context.


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