Over the last 20 years, multiple-point statistics (MPS) became a very active field of research for stochastic reservoir modeling (see for example the special issues on MPS published in Mathematical Geoscienecs in 2015).
The aim of this course is to enable users to understand and use the full power of Multiple Point Statistics method.
The main strength of MPS techniques is that they allow the user to incorporate rather precisely a conceptual model within a stochastic simulation framework. The conceptual model can be based on very general geological knowledge, or it can also be based on pre- existing large datasets typically from analog situations allowing to infer high order statistics. MPS methods are particularly well suited for geological modeling when connectivity patterns are expected to play a key role. MPS can simulate both facies or continuous properties such as permeability or porosity.
The course will include the basic theoretical knowledge required to understand how the methods work and practical exercises based essentially on the use of the Direct Sampling algorithm (available as an SGEMS plugin). As compared to other MPS methods, the Direct Sampling allows simulating multivariate data sets, continuous and categorical variables, and account for non stationarity both in the training data as well as in the simulation.
Participants are expected to have some background knowledge on statistics and its application in geology or hydrology. No pre-requisite is expected in geostatistics or reservoir modeling.
Students will be awarded 4 ECTS for participation in the course.
Lecturers
Philippe Renard and Grégoire Mariethoz have been working on the development of MPS techniques during the last 10 years. They were involved in the development of several different pixel based or patch algorithms including IMPALA, DEESSE, RPA, etc. They applied those methods to a variety of field of applications including geological modeling, simulation of rainfall, climatic variables, hyperspectral imaging, etc.
Location
Department of Geosciences and Natural Resource Management, University of Copenhagen, Øster Voldgade 10, 1350 Copenhagen K.
The course will start every morning at 9 am and end around 5 pm every day.
Morning. General introduction:
Afternoon. Practical session using SGeMS:
Day 2.
Morning. Non stationarity:
Day 3.
Morning. Advanced possibilities and applications offered by DeeSse
Direct Sampling in the continuous case
Extension to multivariate problems
Handling non stationarity in the training image (e.g. analog data, outcrop scan, or previous model)
Conditioning continuous MPS simulations with averaged block data (ex. tomography)
Time series simulation and filtering
Using a non stationary training image
Reconstruction of incomplete data sets
Multivariate data sets and alternative applications (remote sensing, climate data)
A short introduction to Conditional Image Quilting
Day 4.
Morning. Synthesis of the first 3 days: the overall MPS workflow
Late morning + early afternoon. Practical session using SGeMS:
Afternoon. Closing:
Course fee
The course is free of charge for national and international PhD students.
Participants are requested to secure funding for their own travel, accommodation and meals.
Registration
Please use this link http://www.hobecenter.dk/index.php/registration/meetings/introduction-to-the-theory-and-practice-of-multiple-point-statistics
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