eprintid: 185
rev_number: 4
eprint_status: archive
userid: 6
dir: disk0/00/00/01/85
datestamp: 2008-10-31
lastmod: 2015-05-29 19:48:56
status_changed: 2009-04-08 16:55:31
type: report
metadata_visibility: show
item_issues_count: 0
creators_name: Bose, Christopher
contributors_name: Cui, Zhenlu
contributors_name: Deng, Xinghua
contributors_name: Han, Ying
contributors_name: Li, Qingguo
contributors_name: Piché, Robert
contributors_name: Venkataramanan, Lalitha
contributors_name: Wang, Qian
contributors_name: Zhou, Lin
title: Inversion of 2D NMR Data
ispublished: pub
subjects: utilities
studygroups: ipsw7
companyname: Schlumberger Limited
full_text_status: public
abstract: Schlumberger Limited is a multinational company supplying oilfield and  nformation services to a worldwide energy market. These services include both exploration and production tools ranging through seismic and remote sensing, well-logging and reservoir optimization. The problem described in this report is related to well-logging via Nuclear Magnetic Resonance (NMR), a relatively new and developing tool with potential to reveal a range of reservoir properties including porosity and saturation, as well as physical properties of the petroleum deposit.

In order to recover this information from NMR spectra the company must have an effective, efficient and robust algorithm to perform inversion from the dataset to the unknown probability distribution on magnetic relaxation times. This ill-posed problem is encountered in diverse areas of magnetic imaging and there does not appear to be an ‘off-the-shelf’ solution which the company can apply to its problem. Company scientists have developed a sophisticated algorithm which  performs well on some simple test datasets, but they are interested in knowing if there are simpler approaches which could work effectively, or if some limited but useful properties of the density are accessible with a totally different approach.

Our report is organised as follows. In Section 1.2 we present a careful and complete description of the problem and the work already done by the company. In Section 1.3 we discuss Truncated Singular Value Regularisation and Tikhonov Regularisation and show how some ‘off-the-shelf’ Matlab code may be used to good effect on the test datasets provided by the company. In Section 1.4 we show that one can incorporate higher order regularisation into the company’s existing algorithm, answering one specific question raised at the beginning of the workshop. Finally, in Section 1.5 we record our unsuccessful attempt to establish an iterative algorithm for the positively constrained inversion. Finally in the last section we review our conclusions and make suggestions for future work.
problem_statement: Schlumberger is interested in using Nuclear Magnetic Resonance (NMR) analysis for exploration in the oil and gas industry. The model problem presented to our group at the workshop involved the recovery of a two-dimensional probability distribution $f(x,y)$ on magnetic field relaxation times in two directions, $x$, the so-called longitudinal relaxation time and $y$, the transverse relaxation time.
date: 2003
date_type: published
pages: 19
citation:   Bose, Christopher  (2003) Inversion of 2D NMR Data.  [Study Group Report]     
document_url: http://miis.maths.ox.ac.uk/miis/185/1/schlumberger.pdf