?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F185%2F&rft.title=Inversion+of+2D+NMR+Data&rft.creator=Bose%2C+Christopher&rft.subject=Energy+and+utilities&rft.description=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%2C+well-logging+and+reservoir+optimization.+The+problem+described+in+this+report+is+related+to+well-logging+via+Nuclear+Magnetic+Resonance+(NMR)%2C+a+relatively+new+and+developing+tool+with+potential+to+reveal+a+range+of+reservoir+properties+including+porosity+and+saturation%2C+as+well+as+physical+properties+of+the+petroleum+deposit.%0A%0AIn+order+to+recover+this+information+from+NMR+spectra+the+company+must+have+an+effective%2C+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+%E2%80%98off-the-shelf%E2%80%99+solution+which+the+company+can+apply+to+its+problem.+Company+scientists+have+developed+a+sophisticated+algorithm+which++performs+well+on+some+simple+test+datasets%2C+but+they+are+interested+in+knowing+if+there+are+simpler+approaches+which+could+work+effectively%2C+or+if+some+limited+but+useful+properties+of+the+density+are+accessible+with+a+totally+different+approach.%0A%0AOur+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+%E2%80%98off-the-shelf%E2%80%99+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%E2%80%99s+existing+algorithm%2C+answering+one+specific+question+raised+at+the+beginning+of+the+workshop.+Finally%2C+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.&rft.date=2003&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F185%2F1%2Fschlumberger.pdf&rft.identifier=++Bose%2C+Christopher++(2003)+Inversion+of+2D+NMR+Data.++%5BStudy+Group+Report%5D+++++