?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%2F543%2F&rft.title=Inversion+for+Anisotropic+Velocity+Parameter&rft.creator=Lamoureux%2C+M.&rft.subject=Energy+and+utilities&rft.subject=Materials&rft.description=The+problem+under+study+concerns+the+robust+computation+of+a+certain+parameter+of+anisotropy+from+observed+travel-times+of+a+seismic+shear+wave+propagating+through+a+geological+medium.%0D%0A%0D%0AWe+have+obtained+an+exact+mathematical+description+of+a+geoseismic+signal+propagating+through+an+anisotropic+medium+using+a+constant+coefficient+wave+equation+as+the+basic+model.+This+model+captures+exactly+the+elliptical+velocity+profile+required+in+the+formulation+of+the+geophysical+model+from+which+we+obtained+exact+formulas+describing+the+travel-time+through+a+two+layer+geological+structure%2C+and+an+exact+inversion+formula+for+computing+the+anisotropic+velocity+parameter+(gamma).+A+robust+numerical+method+based+on+a+minimization+technique+was+presented+as+an+accurate+method+of+computing+both+travel-time+and+the+inverted+gamma.%0D%0A%0D%0AThe+exact+formulas+and+robust+numerical+methods+are+significant+improvements+over+the+approximations+and+root+finding+methods+discussed+in+the+background+material%2C+and+we+note+our+formulation+is+no+more+difficult+than+these+background+methods.%0D%0A%0D%0AWe+derived+asymptotic+formulas+valid+for+the+near+vertical+case%2C+which+describe+accurately+the+high+sensitivity+of+gamma+to+the+input+parameters+in+this+case.+Our+numerical+work+also+confirms+this+sensitivity%2C+even+using+exact+formulas+and+robust+numerical+methods.%0D%0A%0D%0AWe+conclude+that+the+computation+of+the+anisotropic+velocity+parameter+(gamma)+for+the+given+physical+measurements+from+a+series+of+surface+signals+and+single+borehole+receiver+is+intrinsically+unstable.+By+changing+to+the+alpha%2Cbeta+velocity+parameter+space%2C+we+obtain+an+inversion+method+that+is+much+less+sensitive+to+input+errors.+For+certain+geophysical+problems%2C+the+alpha%2Cbeta+parameters+may+suffice+for+an+accurate+description+of+the+material.%0D%0A%0D%0AWhen+the+anisotropic+velocity+parameter+(gamma)+is+needed+directly%2C+a+different+measurement+technique+is+required.+This+route+will+require+further+investigation%2C+and+we+have+proposed+a+number+of+promising+possibilities+involving+a+differential+time+measure.&rft.date=1997&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%2F543%2F1%2FInversion-for-anisotropic-velocity-parameter.pdf&rft.identifier=++Lamoureux%2C+M.++(1997)+Inversion+for+Anisotropic+Velocity+Parameter.++%5BStudy+Group+Report%5D+++++