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Difference between model parameter estimation and curve fitting
Authors:Jason E Curoe and R E Nasburg
Institution:(1) Mobil Exploration & Producing Services Inc., P.O. Box 900, 75221 Dallas, Texas, USA;(2) Texas Instruments, Dallas, Texas, USA
Abstract:Within a single well, a least-squares model such as Ø = a +bDeltaT sonic may be appropriate, insofar as random errors in core measurement and in sonic tool response are concerned. However, if several wells are in the reservoir, and if structural variation across the field exists, no single least-squares solution will adequately describe all wells with the same precision. Interpolation, via a cubic spline, is offered as an alternative to model this type of variation. However, to control both inter- and intra-well variability, a combination of least squares and interpolation is the model of choice.
Keywords:Model parameter estimation  porosity  bicubic spline  least squares
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