Difference between model parameter estimation and curve fitting
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Within a single well, a least-squares model such as Ø = a +bΔTsonicmay 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.