Abstract
The problem of determining capillary pressure functions from centrifuge data leads to an integral equation of the form
∫ a x K(x,t)f(t) dt=g(x),x∈[a,b],(1)
where the kernel K is known exactly and given by the underlying mathematical model. g is only known with a limited degree of accuracy in a finite and discrete set of points x 1,...,x M . However, the sought function f(t) is continuous. By the nature of the right-hand side, g(x), equation (1) is a discrete inverse problem which is ill-posed in the sense of Hadamard [9]. By a parameterization of the sought function, equation (1) reduces to a system of linear equations of the form
Ac=b+ ε,
where b is the observation vector and A arises from discretization of the forward problem. ε is the error vector associated with b, and c contains the model parameters. The matrix A is usually ill-conditioned. The ill-conditioning is closely connected to the parameterization of the problem [23].
In this paper a semi-iterative regularization method for solving the Volterra integral equation in the ℓ2-norm, namely, Brakhage's ν-method [2], is investigated. The iterative method is tested on synthetically generated, and on experimental data.
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Subbey, S., Nordtvedt, JE. Capillary Pressure Curves from Centrifuge Data: A Semi-Iterative Approach. Computational Geosciences 6, 207–224 (2002). https://doi.org/10.1023/A:1019943419164
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DOI: https://doi.org/10.1023/A:1019943419164