### Abstract

The problem of determining capillary pressure functions from centrifuge data leads to an integral equation of the form ?^{x}_{a} K (x.t) f(t)dt = g(x). x ? [a.b]. 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 + e. where b is the observation vector and A arises from discretization of the forward problem. e 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 e_{2}-norm, namely, Brakhage's v-method [2], is investigated. The iterative method is tested on synthetically generated, and on experimental data.

Original language | English |
---|---|

Pages (from-to) | 207-224 |

Number of pages | 18 |

Journal | Computational Geosciences |

Volume | 6 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2002 |

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### Keywords

- Capillary pressure
- Ill-posed
- Inverse
- Regularization
- Semi-iterative

### Cite this

*Computational Geosciences*,

*6*(2), 207-224. https://doi.org/10.1023/A:1019943419164

}

*Computational Geosciences*, vol. 6, no. 2, pp. 207-224. https://doi.org/10.1023/A:1019943419164

**Capillary pressure curves from centrifuge data : A semi-iterative approach.** / Subbey, S.; Nordtvedt, J. E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Capillary pressure curves from centrifuge data

T2 - A semi-iterative approach

AU - Subbey, S.

AU - Nordtvedt, J. E.

PY - 2002/6

Y1 - 2002/6

N2 - The problem of determining capillary pressure functions from centrifuge data leads to an integral equation of the form ?xa K (x.t) f(t)dt = g(x). x ? [a.b]. 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 x1.....XM. 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 + e. where b is the observation vector and A arises from discretization of the forward problem. e 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 e2-norm, namely, Brakhage's v-method [2], is investigated. The iterative method is tested on synthetically generated, and on experimental data.

AB - The problem of determining capillary pressure functions from centrifuge data leads to an integral equation of the form ?xa K (x.t) f(t)dt = g(x). x ? [a.b]. 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 x1.....XM. 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 + e. where b is the observation vector and A arises from discretization of the forward problem. e 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 e2-norm, namely, Brakhage's v-method [2], is investigated. The iterative method is tested on synthetically generated, and on experimental data.

KW - Capillary pressure

KW - Ill-posed

KW - Inverse

KW - Regularization

KW - Semi-iterative

UR - http://www.scopus.com/inward/record.url?scp=0036379362&partnerID=8YFLogxK

U2 - 10.1023/A:1019943419164

DO - 10.1023/A:1019943419164

M3 - Article

VL - 6

SP - 207

EP - 224

JO - Computational Geosciences

JF - Computational Geosciences

SN - 1420-0597

IS - 2

ER -