Descripción
|
|
---|---|
In this paper, we present a methodology to perform geophysical inversion of large- scale linear systems via a covariance-free orthogonal transformation: the discrete cosine transform. The methodology consists of compressing the matrix of the linear system as a digital image and using the interesting properties of orthogonal trans- formations to define an approximation of the Moore?Penrose pseudo-inverse. This methodology is also highly scalable since the model reduction achieved by these tech- niques increases with the number of parameters of the linear system involved due to the high correlation needed for these parameters to accomplish very detailed forward predictions and allows for a very fast computation of the inverse problem solution. We show the application of this methodology to a simple synthetic two-dimensional gravimetric problem for different dimensionalities and different levels of white Gaus- sian noise and to a synthetic linear system whose system matrix has been generated via geostatistical simulation to produce a random field with a given spatial correla- tion. The numerical results show that the discrete cosine transform pseudo-inverse outperforms the classical least-squares techniques, mainly in the presence of noise, since the solutions that are obtained are more stable and fit the observed data with the lowest root-mean-square error. Besides, we show that model reduction is a very effective way of parameter regularisation when the conditioning of the reduced dis- crete cosine transform matrix is taken into account. We finally show its application to the inversion of a real gravity profile in the Atacama Desert (north Chile) ob- taining very successful results in this non-linear inverse problem. The methodology presented here has a general character and can be applied to solve any linear and non-linear inverse problems (through linearisation) arising in technology and, par- ticularly, in geophysics, independently of the geophysical model discretisation and dimensionality. Nevertheless, the results shown in this paper are better in the case of ill-conditioned inverse problems for which the matrix compression is more efficient. In that sense, a natural extension of this methodology would be its application to the set of normal equations. | |
Internacional
|
Si |
JCR del ISI
|
Si |
Título de la revista
|
Geophysical Prospecting |
ISSN
|
1365-2478 |
Factor de impacto JCR
|
1,846 |
Información de impacto
|
|
Volumen
|
65 |
DOI
|
10.1111/1365-2478.12548 |
Número de revista
|
S1 |
Desde la página
|
94 |
Hasta la página
|
111 |
Mes
|
DICIEMBRE |
Ranking
|