COMPARISON BETWEEN TIKHONOV REGULARIZATION AND TRUNCATED SVD IN GRAVITY DATA INVERSION

Q: How can I download an article?

To download an article from SID, first log in to the site, search for the article title, and click on the 'Download Article' option.

Q: How can I download an ISI article?

To download an ISI article on SID, enter the keyword or article title in the search bar, view the relevant results, click on the desired article, and select the 'Download Article' option.

Q: How can I access the SID database?

To access the SID database, visit SID.ir, create an account, and log in to access scientific resources.

Q: Is downloading articles from SID free?

Some articles on SID are available for free, while others require payment. Details are specified on the article's page.

ARDESTANI E.V.; VATANKHAH S.; SOLTANABADI R.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

Paper Information

Journal: Journal of the Earth and Space Physics Year:2016 | Volume:42 | Issue:3 Page(s): 523-534

Download Full-Text

Persian Verion

View:

800

Download:

Cites:

Information Journal Paper

Title

COMPARISON BETWEEN TIKHONOV REGULARIZATION AND TRUNCATED SVD IN GRAVITY DATA INVERSION

Author(s)

ARDESTANI E.V. | VATANKHAH S. | SOLTANABADI R. | Issue Writer Certificate

Keywords

GRAVIMETRYQ2

INVERSIONQ2

TIKHONOVEREGULARIZATIONQ1

TSVDQ1

REGULARIZATION PARAMETERQ1

GOTVANDQ1

Abstract

In this paper the 3D INVERSION of gravity data using two different regularization methods, namely Tikhonov regularization and truncated singular value decomposition (TSVD), is considered. The earth under the survey area is modeled using a large number of rectangular prisms, in which the size of the prisms are kept fixed during the INVERSION and the values of densities of the prisms are the model parameters to be determined. A depth weighting matrix is used to counteract the natural decay of the kernel, so the INVERSION obtains reliable information about the source distribution with respect to depth. To generate a sharp and focused model, the minimum support (MS) constraint is used, which minimizes the total area with non zero departure of the model parameters from a given a priori model. Then, the application of iteratively reweighted least square algorithm is required to deal with non-linearity introduced by MS constraint. At each iteration of the INVERSION, a priori variable weighting matrix is updated using model parameters obtained at the previous iteration. We use the singular value decomposition (SVD) for computing Tikhonov solution, which also helps us to compare the results with the solution obtained by TSVD. Thus, the algorithms presented here are suitable for small to moderate size problems, where it is feasible to compute the SVD. In Tikhonov regularization method, the optimal REGULARIZATION PARAMETER at each iteration is obtained by application of the x2 - principle parameter-choice method. The method is based on the statistical distribution of the minimum of the Tikhonov function. For weighting of the data fidelity by a known Gaussian noise distribution on the measured data and, when the regularization term is considered to be weighted by unknown inverse covariance information on the model parameters, the minimum of the Tikhonov functional becomes a random variable that follows a x2 distribution. Then, a Newton rootfinding algorithm can be used to find the REGULARIZATION PARAMETER. For truncated SVD regularization, the Picard plot is used to find a suitable value of truncation index. In math literature, a plot of singular values together with SVD and solution coefficients is often referred to as Picard plot. To test the algorithms, a density model which consists of a dipping dike embedded in a uniform half-space is used. The surface gravity anomaly produced by this model is contaminated with three different noise levels, and are used as input for introduced INVERSION algorithms. The results indicate that the algorithms are able to recover the geometry and density distribution of the original model. In general, the reconstructed model is more sparse using TSVD method as compare with Tikhonov solution. This especially happens for high noise level, where there is an important difference between two solutions. In this case, while TSVD produces a sparse model, the solution of Tikhonov regularization is not sparse. Furthermore, the number of iterations, which is required to terminate the algorithms, is more for TSVD as compare with Tikhonov method. This feature, along with automatic determination of REGULARIZATION PARAMETER, makes the implementation of the Tikhonov regularization method faster than TSVD. The INVERSION methods are used on real gravity data acquired over the GOTVAND dam site in the south-west of Iran. Tertiary deposits of the Gachsaran formation are the dominant geological structure in this area, and it is mainly comprised of marl, gypsum, anhydrite and halite.There are several solution cavities in the area so that relative negative anomalies are distinguishable in the residual map. A window of residual map consists of 640 gridded data, which includes three negative anomalies, that is selected for modeling. The reconstructed models are shown and compare with results obtained by bore holes.

Cites

No record.

References

No record.

Cite

APA: Copy

ARDESTANI, E.V., VATANKHAH, S., & SOLTANABADI, R.. (2016). COMPARISON BETWEEN TIKHONOV REGULARIZATION AND TRUNCATED SVD IN GRAVITY DATA INVERSION. JOURNAL OF THE EARTH AND SPACE PHYSICS, 42(3 ), 523-534. SID. https://sid.ir/paper/80550/en

Vancouver: Copy

ARDESTANI E.V., VATANKHAH S., SOLTANABADI R.. COMPARISON BETWEEN TIKHONOV REGULARIZATION AND TRUNCATED SVD IN GRAVITY DATA INVERSION. JOURNAL OF THE EARTH AND SPACE PHYSICS[Internet]. 2016;42(3 ):523-534. Available from: https://sid.ir/paper/80550/en

IEEE: Copy

E.V. ARDESTANI, S. VATANKHAH, and R. SOLTANABADI, “COMPARISON BETWEEN TIKHONOV REGULARIZATION AND TRUNCATED SVD IN GRAVITY DATA INVERSION,” JOURNAL OF THE EARTH AND SPACE PHYSICS, vol. 42, no. 3 , pp. 523–534, 2016, [Online]. Available: https://sid.ir/paper/80550/en

Related Journal Papers