Effective Data Weighting and Cross-model Constraint in Time-lapse Inversion of Resistivity Monitoring Data

doi:10.12972/ksmer.2013.50.2.264

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2013 Vol.50, Issue 2 Preview Page Next Page

Research Paper

Effective Data Weighting and Cross-model Constraint in Time-lapse Inversion of Resistivity Monitoring Data 전기비저항 자료의 시간경과 역산에서 효과적 자료가중 및 교차모델 제한자: 조인기 · 하명진 · 용환호
In-Ky Cho, Myung-Jin Ha and Hwan-Ho Yong

30 April 2013. pp. 264-277

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Abstract

The resistivity method has been widely used to image the electrical properties of the subsurface. This method has become particularly suitable for monitoring because of rapid/automatic data acquisition and data communication. In this study, we proposed a new data weighting and cross-model constraint in the time-lapse inversion for the effective interpretation of long-term resistivity monitoring data. We impose a small weighting on the data with large difference between time-lapse and reference data, but a large weighting on the data with small difference. This data weighting enforces the estimated model to approach to the reference model and effectively suppresses random noise. Generally, the cross-model constraint in time-lapse inversion of long-term resistivity monitoring data has been calculated using the normalized change in physical property between time-lapse and reference model. However, the amount of normalized changes shows fairly different value with the increase or decrease of electrical conductivity. By taking the inverse of normalized change when the conductivity decreases, the same amount of change can be obtained regardless the increase or decrease of electrical conductivity. In addition, we proposed a cross-model constraint that reflects not only changes in physical property but also the resolution of model parameters. Through the numerical tests, we confirmed that this approach dramatically enhances the resolving power of time-lapse inversion, especially when the model parameter has low resolution. However, time-lapse inversion with this approach does not effectively suppress noise.

Keywords

Long-term resistivity monitoring

Time-lapse inversion

Data weighting

Cross-model constraint

전기비저항 탐사법은 지하 매질의 전기비저항 분포를 영상화하는데 널리 사용되어 왔다. 이 방법은 신속한 자동측정과 통신기술의 발달로 인하여 모니터링으로 발전하게 되었다. 본 연구에서는 장주기 전기비저항 모니터링 자료의 효과적인 시간경과 역산을 위하여 새로운 자료가중법 및 교차모델 제한자를 개발하였다. 기준자료와 시간경과 자료 사이의 변화가 큰 자료에는 낮은 가중을 가하고, 반대로 작은 자료에는 큰 가중값을 부여하였다. 이러한 자료가중법은 추정 모델을 가능하면 기준모델에 근접하도록 강요하며, 무작위 잡음을 억제하는데 효과적이다. 일반적으로 시간경과 역산에서 교차모델 제한자는 기준모델과 시간경과 모델 사이의 정규화된 변화량에 의하여 그 크기가 결정된다. 그러나 이 변화량은 전기전도도의 증감에 따라 다른 값을 보이는 문제점을 가지고 있다. 본 연구에서는 전기전도도가 감소할 경우, 변화량에 역수를 취하는 방법을 사용하여 증감에 관계없이 동일한 변화량을 나타내도록 하였다. 또한 교차모델 제한자의 계산에 변화량은 물론 모델변수의 분해능을 고려하는 방법을 제안하였다. 수치실험 결과, 이 방법은 시간경과 역산의 분해능 향상에 크게 기여하였으며, 특히 분해능이 낮은 모델변수 탐지에 효과적인 것으로 나타났다. 그러나 이 방법은 잡음에 취약한 단점을 가지고 있다.

키워드

장주기 전기비저항 모니터링

시간경과 역산

자료가중

교차모델 제한자

References

Cassiani, G., Bruno, V., Villa, A., Fusi, N. and Binley, A. M., 2006, “A saline trace test monitored via time-lapse surface electrical resistivity tomography,” J. of Applied Geophysics, Vol. 59, pp. 244-259.
Constable, S. C., Parker, R. L. and Constable, C. G., 1987, “Occam's inversion: a practical algorithm for generating smooth models from EM sounding data:,” Geophysics, Vol. 52, pp. 289-300.
Day-Lewis, F. D., Harris, J. M. and Gorelick, S. M., 2002, “Time-lapse inversion of crosswell radar data,” Geophysics, Vol. 66, pp. 1740-1752.
Day-Lewis, F. D., Lane, Jr, J. W., Harris, J. M. and Gorelick, S. M., 2003, “Time-lapse imaging of saline-tracer tests in fractured rock difference-attenuation radar tomography,” Water Resources Research, Vol. 39, No. 10, doi:10.1029/2002WR001722.
Day-Lewis, F. D., Singha, K. and Binley, A. M., 2005, “Applying pertrophysical models to radar travel time and electrical resistivity tomograms: Resolution-dependent limitations,” J. of Geophysical Research, Vol. 110, B08206, doi:10.1029/2004JB003569
Kemna, A., Vanderborght, J., Kulessa, B. and Vereecken, H., 2002, “Imaging and characterization of subsurface solute transport using electrical resistivity tomography (ERT) and equivalent transport models,” J. of Hydrology, Vol. 267, pp. 125-146.
Kim, J.H., Yi, M.J., Park, S.G. and Kim, J.G., 2009, “4-D inversion of DC resistivity monitoring data acquired over a dynamically changing earth model,” J. of Applied Geophysics, Vol. 68, pp. 522-532.
Kim, K. J. and Cho, I. K., 2011, “Time-lapse inversion of 2D resistivity monitoring data with a spatially varying cross-model constraint,” J. of Applied Geophysics, Vol. 74, pp. 114-122.
Kneisel, C.h., 2006, “Mapping and monitoring mountain permafrost using electrical resistivity tomography,” European Geosciences Union 2006, 8, Geophysical research abstracts 04181.
LaBrecque, D. J. and Yang, X., 2001, “Difference inversion of ERT data, A fast inversion method for 3-D in-situ monitoring,” J. of Environmental and Engineering Geophysics, Vol.6, pp. 83-89.
Loke, M.H., 1999, “Time-lapse resistivity imaging inversion,” Proceedings of the 5th Meeting of the Environmental and Engineering European Section, Em1.
Menke, W., 1984, Geophysical data analysis: Discrete inverse theory, Academic Press Inc.
Miller, C. R., Routh, P. S., Brosten, T. R. and McNamara, J. P., 2008, “Application of time-lapse ERT imaging to watershed characterization,” Geophysics, Vol. 73, G7-G17.
Nguyen, F. and Kemna, A., 2005, “Time-lapse Inversion of Electrical Resistivity Data,” American Geophysical Union, Fall Meeting 2005, AGU, abstract #H13C-1346.
Oldenborger, G. A., Knoll, M. D., Routh, P. S. and LaBrecque, D. J., 2007, “Time-lapse ERT monitoring of an injection/withdrawal experiment in a shallow unconfined aquifer,” Geophysics, Vol. 72, F177-F188.
Slater, L., Binley, A., Cassiani, G., Birken, R. and Sandberg, S., 2002, “A 3D study solute transport in a large experimental tank,” J. of Applied Geophysics, Vol. 49, pp. 211-229.
Yi, M. J., Kim, J. H. and Chung, S. H., 2003, “Enhancing the resolving power of least-squares inversion with active constraint balancing,” Geophysics, Vol. 68, pp. 931-941.

Information

Publisher :The Korean Society of Mineral and Energy Resources Engineers
Publisher(Ko) :한국자원공학회
Journal Title :Journal of the Korean Society of Mineral and Energy Resources Engineers
Journal Title(Ko) :한국자원공학회지
Volume : 50
No :2
Pages :264-277
DOI :https://doi.org/10.12972/ksmer.2013.50.2.264

[1] Cassiani, G., Bruno, V., Villa, A., Fusi, N. and Binley, A. M., 2006, “A saline trace test monitored via time-lapse surface electrical resistivity tomography,” J. of Applied Geophysics, Vol. 59, pp. 244-259.

[2] Constable, S. C., Parker, R. L. and Constable, C. G., 1987, “Occam's inversion: a practical algorithm for generating smooth models from EM sounding data:,” Geophysics, Vol. 52, pp. 289-300.

[3] Day-Lewis, F. D., Harris, J. M. and Gorelick, S. M., 2002, “Time-lapse inversion of crosswell radar data,” Geophysics, Vol. 66, pp. 1740-1752.

[4] Day-Lewis, F. D., Lane, Jr, J. W., Harris, J. M. and Gorelick, S. M., 2003, “Time-lapse imaging of saline-tracer tests in fractured rock difference-attenuation radar tomography,” Water Resources Research, Vol. 39, No. 10, doi:10.1029/2002WR001722.

[5] Day-Lewis, F. D., Singha, K. and Binley, A. M., 2005, “Applying pertrophysical models to radar travel time and electrical resistivity tomograms: Resolution-dependent limitations,” J. of Geophysical Research, Vol. 110, B08206, doi:10.1029/2004JB003569

[6] Kemna, A., Vanderborght, J., Kulessa, B. and Vereecken, H., 2002, “Imaging and characterization of subsurface solute transport using electrical resistivity tomography (ERT) and equivalent transport models,” J. of Hydrology, Vol. 267, pp. 125-146.

[7] Kim, J.H., Yi, M.J., Park, S.G. and Kim, J.G., 2009, “4-D inversion of DC resistivity monitoring data acquired over a dynamically changing earth model,” J. of Applied Geophysics, Vol. 68, pp. 522-532.

[8] Kim, K. J. and Cho, I. K., 2011, “Time-lapse inversion of 2D resistivity monitoring data with a spatially varying cross-model constraint,” J. of Applied Geophysics, Vol. 74, pp. 114-122.

[9] Kneisel, C.h., 2006, “Mapping and monitoring mountain permafrost using electrical resistivity tomography,” European Geosciences Union 2006, 8, Geophysical research abstracts 04181.

[10] LaBrecque, D. J. and Yang, X., 2001, “Difference inversion of ERT data, A fast inversion method for 3-D in-situ monitoring,” J. of Environmental and Engineering Geophysics, Vol.6, pp. 83-89.

[11] Loke, M.H., 1999, “Time-lapse resistivity imaging inversion,” Proceedings of the 5th Meeting of the Environmental and Engineering European Section, Em1.

[12] Menke, W., 1984, Geophysical data analysis: Discrete inverse theory, Academic Press Inc.

[13] Miller, C. R., Routh, P. S., Brosten, T. R. and McNamara, J. P., 2008, “Application of time-lapse ERT imaging to watershed characterization,” Geophysics, Vol. 73, G7-G17.

[14] Nguyen, F. and Kemna, A., 2005, “Time-lapse Inversion of Electrical Resistivity Data,” American Geophysical Union, Fall Meeting 2005, AGU, abstract #H13C-1346.

[15] Oldenborger, G. A., Knoll, M. D., Routh, P. S. and LaBrecque, D. J., 2007, “Time-lapse ERT monitoring of an injection/withdrawal experiment in a shallow unconfined aquifer,” Geophysics, Vol. 72, F177-F188.

[16] Slater, L., Binley, A., Cassiani, G., Birken, R. and Sandberg, S., 2002, “A 3D study solute transport in a large experimental tank,” J. of Applied Geophysics, Vol. 49, pp. 211-229.

[17] Yi, M. J., Kim, J. H. and Chung, S. H., 2003, “Enhancing the resolving power of least-squares inversion with active constraint balancing,” Geophysics, Vol. 68, pp. 931-941.

Journal of the Korean Society of Mineral and Energy Resources Engineers ISSN:2288-0291(Print) 2288-2790(Online) 한국자원공학회지

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