Abstract
Geometric anisotropy is commonly assumed in the investigation of the spatial variations of geophysical parameters. However, this assumption is not always satisfied in practice. We propose a novel method to determine the anisotropy of geophysical parameters. In the proposed method, the variograms are first normalized in all directions. Then, the normalized samples are fitted by the unit range variation increment (URVI) function to estimate the intensities of the variograms in each direction, from which the anisotropy can be finally determined. The performance of the proposed method is validated using InSAR atmospheric delay measurements over the Shanghai region. The results show that the deviation of the method is 6.4%, and that of the geometric anisotropy-based method is 21.2%. In addition, the computational efficiency of the new method is much higher. Subsequently, the URVI- and the geometric anisotropy-based methods are cross-validated in the cross-validation experiments by using Kriging interpolation. The results demonstrate that the structure functions generated with the proposed method are more accurate and can better reflect the spatial characteristics of the random field. Therefore, the proposed method, which is more accurate and efficient to determine the anisotropy than the conventional geometry anisotropy-based method, provides a better foundation to estimate the geophysical parameters of interest.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chorti, A., Hristopulos, D. T., 2008, Nonparametric identification of anisotropic (Elliptic) correlations in spatially distributed data sets: IEEE Translations on Signal Processing, 56, 4738–4751.
Chilès, J. P., and Delfiner, P., 1999, Geostatistics: Modeling Spatial Uncertainty: A Wiley-Interscience Publication.
Delfiner, P., 1999, Geostatistics: modeling spatial uncertainty: A Wiley-Interscience Publication.
Ecker, M. D., and Gelfand, A. E., 1999, Bayesian modeling and inference for geometrically anisotropic spatial data: Math Geology, 32(1), 67–82.
Elogne, S. N., Hristopulos, D. T., Varouchakis, E., 2008, An application of spartan spatial random fields in environmental mapping: Focus on automatic mapping capabilities: Stochastic Environmental Research Risk Assessment, 22(5), 633–646.
Gao, Y. and Teng, J. W., 2005, Studies on seismic anisotropy in the crust and mantle on Chinese mainland: Progress in Geophysics, 20(1), 180–185.
Goovaerts, P., 1997, Geostatistics for Natural Resources Evaluation: Oxford University Press, London.
Hou, J. R., and Huang, J. X., 1982, Geostatistics and the application in mineral reserves: Geological Publishing House, Beijing.
Igúzquiza, E. P., 1998, Maximum likelihood estimation of spatial covariance Parameters: Math Geology, 30(1), 95–108.
Jin, Y., Zheng, D. S., Pan, M., et al, 2011, 3D Geological Modeling of Anisotropic Mineralization and Its Application in Reserves Estimation: Acta Geological Sinica, 85(9), 1519–1527.
Journel, A. G., and Huijbregts, C. J., 1987, Mining Geostatistics: Academic Press, London
Jupp, D. L. B., Strahler, A. H., and Woodcock, C. E., 1998, Autocorrelation and regularization in digital images. I. Basic theory: Geoscience and Remote Sensing, 26(4), 463–473.
Kazuo, O., 2013, Recent Trend and Advance of Synthetic Aperture Radar with Selected Topics: Remote Sensing, 5(2), 716–807.
Kitanidis, P. K., 1983, Statistical estimation of polynomial generalized covariance functions and hydrologic applications: Water Resources Res, 19(2), 909–921.
Kitanidis, P. K., 1987, Parametric estimation of covariances of regionalized Variables: Water Resources Res, 23(4), 671–680.
Li, D. H., 2012, Anisotropic Wave field simulation and characteristic analysis of coal reservoirs: Ph. D. thesis, China University of Mining and Technology, Xuzhou.
Li, Z. W., 2005, Modeling atmospheric effects on repeatpass InSAR measurements, Ph.D. thesis, The Hong Kong Polytechnic University, Hong Kong.
Li, Z. W., Xu, W. B., Feng, G. C., et al, 2012, Correcting atmospheric effects on InSAR with MERIS water vapor data and elevation-dependent interpolation model: Geophysical Journal International, 189, 898–910.
Li, Z. W., Ding, X. L., Huang, C., et al, 2007, Atmospheric effects on repeat-pass InSAR measurements over Shanghai region: Journal of Atmospheric and Solar-Terrestrial Physics, 69(12), 1344–1356.
Liao, M. S., and Lin, H., 2003, Synthetic aperture radar interferometry: principle and signal processing (in Chinese): Publishing House of Surveying and Mapping, Beijing.
Mateus, P., Nico, G., Tome, R., et al, 2013, Experimental Study on the Atmospheric Delay Based on GPS, SAR Interferometry, and Numerical Weather Model Data: IEEE Transactions on Geoscience and Remote Sensing, 51(1), 6–11.
Ouchi, K., 2013, Recent Trend and Advance of Synthetic aperture radar with selected topics: Remote Sensing, 5(2), 716–807.
Ramon, F. H., 2002, Radar interferometry data interpretation and error analysis: Kluwer Academic Publishers, Dordrecht.
Rose, P. A., Hensley, S., Joughin, I. R., et al., 2000, Synthetic aperture radar interferometry: Proceedings of the IEEE, 88(3), 333–382.
Swerling, P., 1962, Statistical properties of the contours of random surfaces: IRE Transactions on Information Theory, 8(4), 315–321.
Wackernagel, H., 1997, Multivariate geostatistics. Springer-Verlag, Berlin, Germany.
Wu, J., Gao, Y., Chen, Y. T., et al, 2007, Seismic anisotropy in the crust in northwestern capital area of China: Chinese Journal of Geophysics, 50(1), 209–220.
Zhang, H. Q., 1990, Principles and application of geostatistics: China University of Mining and Technology Press, Xuzhou.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research is sponsored jointly by the National Hi-tech Research and Development Program of China (No. 2012AA121301), National Basic Research Program of China (No. 2012CB719903), the National Natural Science Foundation of China (Nos. 41222027, 41474007, and 41404013), and Hunan Provincial Natural Science Foundation of China (No. 13JJ1006).
Cao Yun-meng is a PhD candidate at the School of Geosciences and Info-Physics, Central South University (CSU), China. His research interests are InSAR data processing and InSAR atmospheric delay modeling.
Li Zhi-Wei is a full professor and Head of Department of Surveying and Remote Sensing, Central South University, China. His research interest includes InSAR deformation monitoring and atmospheric delay modeling.
Rights and permissions
About this article
Cite this article
Cao, YM., Li, ZW., Wei, JC. et al. A novel method for determining the anisotropy of geophysical parameters: unit range variation increment (URVI). Appl. Geophys. 11, 340–349 (2014). https://doi.org/10.1007/s11770-014-0448-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11770-014-0448-y