Abstract The main problems in three-dimensional gravity inversion are the non-uniqueness of the solutions and the high computational cost of large data sets. To minimize the high computational cost, we propose a new sorting method to reduce fluctuations and the high frequency of the sensitivity matrix prior to applying the wavelet transform. Consequently, the sparsity and compression ratio of the sensitivity matrix are improved as well as the accuracy of the forward modeling. Furthermore, memory storage requirements are reduced and the forward modeling is accelerated compared with uncompressed forward modeling. The forward modeling results suggest that the compression ratio of the sensitivity matrix can be more than 300. Furthermore, multiscale inversion based on the wavelet transform is applied to gravity inversion. By decomposing the gravity inversion into subproblems of different scales, the non-uniqueness and stability of the gravity inversion are improved as multiscale data are considered. Finally, we applied conventional focusing inversion and multiscale inversion on simulated and measured data to demonstrate the effectiveness of the proposed gravity inversion method.
This work was supported by the Key National Research Project of China (Nos. 2017YFC0601900 and 2016YFC0303100) and the Key Program of National Natural Science Foundation of China (Nos. 41530320 and 41774125).
Cite this article:
. Gravity compression forward modeling and multiscale inversion based on wavelet transform[J]. APPLIED GEOPHYSICS, 2018, 15(2): 342-352.
Abedi, M., Siahkoohi, H. R., Gholami, A., et al., 2015, 3D inversion of magnetic data through wavelet based regularization method: Int. Journal of Mining & Geo-Engineering, 49(1), 1-18.
Ascher, U. M., and Haber, E., 2001, Grid refinement and scaling for distributed parameter estimation problems: Inverse Problems, 17(3), 571-590.
Bunks, C., Saleck, F. M., Zaleski, S., et al., 1995, Multiscale seismic waveform inversion: Geophysics, 60(5), 1457-1473.
Chiao, L. Y., and Kuo, B. Y., 2001, Multiscale seismic tomography: Geophysical Journal International, 145, 517-527.
Chiao, L. Y., and Liang, W. T., 2003, Multiresolution parameterization for geophysical inverse problems: Geophysics, 68, 199-209.
Coker, M. O., Bhattacharya, J. P., and Marfurt, K. J., 2007, Fracture patterns within mudstones on the flanks of a salt dome: Syneresis or slumping?: Gulf Coast Association of Geological Societies, 57, 125-137.
Daubechies, I., 1992, Ten Lectures on Wavelets: Society for Industrial and Applied Mathematics, Philadelphia, USA.
Davis, K., and Li, Y., 2011, Fast solution of geophysical inversion using adaptive mesh, space-filling curves and wavelet compression: Geophysical Journal International, 185(1), 157-166.
Davis, K., and Li, Y., 2013, Efficient 3D inversion of magnetic data via octree-mesh discretization, space-filling curves, and wavelets: Geophysics, 78(5), J61-J73.
Ennen, C., 2012, Mapping gas-charged fault blocks around the Vinton Salt Dome, Louisiana using gravity gradiometry data: Master thesis, University of Houston, Houston.
Farquharson, C. G., and Mosher, C. R. W., 2009, Three-dimensional modelling of gravity data using finite differences: Journal of Applied Geophysics, 68(3), 417-422.
Fedi, M., and Quarta, T., 1998, Wavelet analysis for the regional-residual and local separation of potential field anomalies: Geophysical Prospecting, 46(5), 507-525.
Foks, N. L., Krahenbuhl, R., and Li, Y., 2014, Adaptive sampling of potential-field data: A direct approach to compressive inversion: Geophysics, 79(1), IM1-IM9.
Gallardo, L. A., and Meju, M. A., 2004, Joint two-dimensional DC resistivity and seismic travel time inversion with cross gradients constraints: Journal of Geophysical Research, Solid Earth, 109(B3).
Holland, J. H., 1992, Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence: MIT press, Cambridge.
Hung, S. H., Chen, W. P., and Chiao, L. Y., 2011, A data-adaptive, multiscale approach of finite-frequency, traveltime tomography with special reference to P and S wave data from central Tibet: Journal of Geophysical Research: Solid Earth, 116(B6).
Jahandari, H., and Farquharson, C. G., 2013, Forward modeling of gravity data using finite-volume and finite-element methods on unstructured grids: Geophysics, 78(3), G69-G80.
Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P., 1983, Optimization by simulated annealing: Science, 220, 671-80.
Last, B. J., and Kubik, K., 1983, Compact gravity inversion: Geophysics, 48, 713-721.
Leblanc, G. E., and Morris, W. A., 2001, Denoising of aeromagnetic data via the wavelet transform: Geophysics, 66(6), 1793-1804.
Li, Y., and Oldenburg, D. W., 2003, Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method: Geophysical Journal International, 152(2), 251-265.
Martin, R., Monteiller, V., Komatitsch, D., et al., 2013, Gravity inversion using wavelet-based compression on parallel hybrid CPU / GPU systems: Application to southwest Ghana: Geophysical Journal International, 195, 1594-1619.
Moorkamp, M., Jegen, M., Roberts, A., et al., 2010, Massively parallel forward modeling of scalar and tensor gravimetry data: Computers & Geosciences, 36(5), 680-686.
Portniaguine, O., and Zhdanov, M. S., 1999, Focusing geophysical inversion images: Geophysics, 64(3), 874-887.
Ren, Z., Chen, C., Pan, K., et al., 2017a, Gravity anomalies of arbitrary 3D polyhedral bodies with horizontal and vertical mass contrasts: Surveys in Geophysics, 38(2), 479-502.
Ren, Z., Tang, J., Kalscheuer, T., et al., 2017b, Fast 3D large-scale gravity and magnetic modeling using unstructured grids and an adaptive multi-level fast multiple method: Journal of Geophysical Research: Solid Earth, 122(1), 79-109.
Rezaie, M., Moradzadeh, A., Kalate, A. N., et al., 2017, Fast 3D focusing inversion of gravity data using reweighted regularized Lanczos bidiagonalization method: Pure and Applied Geophysics, 174(1), 359-374.
Ridsdill-Smith, T. A., and Dentith, M. C., 1999, The wavelet transform in aeromagnetic processing: Geophysics, 64(4), 1003-1013.
Tikhonov, A. N., and Arsenin, V. Y., 1977, Solutions of ill-posed problems: Washington, V. H. Winston and Sons.
Vatankhah, S., Renaut, R. A., and Ardestani, V. E., 2018, Total variation regularization of the 3-D gravity inverse problem using a randomized generalized singular value decomposition: Geophysical Journal International, 213(1), 695-705.
Xu, Y. X., and Wang, J. Y., 1998, A multiresolution inversion of one-dimensional magnetotelluric data: Chinese Journal of Geophysics, 41(5), 704-711.
Yin, C., and Hodges, G., 2007, Simulated annealing for airborne em inversion: Geophysics, 72(4), F189-F195.
Zhdanov, M. S., 2002, Geophysical inverse theory and regularization problems: Vol. 36, Elsevier.
Zhdanov, M. S., Ellis, R., and Mukherjee, S., 2004, Three-dimensional regularized focusing inversion of gravity gradient tensor component data: Geophysics, 69, 925-937.