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Gravity Inversion of Blocky Basement Relief Using L0 Norm Constraint with Exponential Density Contrast Variation

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Abstract

Depicting the basement relief of a sedimentary basin with gravity data is vital to predicting the hydrocarbon potential of a sedimentary basin and guiding exploration work. We have developed a gravity inversion method to estimate the depth to a blocky basement of a sedimentary basin. The basement rocks are assumed to be homogeneous and have uniform density, while the density of the sediment over the basement increases exponentially with depth. The density contrast between the sediment and the basement at the surface varies horizontally. The decay factor of density contrast is also nonuniform. The sediment above the basement is divided into vertically juxtaposed prisms, and the depth of the bottom of each prism represents the depth to the basement and is the parameter to be estimated. The L0 norm is introduced to limit the gradient of the parameter vector to obtain the model constraint function. We then establish the objective function for inversion by combining the gravity data misfit function, the known depth constraint function, and the model constraint function. The inversion is performed by minimizing the objective function using the nonlinear conjugate gradient algorithm. The inversion method is evaluated using a 2D and a 3D sedimentary basin model. The results show that our proposed method is capable of delineating the blocky basement relief of a sedimentary basin, and the result is sharper than that obtained using the L1 norm constraint. The method is applied to real data from the western part of the Zhu 1 depression in the Pearl River Mouth Basin, northern South China Sea. The solution reveals a strongly faulted basement, which is in accordance with the known tectonic information indicating the basin is a fully developed graben.

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References

  • Barbosa, V. C. F., Silva, J. B. C., & Medeiros, W. E. (1997). Gravity inversion of basement relief using approximate equality constraints on depths. Geophysics, 62(6), 1745–1759.

    Google Scholar 

  • Barbosa, V. C. F., Silva, J. B. C., & Medeiros, W. E. (1999). Gravity inversion of a discontinuous relief stabilized by weighted smoothness constraints on depth. Geophysics, 64(5), 1429–1437.

    Google Scholar 

  • Blakely, R. J. (1995). Potential Theory in Gravity and Magnetic Applications (1st ed.). Cambridge: Cambridge University Press.

    Google Scholar 

  • Bott, M. H. P. (1960). The use of rapid digital computing methods for direct gravity interpretation of sedimentary basin. Geophysical Journal Royal Astronomical Society, 3, 63–67.

    Google Scholar 

  • Chakravarthi, V., Kumar, M. P., Ramamma, B., & Sastry, S. R. (2016). Automatic gravity modeling of sedimentary basins by means of polygonal source geometry and exponential density contrast variation: Two space domain based algorithms. Journal of Applied Geophysics, 124, 54–61.

    Google Scholar 

  • Chakravarthi, V., Sastry, S. R., & Ramamma, B. (2013). MODTOHAFSD—a GUI based JAVA code for gravity analysis of strike limited sedimentary basins by means of growing bodies with exponential density contrast–depth variation: A space domain approach. Computers and Geosciences, 56, 131–141.

    Google Scholar 

  • Chakravarthi, V., & Sundararajan, N. (2006). Gravity anomalies of 2.5-D multiple prismatic structures with variable density: A Marquardt inversion. Pure and Applied Geophysics, 163, 229–242.

    Google Scholar 

  • Chen, G., Chen, S., Wang, C., & Zhang, B. (2013). Geophysical data sparse reconstruction via L0-norm minimization. Applied Geophysics, 10(2), 181–190.

    Google Scholar 

  • Cordell, L. (1973). Gravity anomalies using an exponential density-depth function-San Jacinto graben, California. Geophysics, 38(4), 684–690.

    Google Scholar 

  • Cordell, L., & Henderson, R. G. (1968). Iterative three-dimensional solution of gravity anomaly data using a digital computer. Geophysics, 33(4), 596–601.

    Google Scholar 

  • Fan, Z., Ni, M., Zhu, Q., Sun, C., & Kang, L. (2015). L0-norm sparse representation based on modified genetic algorithm for face recognition. Journal of Visual Communication and Image Representation, 28, 15–20.

    Google Scholar 

  • Feng, X. L., Wang, W. Y., Liu, F. Q., Li, J. G., & Lu, B. L. (2014). 2D gravity inversion of basement relief of rift basin based on a dual interface model. Chinese Journal of Geophysics, 57(6), 1934–1945.

    Google Scholar 

  • Feng, X. L., Wang, W. Y., Song, L. J., & Yuan, B. Q. (2019). Gravity inversion for V-shaped density interface based on Lp-norm regularization. Chinese Journal of Geophysics, 62(3), 1022–1036.

    Google Scholar 

  • Feng, X., Wang, W., & Yuan, B. (2018). 3D gravity inversion of basement relief for a rift basin based on combined multinorm and normalized vertical derivative of the total horizontal derivative techniques. Geophysics, 83(5), G107–G118.

    Google Scholar 

  • Gao, X. H., & Huang, D. N. (2017). Research on 3D focusing inversion of gravity gradient tensor data based on a conjugate gradient algorithm. Chinese Journal of Geophysics, 60(4), 1571–1583.

    Google Scholar 

  • García-Abdeslem, J. (2017). Nonlinear inversion of isostatic residual gravity data from Montage Basin, northern Gulf of California. Geophysics, 82(3), G45–G55.

    Google Scholar 

  • Gardner, G. H. F., Gardner, L. W., & Gregory, A. R. (1974). Formation velocity and density—the diagnostic basics for stratigraphic traps. Geophysics, 39, 770–780.

    Google Scholar 

  • Ghalehnoee, M. H., Ansari, A., & Ghorbani, A. (2017). Improving compact gravity inversion using new weighting functions. Geophysical Journal International, 208, 546–560.

    Google Scholar 

  • Han, J., Sun, Z., & Hao, H. (2015). l0-norm based structural sparse least square regression for feature selection. Pattern Recognition, 48, 3927–3940.

    Google Scholar 

  • Huber, P. J. (1964). Robust estimation of a location parameter. Annals of Mathematical Statistics, 35(1), 73–101.

    Google Scholar 

  • Last, B. J., & Kubik, K. (1983). Compact gravity inversion. Geophysics, 48, 713–721.

    Google Scholar 

  • Li, W. Z., Wang, P. J., Zhang, G. C., & Lu, B. L. (2011). Researches on time-depth conversion of deep-seated basal strata of Pearl River Mouth basin. Chinese Journal of Geophysics, 54(2), 449–456.

    Google Scholar 

  • Li, D., Wu, Z., Wang, Q., & Member, I. E. E. E. (2019). Edge guided compressive sensing for image reconstruction based on two-stage l0 minimization. Journal of Visual Communication and Image Representation, 59, 461–474.

    Google Scholar 

  • Liu, B., Li, J., & Zheng, S. (2018). Seismic sparse spike inversion based on L0 norm approximation. Oil and Gas Prospecting, 53(5), 961–968.

    Google Scholar 

  • Liu, H., Zhang, Z., Liu, S., Shu, J., Liu, T., & Zhang, T. (2015). Blind spectrum reconstruction algorithm with L0-sparse representation. Measurement Science and Technology, 26, 1–7.

    Google Scholar 

  • Mallesh, K., Chakravarthi, V., & Ramamma, B. (2019). 3D gravity analysis in the spatial domain: Model simulation by multiple polygonal cross-section coupled with exponential density contrast. Pure and Applied Geophysics, 176(6), 2497–2511.

    Google Scholar 

  • Martins, C. M., Lima, W. A., Barbosa, V. C. F., & Silva, J. B. C. (2011). Total variation regularization for depth-to-basement estimate: Part1—mathematical details and applications. Geophysics, 76(1), I1–I12.

    Google Scholar 

  • Meng, Z. (2016). 3D inversion of full gravity gradient tensor data using SL0 sparse recovery. Journal of Applied Geophysics, 127, 112–128.

    Google Scholar 

  • Meng, Z. (2017). Three-dimensional potential field data inversion with L0 quasinorm sparse constraint. Geophysical Prospecting, 66(3), 626–646.

    Google Scholar 

  • Meng, Z., Xu, X., & Huang, D. (2018). Three-dimensional gravity inversion based on sparse recovery iteration using approximate zero norm. Applied Geophysics, 15(3–4), 524–535.

    Google Scholar 

  • Portniaguine, O., & Zhdanov, M. S. (1999). Focusing geophysical inversion images. Geophysics, 64(3), 874–887.

    Google Scholar 

  • Rezaie, M., Moradzadeh, A., Kalate, A. N., & Aghajani, H. (2016). Fast 3D focusing inversion of gravity data using reweighted regularized Lanczos bidiagonalization method. Pure and Applied Geophysics, 174(1), 359–374.

    Google Scholar 

  • Rudin, L., Osher, S., & Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D Nonlinear Phenomena, 60, 259–268.

    Google Scholar 

  • Silva, J. B. C., Oliveira, A. S., & Barbosa, V. C. F. (2010). Gravity inversion of 2D basement relief using entropic regularization. Geophysics, 75(3), I29–I35.

    Google Scholar 

  • Su, N., Zeng, L., & Li, P. (1995). Geological features of Mesozoic sags in the eastern part of Pearl River Mouth Basin. China Offshore Oil and Gas (Geology), 9(4), 228–236.

    Google Scholar 

  • Sun, J., & Li, Y. (2014). Adaptive Lp inversion for simultaneous recovery of both blocky and smooth features in a geophysical model. Geophysical Journal International, 197(2), 882–899.

    Google Scholar 

  • Tang, X., Hu, S., Zhang, G., Yang, S., Shen, H., Rao, S., et al. (2014). Characteristic of surface heat flow in the Pearl River Mouth Basin and its relationship with thermal lithosphere thickness. Chinese Journal of Geophysics, 57(6), 1857–1867.

    Google Scholar 

  • Twomey, S. (1963). On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature. Journal of the Association for Computing Machinery, 10, 97–101.

    Google Scholar 

  • Wu, S., Wang, Y., Ma, Y., & Chang, X. (2018). Super-resolution least-squares prestack Kirchhoff depth migration using the L0-norm. Applied Geophysics, 15(1), 69–77.

    Google Scholar 

  • Xie, H., Zhou, D., Li, Y., Pang, X., Li, P., Chen, G., et al. (2014). Cenozoic tectonic subsidence in deepwater sags in the Pearl River Mouth Basin, northern South China Sea. Tectonophysics, 615–616, 182–198.

    Google Scholar 

  • Xing, J., Hao, T., Xu, Y., & Li, Z. (2016). Integration of geophysical constraints for multilayer geometry refinements in 2.5D gravity inversion. Geophysics, 81(5), G95–G106.

    Google Scholar 

  • Zhang, G. (2010). Tectonic evolution of deepwater area of northern continental margin in South China Sea. Acta Petrolei Sinica, 31(4), 528–533.

    Google Scholar 

  • Zhang, G., Xie, X., Wang, W., Liu, S., Wang, Y., Dong, W., et al. (2013). Tectonic types of petroliferous basins and its exploration potential in the South China Sea. Acta Petrolei Sinica, 34(4), 611–627.

    Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (41904115) and the Natural Science Basic Research Plan in Shaanxi Province of China (Program no. 2018JQ4034).

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Authors and Affiliations

  1. School of Earth Sciences and Engineering, Xi’an Shiyou University, Xi’an, 710065, China

    Xuliang Feng

  2. Shaanxi Key Laboratory of Petroleum Accumulation Geology, Xi’an Shiyou University, Xi’an, 710065, China

    Xuliang Feng

  3. Xi’an Center of Geological Survey (Northwest China Center for Geoscience Innovation), Xi’an, 710054, China

    Shengrong Liu

  4. The 12th Oil Production Plant of PCOC, Qingyang, 745400, China

    Ruikun Guo

  5. CCTEG Xi’an Research Institute, Xi’an, 710077, China

    Pengfei Wang

  6. Shaanxi Mineral Resources and Geological Survey, Xi’an, 710068, China

    Jinai Zhang

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  1. Xuliang Feng
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Correspondence to Xuliang Feng.

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Feng, X., Liu, S., Guo, R. et al. Gravity Inversion of Blocky Basement Relief Using L0 Norm Constraint with Exponential Density Contrast Variation. Pure Appl. Geophys. 177, 3913–3927 (2020). https://doi.org/10.1007/s00024-020-02423-1

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  • DOI: https://doi.org/10.1007/s00024-020-02423-1

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