New method for estimating strike and dip based on structural expansion orientation for 3D geological modeling

doi:10.1007/s11707-021-0903-z

Front. Earth Sci.

2021, Vol. 15

Issue (3) : 676-691 https://doi.org/10.1007/s11707-021-0903-z

RESEARCH ARTICLE

New method for estimating strike and dip based on structural expansion orientation for 3D geological modeling

Yabo ZHAO¹, Weihua HUA¹, Guoxiong CHEN², Dong LIANG¹, Zhipeng LIU¹, Xiuguo LIU¹(

)

¹. School of Geography and Information Engineering, China University of Geosciences, Wuhan 430074, China
². State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan 430074, China

Download: PDF(10210 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

Strike and dip are essential to the description of geological features and therefore play important roles in 3D geological modeling. Unevenly and sparsely measured orientations from geological field mapping pose problems for the geological modeling, especially for covered and deep areas. This study developed a new method for estimating strike and dip based on structural expansion orientation, which can be automatically extracted from both geological and geophysical maps or profiles. Specifically, strike and dip can be estimated by minimizing an objective function composed of the included angle between the strike and dip and the leave-one-out cross-validation strike and dip. We used angle parameterization to reduce dimensionality and proposed a quasi-gradient descent (QGD) method to rapidly obtain a near-optimal solution, improving the time-efficiency and accuracy of objective function optimization with the particle swarm method. A synthetic basin fold model was subsequently used to test the proposed method, and the results showed that the strike and dip estimates were close to the true values. Finally, the proposed method was applied to a real fold structure largely covered by Cainozoic sediments in Australia. The strikes and dips estimated by the proposed method conformed to the actual geological structures more than those of the vector interpolation method did. As expected, the results of 3D geological implicit interface modeling and the strike and dip vector field were much improved by the addition of estimated strikes and dips.

Keywords strike and dip structural expansion orientation leave-one-out cross-validation covered area

Corresponding Author(s): Xiuguo LIU

Online First Date: 29 October 2021 Issue Date: 17 January 2022

Cite this article:

Yabo ZHAO,Weihua HUA,Guoxiong CHEN, et al. New method for estimating strike and dip based on structural expansion orientation for 3D geological modeling[J]. Front. Earth Sci., 2021, 15(3): 676-691.

URL:

https://academic.hep.com.cn/fesci/EN/10.1007/s11707-021-0903-z
https://academic.hep.com.cn/fesci/EN/Y2021/V15/I3/676

Tab.1 Common data sources and methods for extracting structural expansion orientation

Fig.1 (a) Schematic diagrams of strikes and dips at structural expansion orientation points (SEOSD) and (b) its angle parameterization.

Fig.2 Flow chart of optimization strategy. (a) Main steps of optimization strategy. (b) Details of quasi-gradient descent method. LOOCV: leave-one-out cross-validation; SEOSD: strike and dip at structural expansion orientation points; SEO: structural expansion orientation.

Fig.3 Basin fold simulation model and sampling. (a) Multiple formation interfaces (iso-time interfaces, the relationship between the deposition time of interfaces is

S 1 >S 2 >S 3

) of simulated basin fold and the profile AA′. (b) Simulated measured strike and dip points were randomly sampled on surface

z = 0 ? m

, and simulated structural expansion orientation (SEO) points were randomly sampled in whole space.

Fig.4 Convergence process comparison of (a) traditional particle swarm optimization (PSO) and (b) our optimization strategy.

Fig.5 Comparison of true strike and dip at structural expansion orientation points (SEOSD) and estimated SEOSD before ((a) and (b)) and after ((c) and (d)) our optimization strategy. PCC: Pearson correlation coefficient;

R 2

: coefficient of determination.

Fig.6 Structure visualization for profile AA'. Vector texture of (a) true model strike and dip field of full space, (b) measured strike and dip vectors, (c) measured strike and dip vectors and true SEOSD vectors, and (d) measured strike and dip vectors and SEOSD vectors to be solved.

Fig.7 Statistical results from quasi-gradient descent method with different numbers of structural expansion orientation (SEO) and measured strike and dip after 100 simulations. (a) Average of mean included angle (MIA). (b) Standard deviation of MIA. (c) Average number of iterations.

Fig.8 (a) Geological map and (b) aeromagnetic map of study area and their extracted structural expansion orientation (SEO). Elliptical principal axis orientation represents SEO, and eccentricity of ellipse represents uncertainty of SEO. Uncertainty decreased with increasing uncertainty.

Fig.9 Expert profile AA' and comparison of structure visualizations. (a) Profile BB' and its extracted structural expansion orientation (SEO). (b) Initial strike and dip at SEO points (SEOSD) obtained by 3D vector interpolation and vector field texture of interpolated strike and dip field using only measured strike and dip. (c) SEOSD estimated using our method and vector field texture of interpolated strike and dip field using both measured strike and dip and estimated SEOSD. The blue circle indicates the position where the textures of the two methods have significantly different.

Fig.10 Comparison between initial strike and dip at structural expansion orientation points (SEOSD) obtained by 3D vector interpolation (a) and SEOSD estimated using our method (b).

Fig.11 Optimization process of quasi-gradient descent method. (a) Convergence curve of quasi-gradient descent method; (b) initial included angle distribution; (c) included angle distribution after optimization.

Fig.12 Structure visualizations when using only measured strike and dip ((a) and (c)) and using both measured strike and dip and estimated strike and dip at structural expansion orientation points ((b) and (d)) of profile BB' ((a) and (b)) and profile CC' ((c) and (d)). The blue circle indicates the position where the textures of the two methods have significantly different.

Fig.13 Implicit surface modeling results of geological interfaces between kudinga basalt or frew river formation and coulters sandstone: (a) using measured strike and dip as gradient constraint and (b) using measured strike and dip and estimated strike and dip at structural expansion orientation points (SEOSD) as gradient constraints. Since number of estimated SEOSD (Figs. 9b and 11c) was large, it is not shown in figures. The blue circle indicates the position where the modeled interfaces of the two modeling data sets have significantly different.

Fig. A1 Illustration of different steps followed in computing vector field texture of strike and dip vector field. Red arrows are interpolated strike and dip vectors, blue arrows are rotating dip vectors, and black arrow is reference vector chosen as profile direction.

1	N Archibald, P Gow, F Boschetti (1999). Multiscale edge analysis of potential field data. Explor Geophys, 30(1–2): 38–44 https://doi.org/10.1071/EG999038
2	S Banerjee, S Mitra (2004). Remote surface mapping using orthophotos and geologic maps draped over digital elevation models: application to the Sheep Mountain anticline, Wyoming. AAPG Bull, 88(9): 1227–1237 https://doi.org/10.1306/02170403091
3	J Boisvert (2010). Geostatistics with Locally Varying Anisotropy. Dissertation for the Doctor Degree. Alberta: University of Alberta
4	J B Boisvert, J G Manchuk, C V Deutsch (2009). Kriging in the presence of locally varying anisotropy using non-Euclidean distances. Math Geosci, 41(5): 585–601 https://doi.org/10.1007/s11004-009-9229-1
5	R J Brown, H Borg, M Båth (1971). Strike and dip of crustal boundaries — a method and its application. Pure Appl Geophys, 88(1): 60–74 https://doi.org/10.1007/BF00877893
6	W H Bucher (1943). Dip and strike from three not parallel drill cores lacking key beds (stereographic method). Econ Geol, 38(8): 648–657 https://doi.org/10.2113/gsecongeo.38.8.648
7	B Cabral, L C Leedom (1993). Imaging vector fields using line integral convolution. In: Kajiya J T, ed. SIGGRAPH ’93: Proceedings of the 20th annual conference on Computer graphics and interactive techniques. Anaheim, CA, 263–270
8	L Carr, B Ayling, R Morris, K Higgins, D Edwards, K Khider, T Smith, J Lawrie, M Morse, C Boreham, E Tenthorey, T Buckler, W Cox, L Hatch, M Woods, A Cortese, C Southby, A Chirinos (2016). Georgina Basin geoscience data package, Various repository formats https://doi.org/10.4225/25/55499D492CB88
9	T Carmichael, L Ailleres (2016). Method and analysis for the upscaling of structural data. J Struct Geol, 83: 121–133 https://doi.org/10.1016/j.jsg.2015.09.002
10	J Chorowicz, J Breard, R Guillande, C Morasse, D Prudon, J Rudant (1991). Dip and strike measured systematically on digitized three-dimensional geological maps. Photogramm Eng Remote Sensing, 57(4): 431–436
11	R M Dalley, E Gevers, G M Stampfli, D J Davies, C N Gastaldi, P A Ruijtenberg, G Vermeer (2007). Dip and azimuth displays for 3D seismic interpretation. First Break, 25(12): 101–108 https://doi.org/10.3997/1365-2397.2007031
12	G E Fasshauer, J G Zhang (2007). On choosing “optimal” shape parameters for RBF approximation. Numer Algorithms, 45: 345–368 https://doi.org/10.1007/s11075-007-9072-8
13	D Grancher, A Bar-Hen, R Paris, F Lavigne, D Brunstein (2012). Spatial interpolation of circular data: application to tsunami of December 2004. Adv Appl Stat, 30(1): 19–29
14	L Grose, L Ailleres, G Laurent, R Armit, M Jessell (2019). Inversion of geological knowledge for fold geometry. J Struct Geol, 119: 1–14 https://doi.org/10.1016/j.jsg.2018.11.010
15	J Guo, L Wu, W Zhou, C Li, F Li (2018). Section-constrained local geological interface dynamic updating method based on the HRBF surface. J Struct Geol, 107: 64–72 https://doi.org/10.1016/j.jsg.2017.11.017
16	R L Haupt, S Ellen Haupt (2004). Practical Genetic Algorithms. 2nd ed. New Jersey: John Wiley & Sons
17	M Hillier, E Kemp, E Schetselaar (2013). 3D form line construction by structural field interpolation (SFI) of geologic strike and dip observations. J Struct Geol, 51: 167–179 https://doi.org/10.1016/j.jsg.2013.01.012
18	M J Hillier, E M Schetselaar, E A de Kemp, G Perron (2014). Three-dimensional modelling of geological surfaces using generalized interpolation with radial basis functions. Math Geosci, 46(8): 931–953 https://doi.org/10.1007/s11004-014-9540-3
19	C Lajaunie, G Courrioux, L Manuel (1997). Foliation fields and 3D cartography in geology: principles of a method based on potential interpolation. Math Geol, 29(4): 571–584 https://doi.org/10.1007/BF02775087
20	S Lajevardi, O Babak, C V Deutsch (2015). Estimating barrier shale extent and optimizing well placement in heavy oil reservoirs. Petrol Geosci, 21(4): 322–332 https://doi.org/10.1144/petgeo2013-039
21	M Lillah, J B Boisvert (2015). Inference of locally varying anisotropy fields from diverse data sources. Comput Geosci, 82: 170–182 https://doi.org/10.1016/j.cageo.2015.05.015
22	F A Macdonald, K Mitchell, A J Stewart (2005). Amelia Creek: a proterozoic impact structure in the Davenport Ranges, Northern Territory. Aust J Earth Sci, 52(4-5): 631–640 https://doi.org/10.1080/08120090500170401
23	D F Machuca-Mory, C V Deutsch (2013). Non-stationary geostatistical modeling based on distance weighted statistics and distributions. Math Geosci, 45(1): 31–48 https://doi.org/10.1007/s11004-012-9428-z
24	D Marcotte (1995). Generalized cross-validation for covariance model selection. Math Geol, 27(5): 659–672 https://doi.org/10.1007/BF02093906
25	G Mariethoz, B F Kelly (2011). Modeling complex geological structures with elementary training images and transform-invariant distances. Water Resour Res, 47(7): W07527 https://doi.org/10.1029/2011WR010412
26	R Martin, D Machuca-Mory, O Leuangthong, J B Boisvert (2019). Non-stationary geostatistical modeling: a case study comparing LVA estimation frameworks. Nat Resour Res, 28(2): 291–307 https://doi.org/10.1007/s11053-018-9384-5
27	L M Martinez-Torres, A Lopetegui, L Eguiluz (2012). Automatic resolution of the three-points geological problem. Comput Geosci, 42: 200–202 https://doi.org/10.1016/j.cageo.2011.08.031
28	S Patnaik, X Yang, K Nakamatsu (2017). Nature-Inspired Computing and Optimization: Theory and Applications. Switzerland: Springer Nature
29	M Perrin, J F Rainaud (2013). Shared Earth Modeling: Knowledge Driven Solutions for Building and Managing Subsurface 3D Geological Models. Paris: Editions Technip
30	S Rippa (1999). An algorithm for selecting a good value for the parameter c in radial basis function interpolation. Adv Comput Math, 11: 193–210 https://doi.org/10.1023/A:1018975909870
31	J D Rodriguez, A Perez, J A Lozano (2010). Sensitivity analysis of kappa-fold cross validation in prediction error estimation. IEEE Trans Pattern Anal Mach Intell, 32(3): 569–575 https://doi.org/10.1109/TPAMI.2009.187 pmid: 20075479
32	C Sammut, G I Webb (2011). Encyclopedia of Machine Learning. New York: Springer Science & Business Media
33	M Scheuerer (2011). An alternative procedure for selecting a good value for the parameter C in RBF-interpolation. Adv Comput Math, 34(1): 105–126 https://doi.org/10.1007/s10444-010-9146-3
34	C Scholl, S Hallinan, F Miorelli, M D Watts (2017). Geological consistency from inversions of geophysical data. In: 79th EAGE Conference and Exhibition, 2017, Paris, France
35	M Smolik, V Skala (2016). Vector field interpolation with radial basis functions. In: Proceedings of SIGRAD 2016, Visby, Sweden, 15–21
36	J A Snyman (2005). Practical Mathematical Optimization. New York: Springer Science+Business Media
37	C J Taylor, D J Kriegman (1994). Minimization on the Lie group SO (3) and related manifolds. Connecticut‎: Yale University
38	S T Thiele, L Grose, T Cui, A R Cruden, S Micklethwaite (2019). Extraction of high-resolution structural orientations from digital data: a Bayesian approach. J Struct Geol, 122: 106–115 https://doi.org/10.1016/j.jsg.2019.03.001
39	M Tomczak (1998). Spatial interpolation and its uncertainty using automated anisotropic inverse distance weighting (IDW)-cross-validation/jackknife approach. J Geogr Inf Decis Anal, 2: 18–30
40	G Verly, M David, A G Journel, A Marechal (1984). Geostatistics for Natural Resources Characterization. New York: Springer Science+Business Media
41	Y Wang, A G Yagola, C Yang (2011). Optimization and Regularization for Computational Inverse Problems and Applications. Heidelberg, Dordrecht, London, New York: Springer
42	W Xu (1996). Conditional curvilinear stochastic simulation using pixel-based algorithms. Math Geol, 28(7): 937–949 https://doi.org/10.1007/BF02066010
43	C Yeh, Y Chan, K Chang, M Lin, Y Hsieh (2014). Derivation of strike and dip in sedimentary terrain using 3D image interpretation based on airborne LiDAR data. Terr Atmos Ocean Sci, 25(6): 775–790 https://doi.org/10.3319/TAO.2014.07.02.01(TT)
44	D S Young (1987a). Indicator kriging for unit vectors: rock joint orientations. Math Geol, 19(6): 481–501 https://doi.org/10.1007/BF00896916
45	D S Young (1987b). Random vectors and spatial analysis by geostatistics for geotechnical applications. Math Geol, 19(6): 467–479 https://doi.org/10.1007/BF00896915

Viewed

Full text

Abstract

Cited

Shared

Discussed