Skip to main content
SpringerLink
Log in

Interface depth modelling of gravity data and altitude variations: a Bayesian neural network approach

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Modelling of anomalous geological source from the gravity data is vital for understanding the crustal/sub-crustal interface depths and associated hazard assessment. Two-dimensional radial power spectra have usually been used to infer average depth of protuberant geological structures, which lack details of dimensional comprehension of lateral interfaces. Here in this study, we implement jointly scaled conjugate gradient-based Bayesian neural network (SCG-BNN) scheme with variogram modelling to carve out shallow and deeper interfaces of complex geological terrain of Eastern Indian Shield, India, using Bouguer gravity anomaly (BGA) and altitude variations data. Our “learner codes” uses the SCG-BNN optimization algorithm to build up a statistical model involving appropriate control parameters for the modelling of shallow and deeper interfaces. We have also compared the proposed SCG-BNN modelling results with the results of both conventional artificial neural networks (ANNs) schemes (e.g. conjugate gradient-based ANNs (CG-ANN) and SCG-ANN) and support vector regression (SVR) modelling to demonstrate the robustness of the underlying method. Comparative analysis suggests that the SCG-BNN model produced superior results than the results of CG-ANN, SCG-ANN and SVR models. The results based on SCG-BNN analysis and variogram modelling have identified the existence of three conspicuous fault structures, namely Malda–Kishanganj Fault, Munger–Saharsha Ridge Marginal Fault and Katihar Fault. The analyses also significantly minimize prediction error in three independent datasets (viz. training, validation and test), enhancing the precision of estimated shallow and deeper interface depths and thereby extenuating feasibility of “SCG-BNN” learner code. We, therefore, conclude that the underlying approach is robust to model various interface depths and generate precisely variation in the shallow and deeper interfaces with appropriate input data from altitude variation and BGA. The “SCG-BNN learner scheme” may potentially be used to exploit interface depths from several other complex tectonic regions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Talwani M, Worzel JL, Landisman M (1959) Rapid gravity computations for two dimensional bodies with application to the Mendocino Submarine Fracture Zone. J Geophys Res 64:49–59

    Google Scholar 

  2. Cordell L, Henderson RG (1968) Iterative three-dimensional solution of gravity anomaly data using a digital computer. Geophysics 33(4):596–601

    Google Scholar 

  3. Lowrie W (2007) Fundamentals of geophysics, 2nd edn. Cambridge University Press, New York

    Google Scholar 

  4. Bott MHP (1960) The use of rapid digital computing methods for direct gravity interpretation of sedimentary basins. Geophys J R Astron Soc 3:63–67

    Google Scholar 

  5. Spector A, Grant FS (1970) Statistical models for interpreting aeromagnetic data. Geophysics 35:293–302

    Google Scholar 

  6. Maus S, Dimri V (1996) Depth estimation from the scaling power spectrum of potential fields? Geophys J Int 124:113–120

    Google Scholar 

  7. Bhattacharyya BK (1966) Continuous spectrum of the total magnetic anomaly due to a rectangular prismatic body. Geophysics 31:97–121

    Google Scholar 

  8. Connard G, Couch R, Gemperle M (1983) Analysis of aeromagnetic measurements from the Cascade Range in central Oregon. Geophysics 48:376–390

    Google Scholar 

  9. Naidu PS (1968) Spectrum of the potential field due to randomly distributed sources. Geophysics 33:337–345

    Google Scholar 

  10. Bansal AR, Dimri VP (2001) Depth estimation from the scaling power spectral density of nonstationary gravity profile. Pure appl Geophys 158:799–812

    Google Scholar 

  11. Dash NB, Panda SN, Remesan R, Sahoo N (2010) Hybrid neural modeling for groundwater level prediction. Neural Comput Appl 19:1251–1263

    Google Scholar 

  12. Karami H, Ehteram M, Mousavi SF et al (2018) Optimization of energy management and conversion in the water systems based on evolutionary algorithms. Neural Comput Appl. https://doi.org/10.1007/s00521-018-3412-6

    Article  Google Scholar 

  13. Ulkat D, Günay ME (2018) Prediction of mean monthly wind speed and optimization of wind power by artificial neural networks using geographical and atmospheric variables: case of Aegean Region of Turkey. Neural Comput Appl 30:3037. https://doi.org/10.1007/s00521-017-2895-x

    Article  Google Scholar 

  14. Najah A, El-Shafie A, Karim OA, El-Shafie AH (2013) Application of artificial neural networks for water quality prediction. Neural Comput Appl 22(Suppl 1):S187–S201

    Google Scholar 

  15. Poulton M (2001) Computational neural networks for geophysical data processing. Pergamon, Oxford

    Google Scholar 

  16. Maiti S, Tiwari RK, Kumpel HJ (2007) Neural network modelling and classification of lithofacies using well log data: a case study from KTB borehole site. Geophys J Int 169:733–746

    Google Scholar 

  17. Devilee RJR, Curtis A, Roy-Chowdhury K (1999) An efficient probabilistic neural network approach to solving inverse problems: inverting surface wave velocities for Eurasian crustal thickness. J Geophys Res 104(12):28841–28856

    Google Scholar 

  18. Abdel Zaher M, Senosy MM, Youssef MM, Ehara S (2009) Thickness variation of the sedimentary cover in the SouthWestern Desert of Egypt as deduced from Bouguer gravity and drill-hole data using neural network method. Earth Planets Space 61:659–674

    Google Scholar 

  19. Abedi M, Afshar A, Ardestani VE, Norouzi GH, Lucas C (2010) Application of various methods for 2D inverse modeling of residual gravity anomalies. Acta Geophys 58(2):317–336

    Google Scholar 

  20. Osman O, Muhittin AA, Ucan ON (2006) A new approach for residual gravity anomaly profile interpretations: forced Neural Network (FNN). Ann Geofis 49(6):1201–1208

    Google Scholar 

  21. Osman O, Muhittin Albora A, Nuri UO (2007) Forward modeling with forced neural networks for gravity anomaly profile. Math Geol 39:593–605

    MATH  Google Scholar 

  22. Eslam E, Salem A, Ushijima K (2001) Detection of cavities and tunnels from gravity data using a neural network. Explor Geophys 32(3/4):204–208

    Google Scholar 

  23. Kaftan I, Salk M, Senol Y (2011) Evaluation of gravity data by using artificial neural network case study: seferihisar geothermal area (Western Turkey). J Appl Geophys 75(4):711–718

    Google Scholar 

  24. Al-Garni MA (2013) Inversion of residual gravity anomalies using neural network. Arab J Geosci 6:1509–1516

    Google Scholar 

  25. Aires F (2004) Neural network uncertainty assessment using Bayesian statistics with application to remote sensing: 1. Network weights. J Geophys Res 109:D10303. https://doi.org/10.1029/2003JD004173

    Article  Google Scholar 

  26. Calster BV, Timmerman D, Nabney IT, Valentin L, Testa AC, Holsbeke CV, Vergote I, Huffel SV (2008) Using Bayesian neural networks with ARD input selection to detect malignant ovarian masses prior to surgery. Neural Comput Appl 17:489–500

    Google Scholar 

  27. Karmakar M, Maiti S (2019) Short term memory efficient pore pressure prediction via Bayesian neural networks at Bering Sea slope IODP expedition 323. Measurement 135:852–868. https://doi.org/10.1016/j.measurement.2018.12.034

    Article  Google Scholar 

  28. Hippert HS, Tylor JW (2010) An evaluation of Bayesian techniques for controlling model complexity and selecting inputs in a neural network for short-term load forecasting. Neural Netw 23:386–395

    Google Scholar 

  29. Maiti S, Tiwari RK (2010) Neural network modeling and an uncertainty analysis in Bayesian framework: a case study from the KTB borehole site. J Geophys Res 115:B10208. https://doi.org/10.1029/2010JB000864

    Article  Google Scholar 

  30. Tiwari RK, Maiti S (2011) Bayesian neural network modeling of tree-ring temperature variability record from the Western Himalayas. Nonlinear Process Geophys 18:515–528. https://doi.org/10.5194/npg-18-515-2011

    Article  Google Scholar 

  31. Ojha M, Maiti S (2016) Sediment classification using neural networks: an example from the site-U1344A of IODP Expedition 323 in the Bering Sea. Deep Sea Res II Top Stud Oceanogr 125–126:202–213. https://doi.org/10.1016/j.dsr2.2013.03.024

    Article  Google Scholar 

  32. Das A, Maiti S, Naidu S, Gupta G (2017) Estimation of spatial variability of aquifer parameters from geophysical methods: a case study of Sindhudurg district, Maharashtra, India. Stoch Environ Res Risk Assess 31:1709–1726. https://doi.org/10.1007/s00477-016-1317-4

    Article  Google Scholar 

  33. Bishop CM (1995) Neural networks for pattern recognition. Oxford University Press, Oxford

    MATH  Google Scholar 

  34. Nabney IT (2004) Netlab algorithms for pattern recognition. Springer, New York

    MATH  Google Scholar 

  35. Wang W, Xu Z, Lu W, Zhang X (2003) Determination of the spread parameter in the Gaussian kernel for classification and regression. Neuro Comput 55:643–663

    Google Scholar 

  36. Naskar DC, Das LK, Rai MK (2016) Insight into the tectonic and crustal understanding of lessar Himalayas along Purnea-Sevoke transect through geophysical studies. J Ind Geophys Union 20:506–515

    Google Scholar 

  37. Verma RK (1991) Geodynamics of the Indian Peninsula and the Indian plate margin. Oxford and IBH Publishing Co. Ltd., New Delhi, p 357. ISBN 978-81-204-0568-4

    Google Scholar 

  38. Valdiya KS (1976) Himalayan transverse faults and their parallelism with subsurface structures of north Indian plains. Tectonophysics 32:352–386

    Google Scholar 

  39. Jade S et al (2007) Estimates of interseismic deformation in northeast India from GPS measurements. Earth Planet Sci Lett 263:221–234

    Google Scholar 

  40. Mukul M, Jade S, Ansari K, Matin A (2014) Seismotectonic implications of strike–slip earthquakes in the Darjiling–Sikkim Himalaya. Curr Sci 2(25):198–210

    Google Scholar 

  41. Mishra OP (2014) Intricacies of the Himalayan seismotectonics and seismogenesis: need for integrated research. Curr Sci 106(2):176–187

    Google Scholar 

  42. Bhukta K, Khan PK, Mandal P (2018) Upper mantle anisotropy inferred from shear wave splitting beneath the Eastern Indian Shield region. Geosci Front 9:1911–1920

    Google Scholar 

  43. Agarwal RP, Bhoj R (1992) Evolution of Kosi river fan, India: structural implications and geomorphic significance. Int J Remote Sens 13(10):1891–1901

    Google Scholar 

  44. Mohanty WK, Verma AK, Vaccari F, Panza GF (2013) Influence of epicentral distance on local seismic response in Kolkata city, India. J Earth Syst Sci 2:321–338

    Google Scholar 

  45. Gupta H, Gahalaut VK (2014) Seismotectonics and large earthquake generation in the Himalayan region. Gondwana Res 25:204–213

    Google Scholar 

  46. Singh DD, Gupta HK (1980) Source dynamics of two great earthquakes of the Indian subcontinent: the Bihar-Nepal earthquake of January 15, 1934 and the earthquake of May 30, 1935. Bull Seismol Soc Am 70(3):757–773

    Google Scholar 

  47. Dasgupta S (1993) In Bihar-Nepal earthquake August 20 1988. Geological Survey of India Special Publication No. 31, pp 60–81

  48. Dasgupta S, Pande D, Ganguly Z, Iqbal K, Sanyal K, Venkatraman NV, Sural B, Harendranath L, Mazumder K, Sanyal S, Roy A, Das LK, Misra PS, Gupta HK (2000) Seismotectonic atlas of India and its environs. Geological Survey of India, Bangalore

    Google Scholar 

  49. Dasgupta S, Mukhopadhyay B, Mukhopadhyay M, Nandy DR (2013) Role of transverse tectonics in the Himalayan collision: further evidences from two contemporary earthquakes. J Geol Soc India 81:241–247

    Google Scholar 

  50. Gansser A (1964) Geology of the Himalayas. Interscience Publishers, London, p 289

    Google Scholar 

  51. Jain V, Sinha R (2005) Response of active tectonics on the alluvial Baghmati river, Himalayan foreland basin, eastern India. Geomorphology 70:339–356

    Google Scholar 

  52. Singh AP, Kumar N, Singh B (2004) Magmatic underplating beneath the Rajmahal Traps: gravity signature and derived 3-D configuration. Earth Plant Sci 113:759–769

    Google Scholar 

  53. Roy AK, Paine DP, Sett S, Bhattacharya HN (2012) Gravity-magnetic and magneto-telluric surveys in Purnea Onland Basin, India: a case history. In: 9th Biennial international conference and exposition on petroleum geophysics, Hyderabad, p 281

  54. Dasgupta S, Mukhopadhyay M, Nandy DR (1987) Active tectonic feature in the central part of Himalaya. Tectonophysics 136:255–264

    Google Scholar 

  55. Banerjee P, Burgmann R (2002) Convergence across the northwest Himalaya from GPS measurements. Geophys Res Lett 29(13):31–34. https://doi.org/10.1029/2002GL015184

    Article  Google Scholar 

  56. MacKay DJC (1992) A practical Bayesian framework for back-propagation networks. Neural Comput 4(3):448–472

    Google Scholar 

  57. Van der Baan M, Jutten C (2000) Neural networks in geophysical applications. Geophysics 65:1032–1047

    Google Scholar 

  58. Willmott CJ (1981) On the validation of models. Phys Geogr 2:184–194

    Google Scholar 

Download references

Acknowledgements

Authors are thankful to the Director, IIT (ISM), Dhanbad, for his kind permission to publish the work. RKT is grateful to DAE for the award of RRF. We gratefully acknowledge the full financial support from the Ministry of Earth Sciences (MoES), Govt. of India, New Delhi, India (Grant No: MoES/P.O. (Geosci)/44/2015), for this research. We are grateful to the editor, associate editor and three anonymous reviewers for their comments and constructive criticism on earlier versions of this manuscript.

Author information

Authors and Affiliations

  1. Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India

    Saumen Maiti & Prasenjit Sarkar

  2. Geological Survey of India, Bangalore, India

    Ch. Ravi Kumar

  3. CSIR-National Geophysical Research Institute, Hyderbad, 500007, India

    R. K. Tiwari & Uppala Srinu

Authors
  1. Saumen Maiti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ch. Ravi Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Prasenjit Sarkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. K. Tiwari
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Uppala Srinu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saumen Maiti.

Ethics declarations

Conflict of interest

We certify that there is no actual or potential conflict of interest in relation to this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maiti, S., Ravi Kumar, C., Sarkar, P. et al. Interface depth modelling of gravity data and altitude variations: a Bayesian neural network approach. Neural Comput & Applic 32, 3183–3202 (2020). https://doi.org/10.1007/s00521-019-04276-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-019-04276-9

Keywords

Search

Navigation