Pure and Applied Geophysics

, Volume 176, Issue 1, pp 203–214 | Cite as

Stochastic Modeling of the Thermal Structure to Decipher the Lithospheric Thickness: Application to Dharwar Craton

  • Harini GuruhappaEmail author
  • Kirti Srivastava
  • D. Srinagesh
  • T. Vijay Kumar


A wide range of speculation regarding lithospheric thermal thickness in a region calls for quantifying the uncertainties associated with model parameters. In this paper, we present an attempt to decipher it by solving the differential equations governing the heat transfer through the lithosphere. Adequately quantifying the temperature field is very important, since it is highly dependent on the controlling thermal parameters. Thermal conductivity is modeled as a random parameter with a known mean value and correlation structure. We compute the temperatures in the crust and lithospheric mantle, along with their error bounds, using an analytical solution to the steady-state heat equation and the Adomian method of decomposition. We apply these solutions in the Archean Dharwar craton, which is divided into western Dharwar craton (WDC) and eastern Dharwar craton (EDC). We obtain a Moho temperature estimate of 304 ± 58 °C in WDC, whilst in EDC it is 375 ± 74 °C for a 20% coefficient of variability in thermal conductivity. The range of lithospheric thickness obtained for WDC is 150–280 km, and 110–160 km for the EDC. These values are in agreement with other geophysical and geological findings in the region. The thermal lithosphere obtained from this study is based on the mantle solidus and the surface wave seismological studies considering radial anisotropy reveal that the lithosphere is characterized by higher shear wave velocities, and decrease at the lithosphere–asthenosphere boundary. Average shear velocity model for two different cratonic blocks (EDC and WDC) is used to show the LAB thickness for the eastern and western Dharwar craton. The two independent studies show a correlation in the lithospheric thickness.


Temperature thermal conductivity stochastic error bounds southern Indian shield 



The authors are thankful to the Director, National Geophysical Research Institute, Hyderabad, for his kind permission to publish this work. The first author Mrs. Harini wishes to thank DST-WOS-A scheme, Department of Science and Technology, New Delhi for the fellowship under which this study is performed at NGRI. We are grateful to the two anonymous reviewers for constructive review and improving the quality of the paper significantly.


  1. Adomian, G. (1994). Adomian solving frontier problems in physics—the decomposition method. Boston: Kluwer Academic.CrossRefGoogle Scholar
  2. Agrawal, P. K., & Pandey, O. P. (2004). Unusual lithospheric structure and evolutionary pattern of the cratonic segments of the south Indian shield. Earth Planets Space, 56(2004), 139–150.CrossRefGoogle Scholar
  3. Artemieva, I. M. (2006). Global 1° × 1° thermal model TCI for the continental lithosphere: Implications for lithosphere secular evolution. Tectonophysics, 416, 245–277.CrossRefGoogle Scholar
  4. Artemieva, I. M., & Mooney, W. D. (2001). Thermal thickness and evolution of Precambrian lithosphere a global study. Journal Geophysical Research, 106(B8), 16387–16414.CrossRefGoogle Scholar
  5. Chandrakala, K., Pandey, O. P., Mall, D. M., & Sarkar, D. (2010). Seismic signatures of a proterozoic thermal plume below southwestern part of the Cuddapah Basin, Dharwar Craton. Journal Geological Society of India, 76, 565–572.CrossRefGoogle Scholar
  6. Chapman, D. S., & Pollack, H. N. (1977). Regional geotherms and lithospheric thickness. Geology, 5, 265–268. reprinted in Japanese (1980).CrossRefGoogle Scholar
  7. Cheng, A. H. D., & Lafe, O. E. (1991). Boundary element solution for stochastic groundwater flow: Random boundary condition and recharge. Water Resources Research, 27(1991), 231–242.CrossRefGoogle Scholar
  8. Fisher, K. M., Heather, A. F., David, L. A., & Catherine, A. R. (2010). The lithosphere-asthenosphere boundary. Annual Review of Earth and Planetary Sciences, 38, 551–575.CrossRefGoogle Scholar
  9. Gallagher, K., Ramsdale, M., Lonergan, L., & Marrow, D. (1997). The role thermal conductivities measurements in modeling the thermal histories in sedimentary basins. Marine and Petroleum Geology, 14(1997), 201–214.CrossRefGoogle Scholar
  10. Ganguly, J., & Bhattacharya, P. K. (1987). Xenoliths in Proterozoic kimberlites from southern India: Petrology and geophysical implications. In P. H. Nixon (Ed.), Mantle xenoliths (pp. 249–265). New York: Wiley.Google Scholar
  11. Gass, I. G., Chapman, D. S., Pollack, H. N., & Thorpe, R. S. (1978). Geological and geophysical parameters of mid-plate volcanism. Philosophical Transactions of the Royal Society of London, 288, 581–597.CrossRefGoogle Scholar
  12. Gupta, S., Rai, S. S., Prakasam, K. S., Srinagesh, D., Chadha, R. K., Priestley, K., et al. (2003). The nature of the crust in southern India: Implications for Precambrian crustal evolution. Geophysical Research Letters, 30(2003), 1-1–1-4.Google Scholar
  13. Gupta, M. L., Sharma, S. R., & Sunder, A. (1991). Heat flow and heat generation in the Archaean Dharwar cratons and implications for the southern Indian shield geotherm and lithospheric thickness. Tectonophysics, 194(1991), 107–122.CrossRefGoogle Scholar
  14. Jagadeesh, S., & Rai, S. S. (2008). Thickness, composition, and evolution of the Indian Precambrian crust inferred from broadband seismological measurements. Precambrian Research, 162(1–2), 4–15.CrossRefGoogle Scholar
  15. Jokinen, J., & Kukkonen, I. T. (1999). Random modeling of lithospheric thermal regime: Forward simulation applied in uncertainty analysis. Tectonophysics, 306(1999a), 277–292.CrossRefGoogle Scholar
  16. Kaila, K. L., Roy Chowdhury, K., Reddy, P. R., Krishna, V. G., Narain, H., Subbotin, S. I., et al. (1979). Crustal structure along Kavali-Udipi profile in the Indian peninsular shield from deep seismic sounding. Journal of the Geological Society of India, 20(1979), 307–333.Google Scholar
  17. Kukkonen, I. T., Golovanova, I. V., Khachay, Y. V., Druzhinin, V. S., Kosarev, A. M., & Schapov, V. V. (1997). Low geothermal heat flow of the Urals fold belt-implication of low heat production, fluid circulation or paleoclimate? In: Perez-Estaun, A., Brown, D., Gee, D. (Eds.) EUROPROBE’S Uralides Project. Tectonophysics, 276, 63–85.CrossRefGoogle Scholar
  18. Kumar, P., Yuan, X., Ravi Kumar, M., Kind, R., Li, X., & Chadha, R. K. (2007). The rapid drift of the Indian tectonic plate. Nature, 449(2007), 894–897.CrossRefGoogle Scholar
  19. Kumar, N., Zeyen, H., Singh, A. P., & Singh, B. (2013). Lithospheric structure of southern Indian shield and adjoining oceans: Integrated modelling of topography, gravity, geoid and heat flow data. Geophysical Journal International, 2013, 1–15.Google Scholar
  20. Lachenbruch, A. H. (1970). Crustal temperature and heat production: Implications of the linear heat-flow relation. Journal of Geophysical Research, 75, 3291–3300.CrossRefGoogle Scholar
  21. Manglik, A. (2015). Thermo-mechanical structure of the Indian continental lithosphere. Journal of Indian Geophysics Union, 19(3), 243–255.Google Scholar
  22. Maurya, S., Montagner, J. P., Kumar, M. R., Stutzmann, E., Kiselev, S., Burgos, G., et al. (2016). Imaging the lithospheric structure beneath the Indian continent. Journal of Geophysical Research Solid Earth, 121(10), 7450–7468. Scholar
  23. Nielson, S. B. (1987). Steady state heat flow in a random medium and linear heat flow heat production relationship. Geophysical Research Letters, 14(1987), 318–321.CrossRefGoogle Scholar
  24. Pandey, O. P. (2016). Deep scientific drilling results from Koyna and Killari earthquake regions reveal why Indian shield lithosphere is unusual, thin and warm. Geoscience Frontiers, 7(2016), 851–858.Google Scholar
  25. Pandey, O. P., & Agrawal, P. K. (1999). Lithospheric mantle deformation beneath the Indian cratons. Journal of Geology, 107(1999), 683–692.CrossRefGoogle Scholar
  26. Pollack, H. N., & Chapman, D. S. (1997). On the regional variation of heat flow, geotherms, and lithospheric thickness. Tectonophysics, 38(1997), 279–296.Google Scholar
  27. Priestley, K., & Mckenzie, D. (2006). The thermal structure of the lithosphere from shear wave velocities. Earth and Planetary Science Letters, 244(2006), 285–301.CrossRefGoogle Scholar
  28. Ravi Kumar, M., Saikia, D., Singh, A., Srinagesh, D., Baidya, P. R., & Dattatrayam, R. S. (2013). Low shear velocities in the sub-lithospheric mantle beneath the Indian shield? Journal of Geophysical Research Solid Earth, 118, 1–14.Google Scholar
  29. Rogers, J. J. W. (1988). The Arsikere granite of Southern India: Magmatism and metamorphism in a previously depleted crust. Chemical Geology, 67, 155–163.CrossRefGoogle Scholar
  30. Roy, S., & Mareschal, J. C. (2011). Constraints on deep thermal structure of Dharwar Craton, India, from heat flow, Shear wave velocities and mantle Xenoliths. Journal of Geophysical Research, 116, B02409.CrossRefGoogle Scholar
  31. Roy, S., & Rao, R. U. M. (1999). Geothermal investigations in the 1993 Latur earthquake area Deccan volcanic province, India. Tectonophysics, 306(1999), 237–252.CrossRefGoogle Scholar
  32. Roy, S., & Rao, R. U. M. (2003). Towards a crustal thermal model for the Archean Dharwar Craton, Southern India. Physics and Chemistry of Earth, 28(2003), 361–373.CrossRefGoogle Scholar
  33. Royer, J. J., & Danis, M. (1988). Steady state geothermal model of the crust and problems of boundary conditions: Application to a rift system, the southern Rhinegraben. Tectonophysics, 156(1988), 239–255.CrossRefGoogle Scholar
  34. Saikia, U., Rai, S. S., Meena, R., Prasad, B. N. V., & Borah, K. (2016). Moho offset beneath the Western Ghat and the contact of Archean crusts of Dharwar Craton, India. Tecotonophysics, 672–673, 177–189.CrossRefGoogle Scholar
  35. Sarkar, D., Ravi Kumar, M., Saua, R., Kind, P., Raju, S., Chada, R. K., et al. (2003). A receiver function perspective of the Dharwar craton (India) crustal structure. Geophysical Journal International, 154(2003), 205–211.CrossRefGoogle Scholar
  36. Scholz, C. H. (1988). The brittle–plastic transition and the depth of seismic faulting. Geologische Rundschau, 77(1988), 319–328.CrossRefGoogle Scholar
  37. Serrano, S. E. (1995). Forecasting scale dependent dispersion from spills in heterogeneous aquifers. Journal Hydrology, 169(1995), 151–169.CrossRefGoogle Scholar
  38. Simpson, F. (1999). Stress and seismicity in the lower continental crust: A challenge to simple ductility and implications for electrical conductivity mechanisms. Surveys in Geophysics, 20, 201–227.CrossRefGoogle Scholar
  39. Singh, R. N. (2015). Thermal evolution of Indian cratonic lithosphere. Journal of Indian Geophysical Union, 19(4), 375–385.Google Scholar
  40. Singh, A. P., Mishra, D. C., Gupta, S. B., & Rao, M. R. K. P. (2004). Crustal structure and domain tectonics of the Dharwar craton (India): Insight from new gravity data. Journal of Asian Earth Sciences, 23(2004), 141–152.CrossRefGoogle Scholar
  41. Srinagesh, D., & Rai, S. S. (1996). Teleseismic tomographic evidence for contrasting crust and upper mantles in south Indian Archaean terrains. Physics of the Earth and Planetary Interiors, 97(1996), 27–41.CrossRefGoogle Scholar
  42. Srivastava, K. (2002). Stochastic modeling of the subsurface temperature distribution. Dynamics of earth’s fuid system (pp. 159–169). New Delhi: Oxford & IBH Publishing Co. Pvt. Ltd.Google Scholar
  43. Srivastava, K. (2005). Modeling the variability of heat flow due to random thermal conductivity of the crust. Geophysical Journal International, 160(2), 776–782.CrossRefGoogle Scholar
  44. Srivastava, K., Sharma, R., Fatima, B. & Singh, R.N. (2006). Method for analytically obtaining closed form expressions for temperature depth distribution along with its error bounds, patent no: 7, 130, 758, B2, date of patent, Oct 31, 2006.Google Scholar
  45. Srivastava, K., & Singh, R. N. (1998). A model for temperature variation in sedimentary basins due to random radiogenic heat sources. Geophysical Journal International, 135(1998), 727–730.CrossRefGoogle Scholar
  46. Srivastava, K., & Singh, R. N. (1999). A stochastic model to quantify the steady state crustal geotherms subject to uncertainty in thermal conductivity. Geophysical Journal International, 138(1999), 895–899.CrossRefGoogle Scholar
  47. Srivastava, K. & Singh, R.N. (2008). Stochastic analytical solution to quantify the earth’s subsurface mean heat flow and its error bounds, pub no US 2004/0243311 A1, date of patent, 2008.Google Scholar
  48. Swaminath, J., Ramakrishnan, M., & Viswanatha, M. N. (1976). Dharwar stratigraphic model and Karnataka craton evolution. Report of the Geological Survey of India, 107(1976), 145–175.Google Scholar
  49. Taguchi, T., Satish-Kumar, M., Hokada, T., & Jayananda, M. (2012). Petrogenesis of Cr-rich calc-silicate rocks from the Bandihalli supracrustal belt, Archean Dharwar Craton, India. The Canadian Mineralogist, 50(3), 705–718.CrossRefGoogle Scholar
  50. Tse, S. T., & Rice, J. R. (1986). Crustal earthquake instability in relation to the depth variation of frictional slip properties. Journal of Geophysical Research, 91(1986), 9452–9472.CrossRefGoogle Scholar
  51. Vasseur, G., Lucazeau, F., & Bayer, R. (1985). The problem of heat flow density determination from inaccurate data. Tectonophysics, 121(1985), 23–34.Google Scholar
  52. Vasseur, G., & Singh, R. N. (1986). Effect of random horizontal variation in radiogenic heat source distribution on its relationship with heat flow. Journal Geophysical Research, 91(1986), 10397–10404.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Harini Guruhappa
    • 1
    Email author
  • Kirti Srivastava
    • 1
  • D. Srinagesh
    • 1
  • T. Vijay Kumar
    • 2
  1. 1.CSIR-National Geophysical Research InstituteHyderabadIndia
  2. 2.SRTM UniversityNandedIndia

Personalised recommendations