Bulletin of Volcanology

, 78:68 | Cite as

A new interpolation method to model thickness, isopachs, extent, and volume of tephra fall deposits

  • Qingyuan YangEmail author
  • Marcus Bursik
Research Article


Tephra thickness distribution is the primary piece of information used to reconstruct the histories of past explosive volcanic eruptions. We present a method for modeling tephra thickness with less subjectivity than is the case with hand-drawn isopachs, the current, most frequently used method. The algorithm separates the thickness of a tephra fall deposit into a trend and local variations and models them separately using segmented linear regression and ordinary kriging. The distance to the source vent and downwind distance are used to characterize the trend model. The algorithm is applied to thickness datasets for the Fogo Member A and North Mono Bed 1 tephras. Simulations on subsets of data and cross-validation are implemented to test the effectiveness of the algorithm in the construction of the trend model and the model of local variations. The results indicate that model isopach maps and volume estimations are consistent with previous studies and point to some inconsistencies in hand-drawn maps and their interpretation. The most striking feature noticed in hand-drawn mapping is a lack of adherence to the data in drawing isopachs locally. Since the model assumes a stable wind field, divergences from the predicted decrease in thickness with distance are readily noticed. Hence, wind direction, although weak in the case of Fogo A, was not unidirectional during deposition. A combination of the isopach algorithm with a new, data transformation can be used to estimate the extent of fall deposits. A limitation of the algorithm is that one must estimate “by hand” the wind direction based on the thickness data.


Tephra thickness Isopach maps Volume estimation Kriging Interpolation 



This research was supported in part by NSF-IDR CMMI grant number 1131074 to E. B. Pitman, AFOSR grant number FA9550-11-1-0336 to A. K. Patra, an NSF-HSEES type 1 grant to B. Houghton, and NSF-HSEES grant number 1521855 to G. A. Valentine. All results and opinions expressed in the foregoing are those of the authors and do not reflect opinions of NSF or AFOSR. We are grateful for the data and insightful comments from Samantha Engwell. We thank AE Costanza Bonadonna and the anonymous reviewers for their suggestions that greatly improved the presentation of the science. Thank you, Solène.

Supplementary material

445_2016_1061_MOESM1_ESM.docx (888 kb)
ESM 1 (DOCX 887 kb)


  1. Bonadonna C, Costa A (2012) Estimating the volume of tephra deposits: a new simple strategy. Geology 40(5):415–418CrossRefGoogle Scholar
  2. Bonadonna C, Costa A (2013) Plume height, volume, and classification of explosive volcanic eruptions based on the Weibull function. Bull Volcanol 75(8):1–19CrossRefGoogle Scholar
  3. Bonadonna C, Houghton BF (2005) Total grain-size distribution and volume of tephra-fall deposits. Bull Volcanol 67:441–456CrossRefGoogle Scholar
  4. Bonadonna C, Biass S, Costa A (2015) Physical characterization of explosive volcanic eruptions based on tephra deposits: propagation of uncertainties and sensitivity analysis. J Volcanol Geotherm Res 296:80–100CrossRefGoogle Scholar
  5. Bonadonna C, Connor CB, Houghton BF, Connor L, Byrne M, Laing A, Hincks TK (2005) Probabilistic modeling of tephra dispersal: hazard assessment of a multiphase rhyolitic eruption at Tarawera. New Zealand. J Geophys Res-Solid Earth 110:(B3)Google Scholar
  6. Bonadonna C, Ernst GGJ, Sparks RSJ (1998) Thickness variations and volume estimates of tephra fall deposits: the importance of particle Reynolds number. J Volcanol Geotherm Res 81(3):173–187CrossRefGoogle Scholar
  7. Burden RE, Chen L, Phillips JC (2013) A statistical method for determining the volume of volcanic fall deposits. Bull Volcanol 75(6):1–10CrossRefGoogle Scholar
  8. Bursik M (2001) Effect of wind on the rise height of volcanic plumes. Geophys Res Lett 28(18):3621–3624CrossRefGoogle Scholar
  9. Bursik M, Melekestsev IV, Braitseva OA (1993) Most recent fall deposits of Ksudach volcano, Kamchatka, Russia. Geophys Res Lett 20(17):1815–1818CrossRefGoogle Scholar
  10. Bursik M, Sieh K, Meltzner A (2014) Deposits of the most recent eruption in the Southern Mono Craters, California: description, interpretation and implications for regional marker tephras. J Volcanol Geotherm Res 275:114–131CrossRefGoogle Scholar
  11. Bursik MI, Carey SN, Sparks RSJ (1992a) A gravity current model for the May 18, 1980 Mount St. Helens plume Geophys Res Let 19(16):1663–1666CrossRefGoogle Scholar
  12. Bursik MI, Sparks RSJ, Gilbert JS, Carey SN (1992b) Sedimentation of tephra by volcanic plumes: I. Theory and its comparison with a study of the Fogo A Plinian deposit, Sao Miguel (Azores). Bull Volcanol 54(4):329–344CrossRefGoogle Scholar
  13. Carey S, Sparks RSJ (1986) Quantitative models of the fallout and dispersal of tephra from volcanic eruption columns. Bull Volcanol 48(2–3):109–125CrossRefGoogle Scholar
  14. Carey SN, Sigurdsson H (1982) Influence of particle aggregation on deposition of distal tephra from the May 18, 1980, eruption of Mount St. Helens volcano J Geophys Res-Solid Earth 87(B8):7061–7072CrossRefGoogle Scholar
  15. Cioni R, Longo A, Macedonio G, Santacroce R, Sbrana A, Sulpizio R, Andronico D (2003) Assessing pyroclastic fall hazard through field data and numerical simulations: example from Vesuvius. J Geophys Res-Solid Earth 108(B2)Google Scholar
  16. Cressie N (1985) Fitting variogram models by weighted least squares. Math. Geol 17(5):563–586Google Scholar
  17. Cressie N (1990) The origins of kriging. Math Geol 22(3):239–252CrossRefGoogle Scholar
  18. Cressie N (2006) Block kriging for lognormal spatial processes. Math Geol 38(4):413–443CrossRefGoogle Scholar
  19. Delhomme JP (1978) Kriging in the hydrosciences. Adv Water Resour 1(5):251–266CrossRefGoogle Scholar
  20. Engwell SL, Aspinall WP, Sparks RSJ (2015) An objective method for the production of isopach maps and implications for the estimation of tephra deposit volumes and their uncertainties. Bull Volcanol 77(7):1–18CrossRefGoogle Scholar
  21. Engwell SL, Sparks RSJ, Aspinall WP (2013) Quantifying uncertainties in the measurement of tephra fall thickness. J Appl Volcanol 2(1):1–12CrossRefGoogle Scholar
  22. Fierstein J, Nathenson M (1992) Another look at the calculation of fallout tephra volumes. Bull Volcanol 54(2):156–167CrossRefGoogle Scholar
  23. Fierstein J, Houghton BF, Wilson CJN, Hildreth W (1997) Complexities of Plinian fall deposition at vent: an example from the 1912 Novarupta eruption (Alaska). J Volcanol Geotherm Res 76(3):215–227CrossRefGoogle Scholar
  24. Folch A, Costa A, Macedonio G (2009) FALL3D: a computational model for transport and deposition of volcanic ash. Comput Geosci 35(6):1334–1342CrossRefGoogle Scholar
  25. Genton MG (1998) Variogram fitting by generalized least squares using an explicit formula for the covariance structure. Math Geol 30(4):323–345CrossRefGoogle Scholar
  26. Gonzalez-Mellado AO, Cruz-Reyna S (2010) A simple semi-empirical approach to model thickness of ash-deposits for different eruption scenarios. Nat Hazards Earth Syst Sci 10(11):2241–2257CrossRefGoogle Scholar
  27. Hengl T, Heuvelink GB, Stein A (2004) A generic framework for spatial prediction of soil variables based on regression-kriging. Geoderma 120(1):75–93CrossRefGoogle Scholar
  28. Houghton BF, Wilson CJN, Fierstein J, Hildreth W (2004) Complex proximal deposition during the Plinian eruptions of 1912 at Novarupta, Alaska. Bull Volcanol 66(2):95–133CrossRefGoogle Scholar
  29. Hurst AW, Turner R (1999) Performance of the program ASHFALL for forecasting ashfall during the 1995 and 1996 eruptions of Ruapehu volcano. New Zealand J Geol Geophys 42(4):615–622CrossRefGoogle Scholar
  30. Journel AG (1983) Nonparametric estimation of spatial distributions. Math. Geol 15(3):445–468Google Scholar
  31. Kawabata E, Bebbington MS, Cronin SJ, Wang T (2013) Modeling thickness variability in tephra deposition. Bull Volcanol 75(8):1–14CrossRefGoogle Scholar
  32. Kawabata E, Cronin SJ, Bebbington MS, Moufti MRH, El-Masry N, Wang T (2015) Identifying multiple eruption phases from a compound tephra blanket: an example of the AD1256 Al-Madinah eruption, Saudi Arabia. Bull Volcanol 77(1):1–13CrossRefGoogle Scholar
  33. Klawonn M, Houghton BF, Swanson DA, Fagents SA, Wessel P, Wolfe CJ (2014) Constraining explosive volcanism: subjective choices during estimates of eruption magnitude. Bull Volcanol 76(2):1–6CrossRefGoogle Scholar
  34. Koyaguchi T (1994) Grain-size variation of tephra derived from volcanic umbrella clouds. Bull Volcanol 56(1):1–9CrossRefGoogle Scholar
  35. Moore RB (1990) Volcanic geology and eruption frequency, São Miguel, Azores. Bull Volcanol 52(8):602–614CrossRefGoogle Scholar
  36. Muggeo VM (2003) Estimating regression models with unknown break-points. Stat Med 22(19):3055–3071CrossRefGoogle Scholar
  37. Muggeo VM (2008) Segmented: an R package to fit regression models with broken-line relationships. R news 8(1):20–25Google Scholar
  38. Oliver MA, Webster R (1990) Kriging: a method of interpolation for geographical information systems. Int J Geogr Inf Syst 4(3):313–332CrossRefGoogle Scholar
  39. Pardo N, Cronin SJ, Wright HM, Schipper CI, Smith I, Stewart B (2014) Pyroclast textural variation as an indicator of eruption column steadiness in andesitic Plinian eruptions at Mt. Ruapehu Bull Volcanol 76(5):1–19Google Scholar
  40. Paul R, Cressie N (2011) Lognormal block kriging for contaminated soil. Eur J Soil Sci 62(3):337–345CrossRefGoogle Scholar
  41. Payne RJ, Symeonakis E (2012) The spatial extent of tephra deposition and environmental impacts from the 1912 Novarupta eruption. Bull Volcanol 74(10):2449–2458CrossRefGoogle Scholar
  42. Pebesma EJ (2004) Multivariable geostatistics in S: the gstat package. Comput Geosci 30(7):683–691CrossRefGoogle Scholar
  43. Pyle DM (1989) The thickness, volume and grain size of tephra fall deposits. Bull Volcanol 51(1):1–15CrossRefGoogle Scholar
  44. R Core Team (2015) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL
  45. Rhoades DA, Dowrick DJ, Wilson CJN (2002) Volcanic hazard in New Zealand: scaling and attenuation relations for tephra fall deposits from Taupo volcano. Nat Hazards 26(2):147–174CrossRefGoogle Scholar
  46. Sieh K, Bursik M (1986) Most recent eruption of the mono craters, eastern central California. J Geophys Res-Solid Earth 91(B12):12539–12571CrossRefGoogle Scholar
  47. Solow AR (1986) Mapping by simple indicator kriging. Math Geol 18(3):335–352CrossRefGoogle Scholar
  48. Walker GPL (1973) Explosive volcanic eruptions—a new classification scheme. Geol Rundsch 62(2):431–446CrossRefGoogle Scholar
  49. Walker GPL (1980) The Taupo pumice: product of the most powerful known (ultraplinian) eruption? J Volcanol Geotherm Res 8(1):69–94CrossRefGoogle Scholar
  50. Walker GPL, Croasdale R (1971) Characteristics of some basaltic pyroclastics. Bull Volcanol 35(2):303–317CrossRefGoogle Scholar
  51. Yang Q, Bursik MI (2016) “TTD”

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of GeologyUniversity at BuffaloBuffaloUSA

Personalised recommendations