Mathematical Geosciences

, Volume 44, Issue 5, pp 595–617 | Cite as

Spatial Statistical Properties of Pressure Solution Seams in Clastic Rocks in Southwest Ireland

  • Filippo Nenna
  • Xiaoxian Zhou
  • Atilla Aydin


Length, height, thickness and spacing measurements of pressure solution seams at outcrop, hand sample and thin section scale were taken from clastic rocks located in the southwest of Ireland. The lengths and spacings of pressure solution seams have similarly shaped (approximately log-hyperbolic) distributions at the observed scales suggesting that length and spacing distributions are scale-independent over the scales studied with a fractal dimension in the range of 1.4 to 1.6. Pressure solution seam lengths and thicknesses are related by a power-law and their spacings have a linear relationship to bed thickness. Although pressure solution seams are often considered as anticracks (forming under the same remote stresses as joints, but with opposite sign) we describe how the mechanism of pressure solution differs substantially from that of jointing. We use an existing mechanical model to show that stresses around pressure solution seam tips are much lower than those for joints under equal but opposite loading conditions. Pressure solution seams also have a decreasing tendency to lengthen as they grow, which is reflected in their length distributions. We propose that pressure solution seams, unlike joints, do not reach fracture saturation spacing because of transverse coalescence.


Pressure solution seam statistics Pressure solution seam/joint comparison Fracture self-similarity 



Thanks go to Pat Meere and Chloe Parker of University College Cork and Chris Wilson and Vanessa Nenna of Stanford University for their assistance and discussion during fieldwork. We are also grateful to Jef Caers and Alexander Boucher for their assistance with the processing of statistical data. Improvements to the manuscript suggested by John Walsh and one anonymous reviewer were very much appreciated. This work was funded by the Stanford Rock Fracture Project and by a Levorsen Grant from Stanford School of Earth Sciences.


  1. Agosta F, Alessandroni M, Tondi E, Aydin A (2010) Oblique normal faulting along the northern edge of the Majella Anticline, central Italy: inferences on hydrocarbon migration and accumulation. J Struct Geol 32:1317–1333 CrossRefGoogle Scholar
  2. Alvarez W, Engelder T, Geiser PA (1978) Classification of solution cleavage in pelagic limestones. Geology 6:263–266 CrossRefGoogle Scholar
  3. Andrews LM, Railsback LB (1997) Controls on stylolite development: morphologic, lithologic and temporal evidence from bedding parallel and transverse stylolites from the US Appalachians. J Geol 105:59–73 CrossRefGoogle Scholar
  4. Ayling MR, Meredith PG, Murrell SAF (1995) Microcracking during triaxial deformation of porous rocks monitored by changes in rock physical properties, I. Elastic-wave propagation measurements on dry rocks. Tectonophysics 245:205–221 CrossRefGoogle Scholar
  5. Bai T, Pollard DD (2000a) Fracture spacing in layered rocks: a new explanation based on the stress transition. J Struct Geol 22:43–57 CrossRefGoogle Scholar
  6. Bai T, Pollard DD (2000b) Closely spaced fractures in layered rocks: initiation mechanism and propagation kinematics. J Struct Geol 22:1049–1425 CrossRefGoogle Scholar
  7. Barton CC (1995) Fractal analysis of scaling and spatial clustering of fractures. In: Barton CC, LaPointe PR (eds) Fractals in the Earth Sciences. Plenum, New York, pp 141–178 Google Scholar
  8. Benedicto A, Schultz RA (2010) Stylolites in limestone: magnitude of contractional strain accommodated and scaling relationships. J Struct Geol 32:1250–1256 CrossRefGoogle Scholar
  9. Bloomfield J (1996) Characterization of hydrogeologically significant fracture distributions in the Chalk: an example of the Upper Chalk of southern England. J Hydrol 184:355–379 CrossRefGoogle Scholar
  10. Bonnet E, Bour O, Odling NE, Davy P, Main I, Cowie P, Berkowitz B (2001) Scaling of fracture systems in geological media. Rev Geophys 39:347–383 CrossRefGoogle Scholar
  11. Brace WF, Paulding BW, Scholz C (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71:3939–3953 CrossRefGoogle Scholar
  12. Caers J, Vynckier P, Beirlant J, Rombouts L (1996) Extreme value analysis of diamond-size distributions. Math Geol 28:25–43 CrossRefGoogle Scholar
  13. Carrio-Schaffhauser E, Raynaud S, Latiere HJ, Mazerolle F (1990) Propagation and localization of stylolites in limestones, deformation mechanisms, rheology and tectonics. Geol Soc Spec Publ 54:193–199 CrossRefGoogle Scholar
  14. Clark MB, Brantley SL, Fisher DM (1995) Power-law vein-thickness distributions and positive feedback in vein growth. Geology 23:975–978 CrossRefGoogle Scholar
  15. Cooper MA, Collins DA, Ford M, Murphy FX, Trayner PM, O’Sullivan M (1986) Structural evolution of the Irish Variscades. J Geol Soc (Lond) 143:53–61 CrossRefGoogle Scholar
  16. Drummond CN, Sexton DN (1998) Fractal structure of stylolites. J Sediment Res 68:8–10 Google Scholar
  17. Dunnington HV (1967) Aspects of diagenesis and shape change in stylolitic limestone reservoirs. In: Proceedings 7th World petroleum congress, Mexico, vol 2, pp 339–352 Google Scholar
  18. Engelder T (1982) Fossils record the force of continental collision Lamont–Doherty. In: Geological Observatory of Columbia University Yearbook 1981–1982, vol 8, pp 37–39 Google Scholar
  19. Fletcher RC, Pollard DD (1981) Anticrack model for pressure solution surfaces. Geology 9:419–424 CrossRefGoogle Scholar
  20. Ford M, Ferguson CC (1985) Cleavage strain in the Variscan fold belt, County Cork, Ireland, estimated from stretched arsenopyrite rosettes. J Struct Geol 7:217–223 CrossRefGoogle Scholar
  21. Fossen H, Hesthammer J (2000) Possible absence of small faults in the Gullfaks Field, northern North Sea: implications for downscaling of faults in porous sandstones. J Struct Geol 22:851–863 CrossRefGoogle Scholar
  22. Gillespie PA, Howard CB, Walsh JJ, Watterson J (1993) Measurement and characterization of spatial distributions of fractures. Tectonophysics 226:113–141 CrossRefGoogle Scholar
  23. Gillespie PA, Walsh JJ, Watterson J, Bonson CG, Manzocchi T (2001) Scaling relationships of joint and vein arrays from the Burren, Co. Clare, Ireland. J Struct Geol 23:183–201 CrossRefGoogle Scholar
  24. Graham-Wall BR (2006) Influence of depositional setting and sedimentary fabric on mechanical layer evolution in carbonate aquifers. Sediment Geol 184:203–224 CrossRefGoogle Scholar
  25. Graham-Wall BR, Girbacea R, Mesonjesi A, Aydin A (2006) Evolution of fracture and fault-controlled fluid pathways in carbonates of the Albanides fold-thrust belt. Am Assoc Pet Geol Bull 90:1227–1249 Google Scholar
  26. Griggs D, Handin J (1960) Observations on fracture and a hypothesis of earthquakes. Geol Soc Am Mem 79:347–364 Google Scholar
  27. Groshong RH Jr (1988) Low-temperature deformation mechanisms and their interpretation. Geol Soc Am Bull 100:1329–2360 CrossRefGoogle Scholar
  28. Gross MR (1993) The origin and spacing of cross joints: examples from the Monterey Formation, Santa Barbara Coastline, California. J Struct Geol 15:737–751 CrossRefGoogle Scholar
  29. Helgeson D, Aydin A (1991) Characteristics of joint propagation across layer interfaces in sedimentary rocks. J Struct Geol 13:897–911 CrossRefGoogle Scholar
  30. Hewett TA (1994) Fractal methods for fracture characterization. In: Yarus JM, Chambers RL (eds) Stochastic modeling and geostatistics, vol 3. American Association of Petroleum Geologists Computer Applications in Geology, Tulsa, pp 249–260 Google Scholar
  31. Holder J, Olsen JE, Philip Z (2001) Experimental determination of subcritical crack growth parameters in sedimentary rock. Geophys Res Lett 28:599–602 CrossRefGoogle Scholar
  32. Hurd DC, Theyer F (1975) Changes in the physical and chemical properties of biogenic silica from the Central Equatorial Pacific. I. Solubility, specific surface area, and solution rate constants of acid-cleaned samples. In: Advances in Chemistry, vol 147, pp 211–230 Google Scholar
  33. Isaaks EH, Srivastava RM (1989) An introduction to applied geostatistics. Oxford University Press, Oxford, 561 pp Google Scholar
  34. Katsman R, Aharonov E, Scher H (2006) A numerical study on localized volume reduction in elastic media: some insights on the mechanics of anticracks. J Geophys Res 111:B03204 CrossRefGoogle Scholar
  35. Lachenbruch AH (1961) Depth and spacing of tension cracks. J Geophys Res 66:4273–4292 CrossRefGoogle Scholar
  36. Ladeira FL, Price NJ (1981) Relationship between fracture spacing and bed thickness. J Struct Geol 3:179–183 CrossRefGoogle Scholar
  37. Lawn BR, Wilshaw TR (1975) Fracture of brittle solids. Cambridge University Press, Cambridge, 204 pp Google Scholar
  38. Lodder R, Hieftje G (1988) Quantile analysis: a method for characterizing data distributions. Appl Spectrosc 42:1512–1520 CrossRefGoogle Scholar
  39. Mardon D (1988) Localized pressure solution and the formation of discrete solution seams. PhD thesis, College Station, Texas A&M University, Texas, USA Google Scholar
  40. Marrett R, Ortega OJ, Kelsey CM (1999) Extent of power-law scaling for natural fractures in rock. Geology 27:799–802 CrossRefGoogle Scholar
  41. Meere PA (1995) The structural evolution of the western Irish Variscades: an example of obstical tectonics? Techtonophysics 246:97–112 CrossRefGoogle Scholar
  42. Merino E, Ortoleva P, Strickholm P (1983) Generation of evenly-spaced pressure solution seams during (late) diagenesis: a kinetic theory. Contrib Mineral Petrol 82:360–370 CrossRefGoogle Scholar
  43. Narr W, Suppe J (1991) Joint spacing in sedimentary rocks. J Struct Geol 11:1037–1048 CrossRefGoogle Scholar
  44. Nenna F, Aydin A (2011a) The formation and growth of pressure solution seams in clastic rocks: a field and analytical study. J Struct Geol 33:633–643 CrossRefGoogle Scholar
  45. Nenna F, Aydin A (2011b) The role of pressure solution seam and joint assemblages in the formation of strike-slip and thrust faults in a compressive tectonic setting: the Variscan of southwest Ireland. J Struct Geol 33:1595–1610 CrossRefGoogle Scholar
  46. Olson JE (2003) Sublinear scaling of fracture aperture versus length: an exception or the rule? J Geophys Res 108(B9):2413 CrossRefGoogle Scholar
  47. Olson JE (2004) Predicting fracture swarms—the influence of subcritical crack growth and the crack-tip process zone on joint spacing in rock. In: Engelder T, Gosgrove JW (eds) The initiation, propagation, and arrest of joints and other fractures. Special publications, vol 231. Geological Society, London, pp 73–87 Google Scholar
  48. Onasch CM (1993) Determination of pressure solution shortening in sandstones. Tectonophysics 227:145–159 CrossRefGoogle Scholar
  49. Peacock DCP, Azzam IN (2006) Development of scaling relationships of a stylolite population. J Struct Geol 28:1883–1889 CrossRefGoogle Scholar
  50. Pyles DR (2008) Multiscale stratigraphic analysis of a structurally confined submarine fan: carboniferous Ross Sandstone, Ireland. Am Assoc Pet Geol Bull 92:557–587 Google Scholar
  51. Railsback B (1998) Evaluation of spacing of stylolites and its implications for self-organization of pressure dissolution. J Sediment Res 68:2–7 Google Scholar
  52. Renard F, Ortoleva P, Gratier JP (1997) Pressure solution in sandstones: influence of clays and dependence on temperature and stress. Tectonophysics 280:257–266 CrossRefGoogle Scholar
  53. Renshaw CE, Pollard DD (1994) Numerical simulation of fracture set formation: a fracture mechanics model consistent with experimental observations. J Geophys Res 99:9359–9372 CrossRefGoogle Scholar
  54. Renshaw CE, Park JC (1997) Effect of mechanical interactions on the scaling of fracture length and aperture. Nature 386:482–484 CrossRefGoogle Scholar
  55. Rider MH (1974) The Namurian of West County Clare. Proc R Ir Acad 74B:125–143 Google Scholar
  56. Rives T, Razack M, Petit J-P, Rawnsley KD (1992) Joint spacing: analogue and numerical simulations. J Struct Geol 14:925–937 CrossRefGoogle Scholar
  57. Ruf JC, Rust KA, Engelder T (1998) Investigating the effect of mechanical discontinuities on joint spacing. Tectonophysics 295:245–257 CrossRefGoogle Scholar
  58. Scholz CH (2002) The mechanics of earthquakes and faulting. Cambridge University Press, Cambridge, 471 pp CrossRefGoogle Scholar
  59. Schultz RA, Soliva R, Fossen H, Okubo CH, Reeves DM (2008) Dependence of displacement–length scaling relations for fractures and deformation bands on volumetric changes across them. J Struct Geol 30:1405–1411 CrossRefGoogle Scholar
  60. Segall P, Pollard DD (1983) Joint formation in granitic rock of the Sierra Nevada. Geol Soc Am Bull 94:563–575 CrossRefGoogle Scholar
  61. Sleeman AG, Pracht M (1994) Geology of South Cork. Geological survey of Ireland, 58 pp Google Scholar
  62. Sleeman AG, Pracht M (1999) Geology of the Shannon Estuary. Geological survey of Ireland, 77 pp Google Scholar
  63. Stockdale B (1922) Stylolites: their nature and origin. Indiana University studies, vol IX, 97 pp Google Scholar
  64. Tavani S, Storti F, Muñoz JA (2010) Scaling relationships between stratabound pressure solution cleavage and layer thickness in a folded carbonate multilayer of the Northern Apennines (Italy). J Struct Geol 32:278–287 CrossRefGoogle Scholar
  65. Vermilye JM, Scholz CH (1995) Relation between vein length and aperture. J Struct Geol 17:423–434 CrossRefGoogle Scholar
  66. Vermilye JM, Scholz CH (1998) The process zone: a microstructural view of fault growth. J Geophys Res 103:12223–12237 CrossRefGoogle Scholar
  67. Villaescusa E, Brown ET (1992) Maximum likelihood estimation of joint size from trace length measurements. Rock Mech Rock Eng 25:67–87 CrossRefGoogle Scholar
  68. Walsh JJ, Watterson J (1993) Fractal analysis of fracture patterns using the standard box-counting technique: valid and invalid methodologies. J Struct Geol 15:1509–1512 CrossRefGoogle Scholar
  69. Willemse EJM, Pollard DD (1998) On the orientation and patterns of wing cracks and solution surfaces at the tips of a sliding flaw or fault. J Geophys Res 103:2427–2438 CrossRefGoogle Scholar
  70. Wu H, Pollard DD (1995) An experimental study of the relationships between joint spacing and layer thickness. J Struct Geol 17:887–905 CrossRefGoogle Scholar
  71. Yielding G, Walsh JJ, Watterson J (1992) The prediction of small-scale faulting in regional extension. First Break 10:449–460 Google Scholar
  72. Zhou X, Aydin A (2010) Mechanics of pressure solution growth and evolution. J Geophys Res 115:B12207 CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geosciences 2012

Authors and Affiliations

  1. 1.Rock Fracture Project, Department of Geological and Environmental SciencesStanford UniversityStanfordUSA

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