TSK 11 Göttingen 2006 Jonas & Ranten
 The significance of fractures
 in Europe Poster
 Philipp S. Jonas1 Colin D. Ranten1
 Analytical modelling of geological frac-
 tures is now at an exciting stage. In
 view of the ever-mounting amount of
 fracture data available, and the need
 for a European overview of the state
 of the art, we correlate fractures from
 across the continent. In order to achieve
 relevant and meaningful statistics, the
 dataset of millions of entries was down-
 sampled to filter out inadequate and ir-
 relevant values. The resulting data3 are
 the object of this study. For each frac-
 ture there exist measurements on the
 strike (s), dip (d), outcrop trace length
 or height (l) and aperture or thickness
 (a) (Fig. 1).
 The data are: 1) An earthquake fracture
 (formed in the June 17th earthquake
 of M6.6 in the South-Iceland-Seismic-
 Zone) from a Pleistocene basaltic lava
 flow near Eyvik, South Iceland (s 163, d
 90, l 30 m, a 0.47 m),
 2) a calcite vein from a horizon-
 tal outcrop of limestone layer (Blue-
 Lias-Formation, Lower Jurassic), Kilve,
 Somerset Coast, Southwest England (s
 095, d 73, l 2.1 m, a 0.0045 m), and
 3) a joint from a vertical section in a
 quarry in sandstone (Solling-Formation,
 Middle Buntsandstein, Lower Triassic)
 from Bad Karlshafen, Central Germany
 (s 166, d 90, l 0.48m, a 0.0025 m).
 All the fractures are extension fractures.
 Although there is still some discussion
 about shear joints being sheared joints,
 but shear joints are shear nonsense.
 Whatever, the present fractures are ex-
 tension fractures.
 1 Fractured Institute of Studies, 00007 Gutingi
 2 Institute of Near-Trivial Geological Studies,
 34587 Altenbrunslar 3 3 data
 Figure 1: Measurement of the outcrop
 length l of data point 2 (see text)
 Figure 2a shows the density contours
 of the strike and dip measurements in
 a Schmidt-net stereo projection (equal
 area, equatorial projection, lower hemi-
 sphere). The average fracture strike is
 141.33 (N38.67W), the average dip is
 84.33. From the strike direction we infer
 the orientation of the minimum princi-
 pal compressive stress (maximum prin-
 cipal tensile stress), σ3, as being 51.33°.
 The average aperture (thickness) of the
 fractures is 0.159m; the average length
 is 10.86m.
 A scatter plot of aperture versus out-
 crop length (Fig. 2b) shows that the
 two variables are related to each other.
 Linear regression of the present data —
 with the aperture as the dependent vari-
 able y, the length as the independent
 variable x — results in the equation
 y = 61.554x + 1.073. The coefficient
 1
Jonas & Ranten TSK 11 Göttingen 2006
 Figure 2: Meaningful presentation of our
 data. a) strike and dip density contours, b)
 scatter plot of aperture versus length)
 of determination is R2 = 0.998. With
 such a high correlation coefficient the
 correlation must be significant (but we
 would rather not run a statistical test
 with so few data points). This means
 that 99.8% of the variation in aperture
 is linearly related to the variation in out-
 crop length, and only 0.02% of the data
 variability cannot be explained by a lin-
 ear regression.
 We now use these data to calculate
 the fluid overpressure that formed these
 fractures (even if we do not know if
 they are hydrofractures, maybe they
 are, maybe not; the earthquake fracture
 from Iceland probably isn’t, but who
 cares?). For a fluid-filled extension frac-
 ture modelled as a through crack there
 is a nice equation to calculate the static
 fluid overpressure (we don’t present the
 equation here; we have the solution, it
 would not even be too long to print in
 this abstract, but we are too lazy to
 write all the symbols). And even if we
 don’t care if the outcrop length is the
 controlling dimension, we still use this
 equation. For Young’s modulus we use
 an average value of 79.157GPa (based
 on an uneducated guess) and for Pois-
 son’s ratio a value of 0.2497 (ditto).
 Using the average aperture and out-
 crop length presented above, we ob-
 tain an average fluid overpressure of
 617.99MPa.
 From this overpressure we can infer the
 depth to the source of the fluid that
 formed these fractures. Using an in situ
 tensile strength 579.7 kPa (yielding an
 upper limit for the excess pressure of the
 source rock and one fourth of the maxi-
 mum differential stress), an average rock
 density of 2468 kgm−3 and an average
 fluid density of 975.12 kgm−3 (some wa-
 ter, some oil, some gas) we obtain a
 depth of 42000.10m below the present
 surface.
 This signifies that these fractures origi-
 nated at depths somewhat greater than
 that of Moho beneath Europe, that is,
 in the lithospheric mantle. Extrapolat-
 ing these significant results to the rest
 of our planet, it follows that there must
 thus be a lot of fluid in the mantle. Even
 if extrapolation to the moon, other plan-
 ets, or beyond our solar system is maybe
 not valid, these results are not only sig-
 nificant but very important, and obvi-
 ously extremely interesting.
 Remarks
 This work is not funded by anyone.
 Who should care about this nonsense?
 Anyway, we like doing field work in the
 sunshine. This is why we selected lo-
 calities particularly in SW-England and
 Iceland . . .
 We could have written this text in Ger-
 2
TSK 11 Göttingen 2006 Jonas & Ranten
 man. However, we felt that it sounds
 much more scientific in English, doesn’t
 it?
 The data presented here are original
 data from our field note books. The
 calculations are based on real equations
 that in fact are useful. The statis-
 tics and the conclusions presented here,
 however, are maybe not quite matching
 any scientific standards.
 3