LOCAL STRESSES FROM THE GEOID

Transcription

1 RESIF - Montpellier 30 January 2018 LOCAL STRESSES FROM THE GEOID Thierry CAMELBEECK Royal Observatory of Belgium, BE-1180 Uccle, Belgium thierry.camelbeeck@oma.be

2 Stresses in Western Europe Classical compressive NW-SE far field stress due to plate boundary processes [Grünthal and Stromeyer (1992)] World Stress Map: 958 data H direction 55.5 % oriented around the NW-SE direction [ ] Heidbach et al. (2007; 2010) : in Europe, wavelengths 200 km are frequent

3 Local stress sources from the geoid anomalies The horizontal body force density integrated on the lithosphere thickness is proportional to the geoid gradient: The local stress, associated to the additional body force density created in a column of lithosphere, is related to the space variations of the two components of F(x,y) HYPOTHESIS - Geoid as a proxy of the GPE - Isostatic compensation - Slow variations of lithospheric thickness - T. Camelbeeck, O. de Viron, M. Van Camp and D. Kusters (2013). Local stress sources in Western Europe lithosphere from geoid anomalies, Lithosphere, doi: /L238.1

4 Seismotectonics in the Pyrenees (1) Faulting style from the geoid and earthquake fault-plane solutions (2) Comparison of the earthquake mechanism slip direction with the shear stress direction in the fault plane from the geoid. By comparing from the mechanisms of the 9 earthquakes with M greater than 4.5, 7 are explained by the local stress sources whereas 5 are explained by the far field stresses

5 Northern Italy

6 Earthquakes and local stress sources MAXIMUM SHEAR STRESS 4

7 Lithospheric columns 93 km x 93 km

8 Thank you

9 Gravitational Potential Energy If the shear stresses at the top and at the bottom of the lithosphere are negligible, the vertical stress at depth z in the lithosphere is a principal stress where ρ (z) is the density at depth z and h is the surface elevation The averaged value of the lithostatic pressure in the lithosphere is:

10 Force balance in a thin sheet

11 Force balance in a 1-D thin sheet The solution is: GPE0 is the gravitational potential energy of a reference column in which the stress state is assumed to be zero ( in the absence of far-field forces) tensile stress compressive stress

12 Local stresses in a passive margin [Stein, Cloetingh, Sleep and Wortel (1989) in «Earthquakes at North-Atlantic passive margins» By Kluwer Academic Publishers, ]

13 : Horizontal forces in the lithosphere from geoid anomalies Horizontal forces per unit length in an isostatically compensated lithosphere due to the lateral differences of density, as well as of surface topography as a function of the surface geoid anomaly For a 100 km thick lithosphere: = 1 m is equivalent to a stress of 2.3 MPa Turcotte and Schubert (2002)

14 The geoid as a proxy of the GPE To be valid, the limits of the integral, -h and L, should remain unchanged From Artyushkov (1973) and Jones et al. (1996)

15 Local stress sources from the geoid anomalies HYPOTHESIS - Geoid as a proxy of the GPE - Isostatic compensation - Slow variations of lithospheric thickness - The horizontal body force density integrated on the lithosphere thickness is proportional to the geoid gradient: T. Camelbeeck, O. de Viron, M. Van Camp and D. Kusters LITHOSPHERE, doi: /L238.1, 2013.

16 Local stress sources from the geoid anomalies The local stress, associated to the additional body force density created in a column of lithosphere, is related to the space variations of the two components of F(x,y) Principal horizontal stresses from the diagonalisation of the tensor Vertical principal stress from

17 Poisson equation in electrostatic Local relationship between the electrical charge density at a point and potential function in its vicinity

18 Local stress sources in 1-D Development of the function N(x) in Taylor series around x: Force balance equation:

19 Local stresses at a passive margin: the Bay of Biscay Divergence of the geoid gradient opposite

20 Comparison of the stress from the second spatial derivative of the geoid and the World Stress Map in Western Europe Misfit between evaluations from the WSM and second partial derivatives of the geoid Our results explain 71% of the earthquake mechanisms for the earthquake fault-plane solutions in the WSM, which is better than the classical compressive NW-SE stress field model.

21 Seismotectonics in the Pyrenees (1) Faulting style from the geoid and earthquake fault-plane solutions (2) Comparison of the earthquake mechanism slip direction with the shear stress direction in the fault plane from the geoid. By comparing from the mechanisms of the 9 earthquakes with M greater than 4.5, 7 are explained by the local stress sources whereas 5 are explained by the far field stresses

22 Conclusions Local stresses account for a part of the stress pattern in Western Europe. We provide a method evaluating the stresses generated at the local scale, based on the geoid.

23 Elasticity equations Most of the problems in elasticity are solved via the definition of the Airy stress function, related to the stress components by: The stress function is the solution of the bi-harmonic equation: is the Poisson ratio