# Coulomb stress transfer

Coulomb stress transfer is a seismic-related geological process of stress changes to surrounding material caused by local discrete deformation events.[1] Using mapped displacements of the Earth's surface during earthquakes, the computed Coulomb stress changes suggest that the stress relieved during an earthquake not only dissipates but can also move up and down fault segments, concentrating and promoting subsequent tremors.[2] Importantly, Coulomb stress changes have been applied to earthquake-forecasting models that have been used to assess potential hazards related to earthquake activity.[1][2][3][4][5]

## Coulomb stress change

The Coulomb failure criterion requires that the Coulomb stress exceeds a value σf defined by the shear stress τB, normal stress σB, pore pressure p, and coefficient of friction μ of a failure plane, such that

σf = τB – μ(σB – p) [1]

It is also often assumed that changes in pore fluid pressure induced by changes in stress are proportional to the normal stress change across the fault plane.[6] These effects are incorporated into an effective coefficient of friction μ’, such that

Δσf = ΔτB – μ’(ΔσB) [6]

This simplification allows for the calculation of Coulomb stress changes on a fault plane to be independent of the regional stress field but instead depends on the fault geometry, sense of slip, and coefficient of friction.

The significance of the Coulomb stress changes was discovered when mapped displacements of neighbouring fault movements were used to calculate Coulomb stress changes along faults. Results revealed that the stress relieved on faults during earthquakes did not simply dissipate, but also moved up and down fault segments. Moreover, mapped lobes of increased and decreased Coulomb stress around local faults exhibited increased and decreased rates of seismicity respectively shortly after neighboring earthquakes, but eventually return to their background rate over time.[7][8]

## Earthquake stress triggering

Stress triggering describes the responsive rupturing of faults from increases in Coulomb stress caused by exogenous deformation events.[1] Although neighboring displacements often yield small magnitude stress changes, areas of disturbed Coulomb stress states have been successfully used to explain the spatial distribution of stress triggered aftershock seismicity.

On June 28, 1992, a M7.3 earthquake that struck near Landers, California was followed (about three hours later) by the M6.5 Big Bear foreshock earthquake 40 km away. Calculated Coulomb stress changes from both of these earthquakes showed a westward lobe of 2.1–2.9 bars of increased Coulomb stress to have resulted from the displacement associated with both earthquakes. Of the roughly 20,000 aftershocks that occurred 25 days after June 28 within a 5 km radius, more than 75% occurred in areas where Coulomb stress had increased and less than 25% occurred in areas where Coulomb stress had dropped.[1]

Another successful case study of earthquake prediction occurred along Turkey's North Anatolian fault system. From 1939 to 1999, the Anatolian fault system had witnessed ten earthquakes of M6.6 or greater. The evolution of the Coulomb stress changes along the North Anatolian fault as a result of these earthquakes showed that 11 of the 13 ruptures occurred in areas of increased Coulomb stress caused by a previous rupture.[3][4] This method has been also used to predict seismicity around active volcanoes submitted to significant variation of stress in the magma chamber.[9]

## Earthquake prediction

Although no official Coulomb stress transfer prediction model is being used by government agencies, geologic surveys often analyze earthquake threats using Coulomb stress theory. As an example, the last of the previous thirteen earthquakes along Turkey's North Anatolian Fault, near the town of Duzce, was successfully predicted by local geologists before the rupture occurred. This allowed for engineers to evacuate unstable structures and limit significant damage.[2] Scientists estimate that the probability of another earthquake along the Anatolian fault system is 62% over the next 30 years and will be located threateningly close to Istanbul.[3]

## References

1. King, G.C.P.; Stein, R.S.; Lin, J. (1994). "Static stress changes and the triggering of earthquakes". Bulletin of the Seismological Society of America. 84 (3): 935–953.
2. ^ a b c Stein, R.S. (2003). "Earthquake Conversations". Scientific American. 288 (1): 72–79. Bibcode:2003SciAm.288a..72S. doi:10.1038/scientificamerican0103-72. PMID 12506427.
3. ^ a b c Stein, R.S.; Barka, A.A.; Dieterich, J.H. (1997). "Progressive failure on the north Anatolian fault since 1939 by earthquake stress triggering". Geophysical Journal International. 128 (3): 594–604. Bibcode:1997GeoJI.128..594S. doi:10.1111/j.1365-246x.1997.tb05321.x.
4. ^ a b Barka, A.A.; Rockwell, T. K.; Reilinger, R.; Imren, C. (1999). "Kinematics of the central marmara sea ridges". Eos, Transactions, American Geophysical Union. 80 (46): 664.
5. ^ Parsons, T.E.; Dreger, D.S. (2000). "Static-stress impact of the 1992 landers earthquake sequence on nucleation and slip at the site of the 1999 M = 7.1 hector mine earthquake, southern California". Geophysical Research Letters. 27 (13): 1949–1952. Bibcode:2000GeoRL..27.1949P. doi:10.1029/1999gl011272. S2CID 49218075.
6. ^ a b Beeler, N.M.; Simpson, R. W., J.; Hickman, S. H.; Lockner, D. A. (2000). "Pore fluid pressure, apparent friction, and coulomb failure". Journal of Geophysical Research. 105 (25): 542. Bibcode:2000JGR...10525533B. doi:10.1029/2000JB900119. S2CID 4685444.`{{cite journal}}`: CS1 maint: multiple names: authors list (link)
7. ^ Dieterick, J.H.; Kilgore, B.D. (1994). "Direct observation of frictional contacts; new insights for state-dependent properties". Pure and Applied Geophysics. 143 (1–3): 283–302. Bibcode:1994PApGe.143..283D. CiteSeerX 10.1.1.494.3198. doi:10.1007/bf00874332. S2CID 129103586.
8. ^ Toda, S.; Stein, R.S. (2003). "Toggling of seismicity by the 1997 Kagoshima earthquake couplet; a demonstration of time-dependent stress transfer". Journal of Geophysical Research. 108 (B12): 12. Bibcode:2003JGRB..108.2567T. CiteSeerX 10.1.1.459.2321. doi:10.1029/2003jb002527.
9. ^ J.Gargani; L.Geoffroy.; S.Gac, S.Cravoisier (2006). "Fault slip and Coulomb stress variations around a pressured magma reservoir : consequences on seismicity and magma intrusion". Terra Nova. 18 (6): 403–411. Bibcode:2006TeNov..18..403G. doi:10.1111/j.1365-3121.2006.00705.x. S2CID 128537724.
10. ^ Zhang, Q.; Zhang P.; Wang C.; Wang Y.; Ellis M.A. (2003). "Earthquake triggering and delaying caused by fault interaction on Xianshuihe fault belt, southwestern China". Acta Seismologica Sinica. 16 (2): 156–165. Bibcode:2003AcSSn..16..156Z. doi:10.1007/s11589-003-0018-5. S2CID 128487233.