The central role of fluids in seismic faulting is known in all stages of the earthquake cycle, i.e., in the nucleation processes, in the dynamic propagation and in the post-seismic evolution. Namely, pore fluid pressure affects the whole earthquake process starting from fault nucleation1,2, continues through thermally-activated pressurization3,4,5,6,7 and mechanical lubrication8,9 and finally plays a role in triggering aftershocks10,11,12,13,14. Interest on the first step of the process (fault reactivation and rupture nucleation) has been recently revived by several cases of human activities, which are indicted for having induced destructive earthquakes. Davies et al.15 compiled a list of 190 possible examples of induced earthquakes, with magnitude spanning between 1.0 and 7.9, connected with mining, artificial reservoir impoundment, geothermal operations16,17, oil and gas field production and hydraulic fracturing (i.e., fracking).

Most earthquakes induced by anthropogenic activities concern small magnitude events (M < 3.0) located in the vicinity of the activities themselves18,19. Here we are not interested in such earthquakes, which generally constitute more a nuisance than a real danger. Indeed, we are interested in the other type of induced seismicity, which regards large events (M > 5.5) on nearby active tectonic faults, at a distance up to a few tens of kilometers20,21. This type of induction is appropriately termed triggered (or activated) seismicity22, since human activities provide the tiny — but fundamental — input to a system which is independently close to instability. A small action produces a large reaction, just as the modest pressure of a finger on a gun trigger releases the large explosive energy stored in the propellant. Such a type of induced seismicity has been so far mostly associated with the impoundment of artificial water reservoirs, but occasionally also with gas and oil production.

Triggered seismicity is the most important and dangerous type of induced seismicity and should not be confused with its stablemate, simply called induced seismicity; the latter is commonly associated with drilling or hydrofracture and generally implies large local stresses, but small earthquakes. In fact, to induce fresh fracture in the bulk rock the applied stresses must be, by definition, equal to those determined by hydrofracture techniques. However, event size is small because these large stresses are spatially concentrated and can only induce fracture on small volumes of rock. On the contrary, triggered seismicity involves large tectonic structures, where the stress has been independently accumulating to a near failure conditions by the internal Earth's dynamics23,24, with the human activity providing only the “last straw”.

Although the unequivocal discrimination between naturally occurring and man-triggered earthquakes is difficult25,26, there exist some hardly questionable cases. The first documented case of reservoir-triggered seismicity occurred in 1932 in Algeria's Oued Fodda Dam. Another prominent example is provided by the realization of the Koyna Dam, India, which was followed in 1967 by the M6.5 Koynanagar earthquake, where 180 people died and 1,500 were injured27. Other relevant cases are the M6.1 Oroville, California, earthquake, also attributed to a reservoir and the M5.4 Aswan, Egypt, earthquake in 198121, which occurred 15 years after the filling of the Nasser artificial lake. The largest and most recent case of reservoir triggered earthquakes is possibly that of the Zipingpu Dam in China, which is indicted for triggering the May 12 2008 M7.9 Wenchuan earthquake, killing some 80,000 people28,29,30.

Dams are most often at the root of man-triggered seismicity, but there are some notable additions. Caused by the injection of pressurized fluids into a 367-m-deep borehole at the Rocky Mountain Arsenal, Colorado was the Denver earthquake sequence in the '60s, which culminated in a M5.3 event31. The injection of pressurized fluids to stimulate the production of an oil field, induced a M5.4 earthquake in Caviaga, Italy, in 195132 and may have also triggered the earthquake sequence of May 20-29 2012 in Emilia, Italy, with two events of M6.0 and another five above M5.3, which resulted in the death of 27 people as well as a major wound to the gasping Italian economy33,34.

The physical problem of quantifying the man-triggering mechanism is a problem still lacking a comprehensive approach, even if the basic constitutive equations have been known since quite long ago. We work out a solution on the basis of the following phenomenological ingredients:

1 Time invariance; since the time scale of earthquake recurrence on the same fault segment is 100-1000 years and the evolution of the driving mechanism is a geological process 3–4 order of magnitudes slower, earthquakes can be taken as repetitions on existing weakness zones — the faults. 2 Stress on faults are close to failure by an unknown extent; the stress history on faults depends on the interaction with neighboring faults and on a variety of factors practically impossible to quantify. 3 Low static friction coefficients; static friction on fault zones is much lower than in bulk (undamaged) rocks and in the laboratory (cf.35) and has values μ < 0.336,37,38,39,40,41. 4 Very low stress thresholds for triggering; additional fluid pressures of 0.05 MPa due to artificial water reservoirs have activated destructive earthquakes17; similar low values occur in the dynamic triggering by nearby earthquakes42,43. 5 Earthquakes triggered with considerable time delay; earthquakes have been triggered with time delays > 10 years17,21. 6 Earthquakes triggered at considerable distance in space; earthquakes have been triggered at up to 30 kilometers17,21.

According to such phenomenological constraints, earthquake triggering is likely to occur only on the most favorably oriented pre-existent faults, which are at an angle θ to the largest (in norm) principal stress. This angle is given by , i.e., according to the above-mentioned values of μ, it is comprised in the 37°–45° range. Given that the exact μ values are impossible to know beforehand, we consider the asymptotic limit μ → 0, which corresponds to the maximum shear stress orientation of 45° to the largest principal stress. In addition, among the optimally oriented faults, only those in close proximity to failure will be triggered. In this framework, we can write the failure criterion as1,44,45:

where μ formally is the static friction coefficient (often written as μ u or μ s in the literature), σ I and σ III are the first and third principal stresses, respectively. p fluid is pore fluid pressure, which we will consider in the range 100–150% of the hydrostatic load (see Numerical results and discussion of the failure threshold section). In other words, we assume that under normal conditions the fluid is in the hydrostatic pressure thanks to a drained percolation-driven circulation46 and we consider the perturbation due to an externally induced pore fluid pressure increase. The failure stress σ R is a material property, which we assume to be fixed. By keeping μ constant, we implicitly assume that it represents an average value over the whole fault surface (i.e. we neglect any possible effect of spatial heterogeneities). Moreover, equation (1) also disregards any possible coupling with temperature variations and second-order effects47,48,49.