Raul Madariaga

The 2010 Mw 8.8 Maule Megathrust Earthquake of Central Chile, Monitored by GPS

Rupture kinematics of this very large earthquake were obtained from high-resolution Global Positioning System data. Large earthquakes produce crustal deformation that can be quantified by geodetic measurements, allowing for the determination of the slip distribution on the fault. We used data from Global Positioning System (GPS) networks in Central Chile to infer the static deformation and the kinematics of the 2010 moment magnitude (Mw) 8.8 Maule megathrust earthquake. From elastic modeling, we found a total rupture length of ~500 kilometers where slip (up to 15 meters) concentrated on two main asperities situated on both sides of the epicenter. We found that rupture reached shallow depths, probably extending up to the trench. Resolvable afterslip occurred in regions of low coseismic slip. The low-frequency hypocenter is relocated 40 kilometers southwest of initial estimates. Rupture propagated bilaterally at about 3.1 kilometers per second, with possible but not fully resolved velocity variations.

Dynamic faulting under rate-dependent friction

We discuss the effects of rate-dependent friction on the propagation of seismic rupture on active faults. Several physicists using Burridge and Knopoffs box and spring model of faulting have proposed that fault complexity may arise from the spontaneous development of a self-similar stress distribution on the fault plane. If this model proves to be correct, it has important consequences for the origin of the complexity of seismic sources. In order to test these ideas on a more realistic earthquake model, we developed a new boundary integral equation method for studying rupture propagation along an antiplane fault in the presence of nonlinear rate-dependent friction. We study rupture dynamics of models with single and twin asperities. In our models, asperities are places on the fault with a higher value of prestress. Othewise all fault parameters are homogeneous. We show that for models with such asperities, a slip velocity weakening friction leads to the propagation of supersonic healing phases and to the spontaneous arrest of fracture if the prestress outside the asperities is low enough. For models with asperities, we can also observe narrow slip velocity pulses, qualitatively similar to the so-called Heaton pulses observed in some earthquake accelerograms. We also observe a complex distribution of stress after the rupture that depends on details of the initial distribution of asperities and on the details of the friction law.

Dynamic modeling of the 1992 Landers earthquake

We have used observed band-pass filtered accelerograms and a previously determined slip distribution to invert for the dynamic rupture propagation of the 1992 Landers earthquake. In our simulations, dynamic rupture grows under the simultaneous control of initial stress and rupture resistance by friction, which we modeled using a simple slip-weakening law. We used a simplified Landers fault model where the fault segments were combined into a single vertical, planar fault. By trial and error we modified an initial stress field, inferred from the kinematic slip distribution proposed by Wald and Heaton [1994], until dynamic rupture generated a rupture history and final slip distribution that approximately matched those determined by the kinematic inversion. We found that rupture propagation was extremely sensitive to small changes in the distribution of prestress and that a delicate balance with energy release rate controls the average rupture speed. For the inversion we generated synthetic 0.5 Hz ground displacements using an efficient Greens function propagator method (AXITRA). This method enables us to propagate the radiation generated by the dynamic rupture to distances greater than those feasible using the finite difference method. The dynamic model built by trial-and-error inversion provides a very satisfactory fit between synthetics and strong motion data. We validated this model using records from stations used in the slip inversion as well as some which were not included. We also inverted for a complementary model that fits the data just as well but in which the initial stress was perfectly uniform while rupture resistance was heterogeneous. This demonstrates that inversion of ground motion is nonunique.

Complexity of seismicity due to highly rate‐dependent friction

We study a simple antiplane fault of finite length embedded in a homogeneous, isotropic, elastic solid in order to understand the origin of seismic source heterogeneity in the presence of nonlinear rate-dependent friction. All the mechanical properties of the medium and friction are assumed to be homogeneous. Starting from a heterogeneous initial stress distribution, we apply a slowly increasing uniform stress load far from the fault and we simulate the seismicity for more than 20,000 events, in some cases. The style of seismicity produced by this model is determined by a control parameter which measures the degree of rate dependence of friction. For classical friction models with rate-independent friction, no complexity appears and seismicity is perfectly periodic. For weakly rate-dependent friction, seismicity becomes slightly nonperiodic but most events are still characteristic earthquakes. When friction is highly rate-dependent, seismicity is completely irregular and ruptures of all sizes occur inside the fault. Highly rate-dependent friction destabilizes the healing process, producing premature healing of slip and partial stress drop. Premature healing causes rupture to take the form of narrow, propagating slip episodes, the so-called Heatons [1990] pulses. Partial stress drop produces large variations in the state of stress which, in turn, produce earthquakes of different sizes. We make the conjecture that all models in which static stress drop is only a fraction of the dynamic stress drop produce stress heterogeneity.

ITERATIVE ASYMPTOTIC INVERSION IN THE ACOUSTIC APPROXIMATION

We propose an iterative method for the linearized prestack inversion of seismic profiles based on the asymptotic theory of wave propagation. For this purpose, we designed a very efficient technique for the downward continuation of an acoustic wavefield by ray methods. The different ray quantities required for the computation of the asymptotic inverse operator are estimated at each diffracting point where we want to recover the earth image. In the linearized inversion, we use the background velocity model obtained by velocity analysis. We determine the short wavelength components of the impedance distribution by linearized inversion of the seismograms observed at the surface of the model. Because the inverse operator is not exact, and because the source and station distribution is limited, the first iteration of our asymptotic inversion technique is not exact. We improve the images by an iterative procedure. Since the background velocity does not change between iterations. There is no need to retrace rays,...

Intense foreshocks and a slow slip event preceded the 2014 Iquique Mw 8.1 earthquake

The earthquake that rocked northern Chile Subduction zones often produce the largest earthquakes on Earth. A magnitude 8.2 earthquake (Iquique) occurred in one such zone off the coast of northern Chile on 1 April 2014, in a seismic gap that had not experienced a large earthquake since the 9.0 one in 1877. Ruiz et al. analyzed continuous GPS data to monitor the movement of plates over time in this region, including before and after major earthquakes. The most recent large quake was preceded by an extended series of smaller earthquakes and creeping westward movement of the coastline. Science, this issue p. 1165 The intense and anomalous seismicity preceding the mainshock was the final step of a slow slip event. The subduction zone in northern Chile is a well-identified seismic gap that last ruptured in 1877. The moment magnitude (Mw) 8.1 Iquique earthquake of 1 April 2014 broke a highly coupled portion of this gap. To understand the seismicity preceding this event, we studied the location and mechanisms of the foreshocks and computed Global Positioning System (GPS) time series at stations located on shore. Seismicity off the coast of Iquique started to increase in January 2014. After 16 March, several Mw > 6 events occurred near the low-coupled zone. These events migrated northward for ~50 kilometers until the 1 April earthquake occurred. On 16 March, on-shore continuous GPS stations detected a westward motion that we model as a slow slip event situated in the same area where the mainshock occurred.

Criticality of Rupture Dynamics in 3-D

We study the propagation of seismic ruptures along a fault surface using a fourth-order finite difference program. When prestress is uniform, rupture propagation is simple but presents essential differences with the circular self-similar shear crack models of Kostrov. The best known is that rupture can only start from a finite initial patch (or asperity). The other is that the rupture front becomes elongated in the in-plane direction. Finally, if the initial stress is sufficiently high, the rupture front in the in-plane direction becomes super-shear and the rupture front develops a couple of ‘‘ears’’ in the in-plane direction. We show that we can understand these features in terms of single nondimensional parameter k that is roughly the ratio of available strain energy to energy release rate. For low values of k rupture does not occur because Griffith’s criterion is not satisfied. A bifurcation occurs when k is larger than a certain critical value, kc. For even larger values of k rupture jumps to super-shear speeds. We then carefully study spontaneous rupture propagation along a long strike-slip fault and along a rectangular asperity. As for the simple uniform fault, we observe three regimes: no rupture for subcritical values of k, sub-shear speeds for a narrow range of supercritical values of k, and super-shear speeds for k\1.3kc. Thus, there seems to be a certain universality in the behavior of seismic ruptures.

A seismological study of the 1835 seismic gap in south-central Chile

We study the possible seismic gap in the Concepcion–Constitucion region of south-central Chile and the nature of the M = 7.8 earthquake of January 1939. From 1 March to 31 May 1996 a seismic network of 26 short period digital instruments was deployed in this area. We located 379 hypocenters with rms travel time residuals of less than 0.50 s using an approximate velocity distribution. Using the VELEST program, we improved the velocity model and located 240 high precision hypocenters with residuals less than 0.2 s. The large majority of earthquakes occurred along the Wadati–Benioff zone along the upper part of the downgoing slab under central Chile. A few shallow events were recorded near the chain of active volcanos on the Andes; these events are similar to those of Las Melozas near Santiago. A few events took place at the boundary between the coastal ranges and the central valley. Well constrained fault plane solutions could be computed for 32 of the 240 well located events. Most of the earthquakes located on the Wadati–Benioff zone had “slab-pull” fault mechanism due to tensional stresses sub-parallel to the downgoing slab. This “slab-pull” mechanism is the same as that of eight earthquakes of magnitude around 6 that are listed in the CMT catalog of Harvard University for the period 1980–1998. This is also the mechanism inferred for the large 1939 Chilean earthquake. A very small number of events in the Benioff zone had “slab-push” mechanisms, that is events whose pressureaxis is aligned with the slab. These events are found in double layered Wadati–Benioff zones, such as in northern Chile or Japan. Our spatial resolution is not good enough to detect the presence of a double layer, but we suspect there may be one.

Intermediate and deep earthquakes in Spain

Recent improvements in the seismological networks on the Ibero-Maghrebian region have permitted estimation of hypocentral location and focal mechanisms for earthquakes which occurred at South Spain, Alboran Sea and northern Morocco of deep and intermediate depth, with magnitudes between 3.5 and 4.5. Intermediate depth shocks, range from 60 to 100 km, with greater concentration located between Granada and Málaga. Fault-plane solutions of 5 intermediate shocks have been determined; they present a vertical plane in NE-SW or E-W direction. Seismic moments of about 1015 Nm and dimensions of about 1 km have been determined from digital records of Spanish stations.P-wave forms are complex. This may be explained by the crustal structure near the station, discontinuities in the upper mantle and inhomogeneities near the source. Deep activity at about 650 km has only 3 shocks since 1954 (1954, 1973, 1990). Shocks are located at a very small region. Fault-plane solutions show a consistent direction of the pressure axis dipping 45° in E direction. For the 1990 shock seismic moment is 1016 Nm and dimensions 2.6 km. TheP-waves are of simpler form with a single pulse. The intermediate and deep activities are not connected and no activity has been detected between 100 and 650 km. The intermediate shocks may be explained in terms of a recent subduction from Africa under Iberia in SE direction. The very deep activity must be related to a sunk detached block of lithospheric material still sufficiently cold and rigid to generate earthquakes.

On the Self-Healing Fracture Mode

We present the analytical solution for a fundamental fracture mode in the form of a self-similar, self-healing pulse. The existence of such a fracture mode was strongly suggested by recent numerical simulations of seismic ruptures but, to our knowledge, no formal proof of their origin has been proposed yet. We present a two-dimensional, anti-plane solution for fixed rupture and healing speeds that satisfies both the wave equation and crack boundary conditions for a simple Coulomb friction law in the absence of any rate or state dependence. This solution is an alternative to the classic self-similar crack solution by Kostrov. In practice, the self-healing impulsive mode rather than the expanding crack mode is selected depending on details of fracture initiation and is thereafter self-maintained. We discuss stress concentration, fracture energy, and rupture velocity and compare them to the case of a crack. The analytical study is complemented by various numerical examples and comparisons. On more general grounds, we argue that an infinity of marginally stable fracture modes may exist in addition to the crack solution or the impulsive fracture described here. Manuscript received 27 March 2002.