Intermediate- and long-term earthquake prediction.

Progress in long- and intermediate-term earthquake prediction is reviewed emphasizing results from California. Earthquake prediction as a scientific discipline is still in its infancy. Probabilistic estimates that segments of several faults in California will be the sites of large shocks in the next 30 years are now generally accepted and widely used. Several examples are presented of changes in rates of moderate-size earthquakes and seismic moment release on time scales of a few to 30 years that occurred prior to large shocks. A distinction is made between large earthquakes that rupture the entire downdip width of the outer brittle part of the earth's crust and small shocks that do not. Large events occur quasi-periodically in time along a fault segment and happen much more often than predicted from the rates of small shocks along that segment. I am moderately optimistic about improving predictions of large events for time scales of a few to 30 years although little work of that type is currently underway in the United States. Precursory effects, like the changes in stress they reflect, should be examined from a tensorial rather than a scalar perspective. A broad pattern of increased numbers of moderate-size shocks in southern California since 1986 resembles the pattern in the 25 years before the great 1906 earthquake. Since it may be a long-term precursor to a great event on the southern San Andreas fault, that area deserves detailed intensified study.

Scale dependence in earthquake phenomena and its relevance to earthquake prediction.

The recent discovery of a low-velocity, low-Q zone with a width of 50-200 m reaching to the top of the ductile part of the crust, by observations on seismic guided waves trapped in the fault zone of the Landers earthquake of 1992, and its identification with the shear zone inferred from the distribution of tension cracks observed on the surface support the existence of a characteristic scale length of the order of 100 m affecting various earthquake phenomena in southern California, as evidenced earlier by the kink in the magnitude-frequency relation at about M3, the constant corner frequency for earthquakes with M below about 3, and the sourcecontrolled fmax of 5-10 Hz for major earthquakes. The temporal correlation between coda Q-1 and the fractional rate of occurrence of earthquakes in the magnitude range 3-3.5, the geographical similarity of coda Q-1 and seismic velocity at a depth of 20 km, and the simultaneous change of coda Q-1 and conductivity at the lower crust support the hypotheses that coda Q-1 may represent the activity of creep fracture in the ductile part of the lithosphere occurring over cracks with a characteristic size of the order of 100 m. The existence of such a characteristic scale length cannot be consistent with the overall self-similarity of earthquakes unless we postulate a discrete hierarchy of such characteristic scale lengths. The discrete hierarchy of characteristic scale lengths is consistent with recently observed logarithmic periodicity in precursory seismicity.

Intermediate-term earthquake prediction.

An earthquake of magnitude M and linear source dimension L(M) is preceded within a few years by certain patterns of seismicity in the magnitude range down to about (M - 3) in an area of linear dimension about 5L-10L. Prediction algorithms based on such patterns may allow one to predict approximately 80% of strong earthquakes with alarms occupying altogether 20-30% of the time-space considered. An area of alarm can be narrowed down to 2L-3L when observations include lower magnitudes, down to about (M - 4). In spite of their limited accuracy, such predictions open a possibility to prevent considerable damage. The following findings may provide for further development of prediction methods: (i) long-range correlations in fault system dynamics and accordingly large size of the areas over which different observed fields could be averaged and analyzed jointly, (ii) specific symptoms of an approaching strong earthquake, (iii) the partial similarity of these symptoms worldwide, (iv) the fact that some of them are not Earth specific: we probably encountered in seismicity the symptoms of instability common for a wide class of nonlinear systems.

A selective phenomenology of the seismicity of Southern California.

Predictions of earthquakes that are based on observations of precursory seismicity cannot depend on the average properties of the seismicity, such as the Gutenberg-Richter (G-R) distribution. Instead it must depend on the fluctuations in seismicity. We summarize the observational data of the fluctuations of seismicity in space, in time, and in a coupled space-time regime over the past 60 yr in Southern California, to provide a basis for determining whether these fluctuations are correlated with the times and locations of future strong earthquakes in an appropriate time- and space-scale. The simple extrapolation of the G-R distribution must lead to an overestimate of the risk due to large earthquakes. There may be two classes of earthquakes: the small earthquakes that satisfy the G-R law and the larger and large ones. Most observations of fluctuations of seismicity are of the rate of occurrence of smaller earthquakes. Large earthquakes are observed to be preceded by significant quiescence on the faults on which they occur and by an intensification of activity at distance. It is likely that the fluctuations are due to the nature of fractures on individual faults of the network of faults. There are significant inhomogeneities on these faults, which we assume will have an important influence on the nature of self-organization of seismicity. The principal source of the inhomogeneity on the large scale is the influence of geometry--i.e., of the nonplanarity of faults and the system of faults.

The repetition of large-earthquake ruptures.

This survey of well-documented repeated fault rupture confirms that some faults have exhibited a "characteristic" behavior during repeated large earthquakes--that is, the magnitude, distribution, and style of slip on the fault has repeated during two or more consecutive events. In two cases faults exhibit slip functions that vary little from earthquake to earthquake. In one other well-documented case, however, fault lengths contrast markedly for two consecutive ruptures, but the amount of offset at individual sites was similar. Adjacent individual patches, 10 km or more in length, failed singly during one event and in tandem during the other. More complex cases of repetition may also represent the failure of several distinct patches. The faults of the 1992 Landers earthquake provide an instructive example of such complexity. Together, these examples suggest that large earthquakes commonly result from the failure of one or more patches, each characterized by a slip function that is roughly invariant through consecutive earthquake cycles. The persistence of these slip-patches through two or more large earthquakes indicates that some quasi-invariant physical property controls the pattern and magnitude of slip. These data seem incompatible with theoretical models that produce slip distributions that are highly variable in consecutive large events.

Hypothesis testing and earthquake prediction.

Requirements for testing include advance specification of the conditional rate density (probability per unit time, area, and magnitude) or, alternatively, probabilities for specified intervals of time, space, and magnitude. Here I consider testing fully specified hypotheses, with no parameter adjustments or arbitrary decisions allowed during the test period. Because it may take decades to validate prediction methods, it is worthwhile to formulate testable hypotheses carefully in advance. Earthquake prediction generally implies that the probability will be temporarily higher than normal. Such a statement requires knowledge of "normal behavior"--that is, it requires a null hypothesis. Hypotheses can be tested in three ways: (i) by comparing the number of actual earth-quakes to the number predicted, (ii) by comparing the likelihood score of actual earthquakes to the predicted distribution, and (iii) by comparing the likelihood ratio to that of a null hypothesis. The first two tests are purely self-consistency tests, while the third is a direct comparison of two hypotheses. Predictions made without a statement of probability are very difficult to test, and any test must be based on the ratio of earthquakes in and out of the forecast regions.

Implications of fault constitutive properties for earthquake prediction.

The rate- and state-dependent constitutive formulation for fault slip characterizes an exceptional variety of materials over a wide range of sliding conditions. This formulation provides a unified representation of diverse sliding phenomena including slip weakening over a characteristic sliding distance Dc, apparent fracture energy at a rupture front, time-dependent healing after rapid slip, and various other transient and slip rate effects. Laboratory observations and theoretical models both indicate that earthquake nucleation is accompanied by long intervals of accelerating slip. Strains from the nucleation process on buried faults generally could not be detected if laboratory values of Dc apply to faults in nature. However, scaling of Dc is presently an open question and the possibility exists that measurable premonitory creep may precede some earthquakes. Earthquake activity is modeled as a sequence of earthquake nucleation events. In this model, earthquake clustering arises from sensitivity of nucleation times to the stress changes induced by prior earthquakes. The model gives the characteristic Omori aftershock decay law and assigns physical interpretation to aftershock parameters. The seismicity formulation predicts large changes of earthquake probabilities result from stress changes. Two mechanisms for foreshocks are proposed that describe observed frequency of occurrence of foreshock-mainshock pairs by time and magnitude. With the first mechanism, foreshocks represent a manifestation of earthquake clustering in which the stress change at the time of the foreshock increases the probability of earthquakes at all magnitudes including the eventual mainshock. With the second model, accelerating fault slip on the mainshock nucleation zone triggers foreshocks.

Slip complexity in earthquake fault models.

We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.

Dynamic friction and the origin of the complexity of earthquake sources.

We study a simple antiplane fault of finite length embedded in a homogeneous isotropic elastic solid to understand the origin of seismic source heterogeneity in the presence of nonlinear rate- and state-dependent friction. All the mechanical properties of the medium and friction are assumed homogeneous. Friction includes a characteristic length that is longer than the grid size so that our models have a well-defined continuum limit. 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 a few 1000 events. The style of seismicity produced by this model is determined by a control parameter associated with 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, large ruptures are still periodic, but small seismicity becomes increasingly nonstationary. When friction is highly rate-dependent, seismicity becomes nonperiodic 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. Partial stress drop produces large variations in the state of stress that in turn produce earthquakes of different sizes. Similar results have been found by other authors using the Burridge and Knopoff model. We conjecture that all models in which static stress drop is only a fraction of the dynamic stress drop produce stress heterogeneity.

The organization of seismicity on fault networks.

Although models of homogeneous faults develop seismicity that has a Gutenberg-Richter distribution, this is only a transient state that is followed by events that are strongly influenced by the nature of the boundaries. Models with geometrical inhomogeneities of fracture thresholds can limit the sizes of earthquakes but now favor the characteristic earthquake model for large earthquakes. The character of the seismicity is extremely sensitive to distributions of inhomogeneities, suggesting that statistical rules for large earthquakes in one region may not be applicable to large earthquakes in another region. Model simulations on simple networks of faults with inhomogeneities of threshold develop episodes of lacunarity on all members of the network. There is no validity to the popular assumption that the average rate of slip on individual faults is a constant. Intermediate term precursory activity such as local quiescence and increases in intermediate-magnitude activity at long range are simulated well by the assumption that strong weakening of faults by injection of fluids and weakening of asperities on inhomogeneous models of fault networks is the dominant process; the heat flow paradox, the orientation of the stress field, and the low average stress drop in some earthquakes are understood in terms of the asperity model of inhomogeneous faulting.

Geometric incompatibility in a fault system.

Interdependence between geometry of a fault system, its kinematics, and seismicity is investigated. Quantitative measure is introduced for inconsistency between a fixed configuration of faults and the slip rates on each fault. This measure, named geometric incompatibility (G), depicts summarily the instability near the fault junctions: their divergence or convergence ("unlocking" or "locking up") and accumulation of stress and deformations. Accordingly, the changes in G are connected with dynamics of seismicity. Apart from geometric incompatibility, we consider deviation K from well-known Saint Venant condition of kinematic compatibility. This deviation depicts summarily unaccounted stress and strain accumulation in the region and/or internal inconsistencies in a reconstruction of block- and fault system (its geometry and movements). The estimates of G and K provide a useful tool for bringing together the data on different types of movement in a fault system. An analog of Stokes formula is found that allows determination of the total values of G and K in a region from the data on its boundary. The phenomenon of geometric incompatibility implies that nucleation of strong earthquakes is to large extent controlled by processes near fault junctions. The junctions that have been locked up may act as transient asperities, and unlocked junctions may act as transient weakest links. Tentative estimates of K and G are made for each end of the Big Bend of the San Andreas fault system in Southern California. Recent strong earthquakes Landers (1992, M = 7.3) and Northridge (1994, M = 6.7) both reduced K but had opposite impact on G: Landers unlocked the area, whereas Northridge locked it up again.

Relationship between piezometric level and ground deformations measured by means of DInSAR in the Vega Media of the Segura River (Spain)

Differential SAR Interferometry (DInSAR) is a remote sensing method with the well demonstrated ability to monitor geological hazards like earthquakes, landslides and subsidence. Among all these hazards, subsidence involves the settlement of the ground surface affecting wide areas. Frequently, subsidence is induced by overexploitation of aquifers and constitutes a common problem that affects developed societies. The excessive pumping of underground water decreases the piezometric level in the subsoil and, as a consequence, increases the effective stresses with depth causing a consolidation of the soil column. This consolidation originates a settlement of ground surface that must be withstood by civil structures built on these areas. In this paper we make use of an advanced DInSAR approach - the Coherent Pixels Technique (CPT) [1] - to monitor subsidence induced by aquifer overexploitation in the Vega Media of the Segura River (SE Spain) from 1993 to the present. 28 ERS-1/2 scenes covering a time interval of about 10 years were used to study this phenomenon. The deformation map retrieved with CPT technique shows settlements of up to 80 mm at some points of the studied zone. These values agree with data obtained by means of borehole extensometers, but not with the distribution of damaged buildings, well points and basements, because the occurrence of damages also depends on the structural quality of the buildings and their foundations. The most interesting relationship observed is the one existing between piezometric changes, settlement evolution and local geology. Three main patterns of ground surface and piezometric level behaviour have been distinguished for the study zone during this period: 1) areas where deformation occurs while ground conditions remain altered (recent deformable sediments), 2) areas with no deformation (old and non-deformable materials), and 3) areas where ground deformation mimics piezometric level changes (expansive soils). The temporal relationship between deformation patterns and soil characteristics has been analysed in this work, showing a delay between them. Moreover, this technique has allowed the measurement of ground subsidence for a period (1993-1995) where no instrument information was available.

Evaluación de la susceptibilidad de las laderas a sufrir inestabilidades inducidas por terremotos: aplicación a la cuenca de drenaje del río Serpis (provincia de Alicante)

Se ha realizado un análisis para estimar la susceptibilidad de las laderas, en suelos de la cuenca de drenaje del río Serpis, a sufrir inestabilidades inducidas por terremotos. Para ello, se ha utilizado el denominado método de Newmark, que ha sido convenientemente modificado para contemplar la variabilidad que, de forma natural, se observa en las propiedades geotécnicas de los materiales. En el cálculo, se ha efectuado una simulación Monte Carlo, donde todas las propiedades geotécnicas que intervienen son tratadas como variables aleatorias. Los resultados obtenidos están expresados como probabilidad de que la aceleración crítica del talud sea menor o igual que 0.1g. Las susceptibilidades más elevadas se observan cuando los materiales están secos, pero en tal caso la extensión de territorio afectado es pequeña. En cambio, cuando el suelo está saturado se observa que gran parte del territorio presenta susceptibilidad Media o Baja, incluso con pendientes de 6 – 10º, frente a susceptibilidad Muy Baja – Nula, que los caracteriza cuando se encuentra seco. Se ha analizado también la posición de las zonas de mayor susceptibilidad con respecto a elementos constructivos existentes en el área.

Using the damage from 2010 Haiti earthquake for calibrating vulnerability models of typical structures in Port-au-Prince (Haiti)

After the 2010 Haiti earthquake, that hits the city of Port-au-Prince, capital city of Haiti, a multidisciplinary working group of specialists (seismologist, geologists, engineers and architects) from different Spanish Universities and also from Haiti, joined effort under the SISMO-HAITI project (financed by the Universidad Politecnica de Madrid), with an objective: Evaluation of seismic hazard and risk in Haiti and its application to the seismic design, urban planning, emergency and resource management. In this paper, as a first step for a structural damage estimation of future earthquakes in the country, a calibration of damage functions has been carried out by means of a two-stage procedure. After compiling a database with observed damage in the city after the earthquake, the exposure model (building stock) has been classified and through an iteratively two-step calibration process, a specific set of damage functions for the country has been proposed. Additionally, Next Generation Attenuation Models (NGA) and Vs30 models have been analysed to choose the most appropriate for the seismic risk estimation in the city. Finally in a next paper, these functions will be used to estimate a seismic risk scenario for a future earthquake.

Noticias de ataques y destrucciones en Orihuela durante el período andalusí (ss. VIII-XIII)

Tras resumirse "Los elementos esenciales de la trama urbana de Orihuela", se estudian los principales hechos históricos durante el período islámico de la ciudad de Orihuela "s. VIII-XIII) en que hay noticia de ataques militares a la ciudad y destrucciones : El ataque de los normandos a Orihuela en 245 H ./859 e.C.; Aceifa del califa ‘Abd al-Raḥmān III al-Nāṣir contra Orihuela y sus rebeldes; La "fitnat al-barbar" o guerra civil que acabó con el califato andalusí; El terremoto posterior a 440 H/1048-9 e.C. que asoló toda la vega del río Segura y finalmente la conquista cristiana de Orihuela. Como conclusiones para el estudio del urbanismo musulmán de Orihuela se demuestra que solo hubo destrucciones en el trazado urbano de importancia como resultado del mencionado terremoto que asoló y destruyó las ciudades de Murcia, Orihuela y toda la Vega Baja del río Segura.