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Aki’s maximum likelihood method of Gutenberg–Richter b-value estimation is based on the premise that magnitudes above a given threshold are distributed exponentially and presupposes that sampling is adequate for all these magnitudes; clearly, sampling will not be adequate for magnitudes having average recurrence times longer than the observation time. Thus, for any given sample, there is a higher-magnitude completeness threshold. The importance of considering this higher-magnitude threshold is discussed, the effect of incomplete large-magnitude sampling is evaluated, and a method is given for correcting the observations.

On a global scale, large earthquakes are Poisson-distributed in time which implies that the inter-earthquake intervals are exponentially distributed. Thus, a simple-minded estimation of the most probable interval could conclude that the most probable occurrence time for a large earthquake would be now! This thesis is unsupported by observations. The apparent paradox is explained when characteristics of the interval cumulative distributions are explored for different seismicity rates.

Charles Darwin, one of the most influential scientists in history, visited South America as a shipboard naturalist on the round‐the‐world voyage of H.M.S. Beagle , a ten‐gun brig of the British Navy. His first‐hand research of the great 1835 Chile earthquake contributed important scientific ideas about the origin of tsunamis, mountain building, and the role of prograde Rayleigh waves in generating earthquake damage (Malischewsky Auning et al. , 2006, 2008; Castanos and Lomnitz, 2012). The great earthquake and tsunami of 20 February 1835, with epicenter near Concepcion, Chile, was among the largest seismic events in Latin American history. It was the only seismic event witnessed, described, and investigated by this scientist. The earthquake had a magnitude of 8–8.5 (Lomnitz, 2004) but recent evidence may suggest the need for an upgrade due to the similarity with the 27 February 2010 M 8.8 Maule megaquake. The tsunami produced waves of 14 m height above mean sea level in the Bay of Concepcion; ports, beaches, and coves between Constitucion and Talcahuano were razed. Darwin was a privileged witness and a superb observer. His careful and accurate description of the 1835 earthquake should occupy a unique position in scientific literature. In this paper we offer a reconstruction of what Darwin actually saw and felt, and an interpretation and re‐evaluation of some of his major conclusions. In a letter addressed to his sister Caroline on 10 March 1835, Darwin wrote, “I continue to suffer so much from sea‐sickness, that nothing, not even geology itself can make up for the misery and vexation of spirit” (Darwin, 1835). Darwin felt ill for most of the five years he spent on board the Beagle . His complaint was kinetosis, commonly known as motion sickness—an infirmity attributed to a discrepancy between visual information going to the brain …

The Parkfield earthquake prediction experiment (1985–2004) was designed to monitor stress accumulation in the lithosphere related to an impending earthquake on the San Andreas fault. However, no precursory signals were detected prior to the 2004 Parkfield earthquake (M6.0). In this paper we re-examine the long-term borehole strain records at Parkfield (Langbein et al., 2006). We find that they are consistent with a stationary tectonic stress field on the order of 55 MPa in the direction of the fault. This is the first measurement of far-field tectonic stresses from borehole strainmeter records. It suggests that logarithmic creep strains from boreholes can be used to interpret the state of stress in the lithosphere surrounding the San Andreas fault. Symmetry of the experimental setup suggests conformal mapping is a useful transformation to interpret the state of stress around a cavity in a prestressed halfspace. The borehole inverts the sign of the displacement, so that compressional tectonic stresses generate extensional strains at the borehole boundary. The stress energy field is conserved under conformal transformation (Noether9s theorem). This transformation facilitates recovery of the state of stress in the lithosphere from long-term Parkfield strain records. Ergodicity constrains the form of the creep function in long-term experiments as follows: , where the decay function is . In conclusion, available experimental evidence suggests that the Parkfield borehole strainmeter data preceding the 2004 earthquake are consistent with a tectonic stress estimate on the order of 55 MPa in agreement with the tectonics of the area. No evidence of long-term stress accumulation has been found.

The Guerrero coast in the subduction zone of west-central Mexico has been a seismic gap for almost 100 years. Large aseismic slow-slip events (SSE) have been frequently observed since GPS stations were established in this area (Lowry et al. 2001; Kostoglodov et al. 2003). The tectonic mechanism of slow-earthquake episodes is not well understood: some are preceded by significant earthquakes, others are not. The coincidental occurrence on 8 October 2001 of a shallow coastal earthquake of magnitude 5.8 in the same area as the slow earthquake of magnitude Mw 7.5 is attributed to a triggering effect. Previous investigators have dismissed the triggering hypothesis for various reasons, mainly because the earthquake was judged to be too small to trigger such a large SSE. However, reexamination of the seismic, tilt, and GPS data suggests that the hypothesis of triggering cannot be excluded. The 2001–2002 SSE ( Mw 7.5) has been extensively described and investigated (Kostoglodov et al. 2003; Yoshioka et al. 2004; Mikumo 2004; Iglesias, Singh, et al. 2004; Iglesias, Pacheco, and Singh 2004; Franco et al. 2005). It generated a long-duration aseismic slip episode over an area of about 550 km by 250 km comprising the southeastern part of the Guerrero gap and extending into the active coast of northwestern Oaxaca (Figure 1). The slip episode was monitored by seven GPS stations over a period of more than eight months. Surface displacements were estimated at about 1.3 cm to 6 cm (Franco et al. 2005). The Coyuca earthquake of 8 October 2001 was an important seismic event. Shallow, normal-faulting earthquakes are rare on the Guerrero subduction coast. However, the Coyuca earthquake has received only cursory attention. We suggest that the triggering of large SSEs by normal earthquakes in the overriding plate may represent a previously …

The existence of prograde particle motion for fundamental-mode Rayleigh waves is studied systematically in models of increasing complexity by using an exact expression of the ellipticity. This expression, together with the secular equation for the phase velocity, are useful to find the most relevant parameters for prograde particle motion, namely Poisson’s ratio in the layer and the shear-wave velocity contrast between the layer and the half-space. The density contrast between layer and half-space, and up to a certain degree Poisson’s ratio in the half-space, are usually less important. The domain of existence of prograde Rayleigh-particle motion is specified for typical combinations of parameters.

No one puts new wine into old wineskins. — Luke 5:37 In 1920, Albert Einstein suggested a famous thought experiment. A man drops an object from his pocket while he is falling from the rooftop of his house. To him the object does not appear to be falling; rather, it remains stationary at his side. Einstein concludes that gravity and acceleration are equivalent, and that “free-fall acceleration is a powerful argument for extending the postulate of relativity to non-uniform motions between coordinate systems.” This formulation of the equivalence principle can be extended to other realms of physics. In electromagnetic induction, for example, there is equivalence between relative motion of the coil or of the magnet, yet “the theoretical interpretation of the phenomenon in each case is quite different,” as Einstein points out. Two tectonic plates are moving against each other while the boundary remains locked. Two different interpretations are possible. Consider the example of earthquakes. Two tectonic plates are moving against each other while the boundary remains locked. Two different interpretations are possible: 1) The stress σ( t ) at the boundary is an increasing function of time t while the strength σ c at the same boundary remains constant; or 2) the stress σ at the boundary remains constant while the strength σ c ( t ) at the same boundary is a decreasing function of time. In either case the rupture will occur when σ ≥ σ c . Let us call the first case “elastic rebound” and the second “strength degradation.” The question I propose to address is: How can we distinguish between the two cases? Geodetic techniques for measuring displacements at the earth's surface are developing rapidly. These techniques include the Global Positioning System (GPS) and Interferometric Synthetic Aperture Radar (InSAR) imaging. Geodetic evidence of systematic relative displacements between …

Mexico City, political and economic center of Mexico, was founded in a lake, at more than 2000 m above sea level. The lacustrine mud under the downtown area is associated with high seismic risk. Twenty years after the destructive 1985 earthquake (Ms = 8.1) we review published research on seismic response in the Mexico Basin, especially seismic and microtremor studies on soft ground and the influence of the seismic response of lake mud on damage.

Recordings of the ground motion induced by two shallow (15–25 km deep), distant (300 and 605 km) earthquakes made on deep, soft lacustrine sediments at Texcoco, Valley of Mexico, show a late monochromatic response at 0.48 Hz. Data from a strong-motion recorder array show that this late response is consistent with slow (60 m/s group velocity) Rayleigh waves generated near the 6 km distant soft/stiff soil interface of the ex-lake surface margin. It is concluded that the excitation of local Rayleigh waves in soft soil deposits by arriving earthquake ground motion provides one mechanism to explain the prolonged duration of resonant motion on soft soils, and hence the extreme damage often associated with soft soils responding to distant earthquakes.

I prove three theorems on earthquake location in the laterally homogeneous, radially concentric layered earth showing that (1) epicenters of earthquakes are locatable without using numerical travel-time information, (2) focal-depth residuals change sign at some epicentral distance that is a function of the focal depth but not of the distance residuals, and (3) the distance Δ between two random points on the surface of a sphere is distributed as sinΔ. Theorem (1) implies that the epicenter can be located without simultaneously solving for hypocentral depth or origin time. Theorem (2) suggests that the focal depth should never be determined by joint regression on all four hypocentral parameters. Theorem (3) suggests a likely reason why late readings tend to overpower accurate readings when a standard least-squares technique is used. Together these theorems suggest that the problem of earthquake location is ill posed. Joint least-square regression will lead to the true hypocenter only if well-posedness is restored by restricting the class of admissible solutions using a priori knowledge, such as a travel-time table. But if the travel-time table is derived from the hypocentral solutions there is a feedback between location errors and errors in the travel-time tables, and local minima cannot be eliminated. Gutenberg instructively attempted to correct for bias due to azimuthal clustering, by assuming that residuals were nonnegative vectors.

This paper is an update of a 1970 publication, “Major Earthquakes and Tsunamis in Chile” (Lomnitz, 1970), which appeared in the Geologische Rundschau , now International Journal of Earth Sciences. The reference has always been hard to find and in recent years has become almost impossible to locate. Additionally, the database was overdue for revision in light of more recent results. The earlier conclusion of the paper, that “Chile emerges as perhaps the most highly seismic region in the world, with the possible exception of Japan”, still stands. One might add that Chilean earthquakes have provided data for important historical advances in the Earth sciences. For example, the 1835 earthquake in southern Chile was described by Darwin (1845) and has provided the earliest reliable observations of geodetic uplift along a subduction zone. The 1960 Chile earthquake ( Mw 9.5), possibly the largest earthquake in world history, continues to provide invaluable data and challenges for research. Tectonic changes in the coastal morphology of Chile may well be unique (Lomnitz, 1969). As part of a 5,000-km subduction system and with a subduction rate of more than 7 cm/year, Chile is located atop one of the most highly active subduction zones in the world. Available information on the history of earthquakes in Chile is limited. This is partly due to the nature of the terrain. The northern part of Chile is a desert, where rain falls about once every 25 years. The southern part is extremely rainy and is covered with a dense rain forest. Farther south along the coast one finds glaciers. The country is also wedged between the Pacific Ocean and the Andes Mountains. With the exception of a few scattered ports, most of the population lives in a narrow longitudinal valley between latitudes 32° and 45° south. I have experienced …

This paper discusses some methodological questions on understanding disasters. Destructive earthquakes continue to claim thousands of lives. Tsunamis may be caused by recoil of the upper plate. Darwin's twin-epicenter hypothesis is applied to a theory of tsunamis. The ergodicity hypothesis may help estimating the return periods of extremely rare events. A social science outline on the causation of the Tôhoku nuclear disaster is provided.

We visited El Salvador two weeks after the disastrous earthquake of 13 January 2001 ( Mw = 7.6) at the request of the Ambassador of E1 Salvador in Mexico. Mexico is dose to El Salvador in many ways, and one of us had studied an earlier earthquake disaster in this country (Lomnitz and Schultz, 1966). One result of our fact-finding emergency mission is the present report. We thank the government of El Salvador for timely and effective assistance and hospitality. It is a pleasure to acknowledge the valuable comments of Jose Luis Chavez and Franz Sauter in the course of field work. The main earthquake ( Mw = 7.6) occurred on Saturday, 13 January 2001 at 11:33 a.m. local time off the south coast of El Salvador at 12.80°N 88.79°W with a focal depth of around 40 km. A second major shock ( Mw = 6.6) occurred on 13 February 2001 inland, at 13.64°N 88.94°W with a focal depth of 13 km. There were over 1,100 deaths, many in landslides. The focal mechanism of the first event suggested intraplate normal faulting in the subducting Cocos Plate. The trend of the fault was nearly parallel to the coast. There were reports of a minor tsunami. Over a thousand aftershocks occurred in a nearly circular area with a diameter of about 50 km (Figure 1). The rate of occurrence of aftershocks decayed roughly according to Omori's Law. The second major shock occurred inland from the first one and caused severe damage in San Vicente; it had a shallow focus and a strike-slip mechanism. This event occurred after our departure. The capital city of San Salvador is located more than 100 km from the epicenter of the Mw 7.6 event. Accelerations of 0.3 g to 0.6 g were recorded in the city, …

In 1958 we heard that the ocean research vessel Vema of Columbia University would be doing research in Chilean waters. Professor Maurice Ewing, head of the geological observatory at Columbia, would be on board, and would I care to join the cruise?

This paper presents use of semiempirical method for seismic hazard zonation. The seismotectonically important region of Uttarakhand Himalaya has been considered in this work. Ruptures along the lineaments in the area identified from tectonic map are modeled deterministically using semi empirical approach given by Midorikawa (1993). This approach makes use of attenuation relation of peak ground acceleration for simulating strong ground motion at any site. Strong motion data collected over a span of three years in this region have been used to develop attenuation relation of peak ground acceleration of limited magnitude and distance applicability. The developed attenuation relation is used in the semi empirical method to predict peak ground acceleration from the modeled rupture planes in the area. A set of values of peak ground acceleration from possible ruptures in the area at the point of investigation is further used to compute probability of exceedance of peak ground acceleration of values 100 and 200 gals. The prepared map shows that regions like Tehri, Chamoli, Almora, Srinagar, Devprayag, Bageshwar, and Pauri fall in a zone of 10% probability of exceedence of peak ground acceleration of value 200 gals.

INTRODUCTION Earthquake prediction is still in its pre-feasibility stage. Empirical techniques based on the concept of seismic gaps (Fedotov, 1965; Sykes, 1968) are difficult to put in quantitative terms. The disagreement, before the destructive 1985 Mexico earthquake, on whether the Michoacan, Mexico gap had rupture potential is an example. Some seismologists actually argued that the gap was aseismic and incapable of generating major earthquakes. Such ambiguous interpretations of seismic gaps are not easily avoided in the present state of the art. Yet most large earthquakes continue to occur in seismic gaps. This may or may not have something to do with the fact that many segments of plate boundaries, perhaps the majority, have been designated as seismic gaps by someone. On the other hand, the gaps assigned maximum seismic potential ( e.g. , by Nishenko and McCann, 1981) correlate rather poorly with the locations of major earthquakes. The MRI algorithm (Lomnitz, 1993)...

An anomalous increase of seismicity was recorded at intermediate distances from the Landers, California, earthquake of 28 June 1992 (M = 7.3). Several authors have suggested that enhanced activity was triggered at distances of up to 17 fault lengths. We test a 90-year catalog of shallow world earthquakes (M > 7) for evidence of this effect. It is found that triggering is present even at these high magnitude levels. The pattern of enhanced activity comprises two concentric regions: (a) the aftershock region and (b) the region of triggered seismicity at distances of 300 to 1000 km. The two regions are activated together; they are separated by a ring-shaped gap at a distance of around 300 km. This “Mexican Hat” pattern is attributed to recovery flows generated by the stress drop of the earthquake in a steady-state convecting system.

The nature-society system is proposed as the relevant analytical unit for the sociological study of disasters. Like other complex systems, this system has emergent properties: its instabilities are the disasters. They often arise as a result of adoption by a community of specific technologies, e.g., housing technologies, that turn out to be unstable in the presence of critical natural or social changes. The following earthquake disasters were caused by unplanned and unforeseen features of housing or siting technologies: Huaxian 1556 (caves in loess), Yungay 1970 (siting in the path of an avalanche), and Mexico 1985 (high-rise buildings on soft ground). Disasters have anarchaeology, in the sense that the instabilities in the nature-society system are not static. This is demonstrated by tracing the 1985 Mexico earthquake disaster back to decisions on urban planning taken after 1521. It is not enough to know the hazard and the vulnerability in order to understand disasters. Technological solutions also have a local history.