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We investigate correlation between the Coulomb stress changes and the spatial distribution of the aftershocks of the 1990 M w 7.3 Rudbar earthquake that occurred on and off the Rudbar fault. The Coulomb stress changes indicate that the Rudbar mainshock encouraged parts of the Kelishom and Kashachal strike‐slip faults (located east of the main rupture), as well as parts of the Manjil Thrust fault (located south of the main rupture). The central part of the Manjil Thrust, which is sandwiched between two stress shadow zones, experienced an increase in Coulomb stress. We observe that the events before and after the Rudbar mainshock have different spatial distribution patterns. We find that most of the aftershocks occurred in an area between the Kabateh and Zardgeli segments where the static Coulomb stress is high, while few aftershocks occurred in the stress shadow zone that extends to the northwest and southeast of the Rudbar rupture. The aftershocks that occurred in the stress shadow zones northwest of the Baklor segment were related to the continuation of the background seismicity after the mainshock. A burst of seismicity following the Rudbar earthquake south of the Zardgeli segment provides evidence for dynamic stress triggering for the aftershocks that affected these regions for the first 1–3 months after the mainshock. We also compare the Coulomb stress changes with the seismicity rate and find that the regions with high seismicity rate are in good agreement with the high stress such as the western end of the Baklor and an area between the Kabateh and Zardgeli segments. To validate the effects of the Coulomb stress on the seismicity rate, we resolved stress changes on the aftershock nodal planes and recognize that the aftershocks located between the Kabateh and Zardgeli segments and the surrounding areas were brought closer to failure.

We investigated seismic velocity and structural changes along the Long- men Shan fault associated with the 2008 Mw 7.9 Wenchuan earthquake using ambient seismic noise data recorded by the regional seismic network of the China Earthquake Administration. We computed cross correlograms of continuous records of station pairs from which we obtained clear Rayleigh-wave signals at periods of 10 to 25 s. We measured the travel speeds of these Rayleigh waves from ambient noise data recorded before and after the earthquake and obtained a total of 77 estimates of group velocity along paths running across the rupture zone of the earthquake. Most of the ray paths showed increasing travel times of Rayleigh waves right after the earth- quake. We inverted the measured differential travel times along different ray paths to constrain regions with significant changes in seismic velocity. Our 2D tomographic image showed a distinct region with an ∼0:4% velocity decrease. The strike and extension of this region match remarkably well with the deep rupture area of the earth- quake. Because the Rayleigh waves that we used in this study travel as deep as ∼25 km below the surface, it is difficult to explain the observed velocity changes solely with shallow damages (

In the classic microseismic band of 5-20 sec, seismic noise consists mainly of fundamental mode Rayleigh and Love waves; however, at shorter periods seismic noise also contains a significant amount of body-wave energy and higher mode surface waves. In this study we perform a global survey of Earth's short-period seismic noise field with the goal of quantifying the relative contributions of these propagation modes. We examined a year's worth of vertical component data from 18 seismic arrays of the International Monitoring System that were sited in a variety of geologic environments. The apertures of the arrays varied from 2 to 28 km, con- straining the periods we analyzed to 0.25-2.5 sec. Using frequency-wavenumber ana- lysis we identified the apparent velocity for each sample of noise and classified its mode of propagation. The dominant component was found to be Lg, occurring in about 50% of the noise windows. Because Lg does not propagate across ocean- continent boundaries, this energy is most likely created in shallow water areas near coastlines. The next most common component was P-wave energy, which accounted for about 28% of the noise windows. These were split between regional P waves (Pn=Pg at 6%), mantle bottoming P waves (14%), and core-sensitive waves (PKP at 8%). This energy is mostly generated in deep water away from coastlines, with a region of the North Pacific centered at 165° W and 40° N being especially prolific. The remainder of the energy arriving in the noise consisted of Rg waves (28%), a large fraction of which may have a cultural origin. Hence, in contrast to the classic micro- seismic band of 5-20 sec, at shorter periods fundamental mode Rayleigh waves are the least significant component.

Hypothetical thermal plumes in the Earth’s mantle are expected to have low seismic-wave speeds and thus would support the propagation of guided elastic waves analogous to fault-zone guided seismic waves, fiber-optic waves, and acoustic waves in the oceanic SOund Fixing And Ranging channel. Plume-guided waves would be insensitive to geometric complexities in the wave guide, and their dispersion would make them distinctive on seismograms and would provide information about wave-guide structure that would complement seismic tomography. Detecting such waves would constitute strong evidence of a new kind for the existence of plumes. A cylindrical channel embedded in an infinite medium supports two classes of axially symmetric elastic-wave modes, torsional and longitudinal-radial. Torsional modes have rectilinear particle motion tangent to the cylinder surface. Longitudinal-radial modes have elliptical particle motion in planes that include the cylinder axis, with retrograde motion near the axis. The direction of elliptical particle motion reverses with distance from the axis: once for the fundamental mode, twice for the first overtone, and so on. Each mode exists only above its cut-off frequency, where the phase and group speeds equal the shear-wave speed in the infinite medium. At high frequencies, both speeds approach the shear-wave speed in the channel. All modes have minima in their group speeds, which produce Airy phases on seismograms. For shear wave–speed contrasts of a few percent, thought to be realistic for thermal plumes in the Earth, the largest signals are inversely dispersed and have dominant frequencies of about 0.1–1 Hz and durations of 15–30 sec. There are at least two possible sources of observable plume waves: (1) the intersection of mantle plumes with high-amplitude core-phase caustics in the deep mantle; and (2) ScS -like reflection at the core-mantle boundary of downward-propagating guided waves. The widespread recent deployment of broadband seismometers makes searching for these waves possible.

Earthquakes in central Nevada (1932-1959) were used to develop a modified Mercalli intensity (MMI) attenuation model for estimating moment mag- nitude M for earthquakes in the Basin and Range province of interior western North America. M is 7.4-7.5 for the 26 March 1872 Owens Valley, California, earthquake, in agreement with Beanland and Clark's (1994) M 7.6 that was estimated from geologic field observations. M is 7.5 for the 3 May 1887 Sonora, Mexico, earthquake, in agreement with Natali and Sbar's (1982) M 7.4 and Suter's (2006) M 7.5, both estimated from geologic field observations. MMI at sites in California for earthquakes in the Nevada Basin and Range appar- ently are not much affected by the Sierra Nevada except at sites near the Sierra Nevada where MMI is reduced. This reduction in MMI is consistent with a shadow zone produced by the root of the Sierra Nevada. In contrast, MMI assignments for earthquakes located in the eastern Sierra Nevada near the west margin of the Basin and Range are greater than predicted at sites in California. These higher MMI values may result from critical reflections due to layering near the base of the Sierra Nevada.

Since 1999 six Sound Fixing and Ranging (SOFAR) hydrophones have been moored along the Mid-Atlantic Ridge (MAR) (15-35 N). These hydrophones (8-bit data resolution) are designed for long-term monitoring of MAR seismicity using the acoustic T waves of seafloor earthquakes. The completeness level of the MAR T- wave earthquake catalog estimated from size-frequency constraints is mb 3.0, a significant improvement in detection compared to the mb 4.6 completeness level estimated from National Earthquake Information Center magnitude-frequency data. The hydrophones also detect the acoustic phase of converted upper mantle P arrivals from regional earthquakes at epicentral distances of 374-1771 km and from events as small as mb 3.6. These regional P waves are used to estimate a Pn velocity of 8.0 0.1 km sec 1 along the east and west MAR flanks. An unexpected result was the identification of P arrivals from earthquakes outside the Atlantic Ocean basin. The hydrophones detected P waves from global earthquakes with magnitudes of 5.8-8.3 at epicentral distances ranging from 29.6 to 167.2. Examination of travel times suggests these teleseismic P waves constitute the suite of body-wave arrivals from direct mantle P to outer- and inner-core reflected/refracted phases. The amplitudes of the teleseismic P waves also exhibit the typical solid-earth wave field phenomena of a P shadow zone and caustic at D 144. These instruments offer a long-term, relatively low-cost alternative to ocean-bottom seismometers that allows for obser- vation of Pn velocities and mantle/core phases arriving at normally inaccessible deep- sea locations.

High-frequency seismic records from the Polynesian Seismic Network are used to investigate in detail the processes of conversion of acoustic (T-wave) energy from and to seismic waves at island shores. On the source side, we study the seismic-to-acoustic conversion based on T phases from Hawaiian events recorded at Polynesian stations located on the coral platter; on the receiver side, we study the acoustic-to-seismic conversion based on T phases from marine sources recorded across the Polynesian islands. In both instances, our results underline the importance of steep slopes (typically 50°) in allowing an efficient conversion between P waves in the island structure and T waves in the water column. These slopes can be coral reefs or the heads of young, presumably unconsolidated, basalt flows. Under this geometry, modeling based on raytracing indicates that the seismic record of the T phase consists of a P wave at distances from the conversion point greater than 9 km; at shorter distances, S waves and surface waves are generated. In the absence of a steep slope, only surface waves are present. These models can be used to compute precise and predictable travel-time station corrections, allowing the use of seismometers located inland to exploit the superb detection and location capabilities of T waves.

We investigate bias in surface-wave magnitude using the complete ISC and NEIC datasets from 1978 to 1993. We conclude that although there are some small differences between the ISC and NEIC magnitudes, there is no major difference between these agencies for this presentation of the global dataset. The frequency-distance plot for reported surface-wave amplitude observations exhibits detailed structure of the body-wave amplitude-distance curve at all distances; the influence of the surface-wave amplitude decay with distance is much less apparent. This censoring via the body waves represents a large deficit in the number of potentially usable surface-wave amplitude observations, particularly in the P-wave shadow zone between Δ = 100° and 120°. We have obtained two new modified Ms formulas based upon analysis of all ISC data between 1978 and 1993. In the first, the conventional logarithmic dependence of the distance correction is retained, and we obtainM s e = log ( A / T ) max + 1.155 log ( Δ ) + 4.269 .In the second, we make allowance for the theoretically known contribution of dispersion and geometrical spreading, to obtainM s t = log ( A / T ) max + 1 3 log ( Δ ) + 1 2 log ( sin Δ ) + 0.0046 Δ + 5.370.Comparison of these formulas with other work confirms the inadequacy of the distance-dependence term in the Gutenberg and Prague formulas, and we show that our first formula, as well as that of Herak and Herak, gives less bias at all epicentral distances to within the scatter of the observed dataset. Our second formula provides an improved overall distance correction, especially beyond Δ = 145°. We show evidence that Airy-phase distance decay predominates at shorter distances (Δ≦30°), but for greater distances, we are unable to resolve whether this or non-Airy-phase decay predominates. Assuming 20-sec surface waves with U = 3.6 km/sec, we obtain a globally averaged apparent Q−1 of 0.00192 ± 0.00026 (Q ≈ 500). We argue that our second formula not only improves the distance correction for surface-wave magnitudes but also promotes the analysis of unexplained amplitude anomalies by formally allowing for those contributions that are theoretically predictable. We conclude that there remains systematic bias in station magnitudes and that this includes the effects of source depth, different path contributions, and differences in seismometer response. For intermediate magnitudes, Mts shows less scatter against log M0 than does Ms calculated using the Prague formula.

This study reanalyzes a refraction seismic profile from NTS, Nevada, to San Francisco transverse to the high Sierra Nevada. Three models of the Earth's crust, with an asymmetrical mountain root, constructed by different authors are tested by the use of ray tracing: model CQM (Carer et al., 1970), with a maximum crustal thickness of 35 km centered about 50 km west of the crest of the Sierra; models A and B (Pakiser and Brune, 1980), with a mountain root extending to a depth of 55 km below the Sierra. In the latter, guided and diffracted waves are used to explain seismic Pn energy in the shadow zone of the root. The preferred model A has a high-velocity layer, dipping from west to east in the upper crust, while model B does not.The present study demonstrates how fallacies in interpretation of complicated structures can occur if all ray types are not quantitatively traced. The influence of the P-wave gradient in the upper mantle on the length of the shadow zone is shown to be important, and it is demonstrated that a modified CQM model explains the observed travel times when diffracted waves are included. (CQM does not, however, explain why the Pn travel times on a separate refraction profile along the Sierra Nevada from a Truckee earthquake are so great.) Model B interprets the Pn signals at Δ > 200 km as diffracted waves, but the computed travel times do not fit the observations. The dipping wave guide in model A does not work as expected and perhaps should be ruled out.

Seismic waves from nuclear explosions and from well-located local earthquakes have been recorded along several profiles through western Nevada, southeast Oregon, and eastern California. Pn delay times from these data and from additional travel times of NTS explosions recorded across the western Nevada seismic network have been interpreted in terms of varying crustal thickness of the western Great Basin. Our interpretation of these data implies that the crust thins from greater than 32 km thick in the vicinity of Mono Lake to 20 to 22 km thick over a broad region in northwest Nevada. The Pn headwave propagates to a distance of about 550 km with a velocity of 7.8 km/sec. At distances greater than 600 km a low velocity (7.44 km/sec), larger amplitude phase is observed. This phase may result from long-period energy diffracting into a shadow zone. A prominent, high-velocity second arrival following Pn by 1 to 2 sec in the distance range 340 to 475 km, is interpreted as a reflection from the base of the lithosphere at 60 to 70-km depth.

Location, shape, and size of near-surface heterogeneities in the Earth may be determined by active or passive seismic diffraction experiments. An array of geophones would be set up to record near-field wave motion resulting from diffraction by the inhomogeneity. As an example of such inhomogeneities, we study the diffraction of plane P and S waves by a finite two-dimensional crack as a function of wavelength and direction of incident wave. We develop a method which can be used to solve for diffraction effects by empty and fluid-filled (zero viscosity) cracks. The magnitude of the effect of the fluid in the crack is governed by a parameter called the crack stiffness factor which is the ratio of bulk modulus of the fluid in the crack to the rigidity of the solid divided by the crack aspect ratio. The diffraction problem is solved using the finite difference scheme developed by Madariaga (1976) to study dynamic crack propagation problems. It is found that a crack has little effect on wave motion for incident wave with wavelengths greater than 10 times the crack length. For wavelengths less than 5 times the crack length there is a complicated diffraction pattern. The amplitude and phase of both components of motion are affected by the crack. We find that the diffraction effect decreases as the crack stiffness factor increases. For wavelengths less than 2 times the crack length there is a region of reduced amplitude (shadow zone) behind an empty crack. Relative phase of two components of particle motion varies rapidly with position inside the shadow zone. The results of the theoretical calculation are used to try to locate the edge of a magma lens in Kilauea Iki Crater, Hawaii. It is found that the ratio of vertical-to-horizontal displacement and the direction of rotation of initial particle motion measured by a seismic array located on the floor of the crater agree qualitatively with what the theory predicts. The edge of the magma found by this method shows excellent agreement with the one inferred from the distribution of seismic events originating in the crust of the lava lake (Aki et al., 1977).

The present paper is based upon the author's recent investigation of "The Partition of Energy among Seismic Waves Reflected and Refracted at the Earth's Core.'' Its purpose is the expression of the amplitudes of certain waves reflected and refracted at the earth's core in terms of the horizontal and vertical components of the displacement which they produce at the surface of the earth.

The presence of a low velocity layer has been indicated from the observation of S waves at small epicentral distances. In this paper we have studied the presence of a shadow zone, and have compared the energies at different epicentral distances.

The problem of the diffraction of a seismic pulse by the core of the Earth is investigated theoretically. The result is compared to that of diffraction by a half-plane. The differences are striking. Laboratory model experiments have been performed to verify the theoretical approximations in their regions of validity, and to complement the theory elsewhere. The curves, thus obtained, of the theoretical amplitude distribution in the shadow of the Earth's core agree very well with the observations of Gutenberg. It is therefore concluded that diffraction is a completely adequate explanation for the amplitude distribution in the shadow zone.

The graphical method developed in the first part of this series of articles is generalized to shells of ‘tangential isotropy’, the spherical analog to transverse isotropy. In order to obtain as complete a list as possible of deviations from waves in isotropic shells, all mathematically possible types of tangential isotropy are investigated, irrespective of their likeliness to occur in some part of the earth. The quantitative background for the classification of transversely anisotropic media implied here is presented in an appendix. In tangentially isotropic spheres, rays are curved even if the material has the same elastic properties everywhere (with the exception of a degenerate case, where SV-rays are straight lines). The geometric shape of SH-rays is controlled by a single parameter. Their curvature has the same sense throughout, and the corresponding t(Δ) curves measured on the sphere are, as on isotropic homogeneous spheres, quarter sine waves, which only differ in range. P-rays generally change their sense of curvature twice, and the wave front charts are considerably more complicated than those of SH-waves. The travel-time curves differ in details from those in isotropic spheres or those of SH-waves, but the general appearance is the same. The most striking differences occur for SV-rays, particularly if the slowness surface of the medium has points of inflection. If the concave part lies about π/4 from the axis of symmetry, cusps in the wave front are formed in the vicinity of the focus. For some distance rays cross over and back, but finally the cusps disappear. There are no major indications of these cusps present at the surface or in the t(Δ)-curve. If the concave part lies in the vicinity of the axis of symmetry, the t(Δ)-curve ends in a receding branch. Correspondingly, the surface of the sphere consists of a singly-covered zone, a doubly-covered zone, and a shadow zone. A concave section near the plane of symmetry of the slowness surface is tantamount to the coexistence of two different SV-rays with different direction of wave normal and polarization; these two rays travel along different paths, but cover the same distance in the same time and thus correspond to a single valued branch of the time versus distance curve. If one or more spherical shells are tangentially isotropic, refraction and reflection at the interfaces cause further deviations from wave propagation in isotropic shells since Snell's law refers to wave normals, which in anisotropic media do not generally coincide with the direction of the ray. A concave section close to the plane of symmetry of the slowness surface of SV-waves can lead to a ray traveling along the inner boundary of the shell. Unlike channel rays this ray loses energy to normal rays and thus should lead to “ghosts” of diminishing strength in the corresponding parts of the time versus distance curves. For shells with sufficiently narrow slowness graphs there exists in addition a double refraction for SV-rays traversing the shell which should lead to multi-valued branches of the time versus distance curve.

Seismic events can be relocated relative to a reference event by using the group-velocity dispersion curves of surface waves. Since group velocity is a function of the travel path, surface waves from two events in the same locale should show identical group velocities when viewed at any one seismograph station. A computer technique has been developed for comparing the group-velocity curves of any event with the curves of a reference event and for determining the relocation which causes the curves to best coincide. The method is evaluated by relocating eight intermediate-size nuclear explosions of the Nevada Test Site series. With precise curve fitting, the surface-wave locations are slightly more accurate in southern Nevada than the standard body-wave determinations. The surface-wave origin times are considerably more accurate. In areas of sparse station coverage or of many small earthquakes, the surface-wave method can be expected to improve seismic locations significantly.

A theory is developed for wave propagation of a given frequency emerging from a seismic surface source in a medium in which the velocity is a continuous function of one coördinate only. It is assumed that the relative change of the elastic parameters is very small over a wave length. The wave equations are then solved in cylindrical coördinates under suitable boundary conditions and integral representations are obtained for the displacements, which are generally valid. These integrals are then evaluated for a special case with an almost linear velocity gradient and the surface displacements are obtained for long ranges. It is found that the amplitude of the body waves (both P and S) inside the shadow zone decays exponentially with the distance from the source at a rate proportional to one-third power of the frequency and two-thirds power of the velocity gradient.

A comparison of the seismic waves generated by a nuclear explosion and an earthquake is discussed. The epicenter of the earthquake was located within the Nevada Test Site. Both events were recorded at the same station with the same type of equipment. The earthquake waves contained slightly lower frequency than the waves generated by the nuclear shot. The early P phases of the shot had larger amplitudes while the phases after Pg for the earthquake were larger. Seismic waves from collapses were generally found to be composed of lower frequencies than the waves from the original shot. Aftershocks of the Hebgen Lake earthquake were found to generate seismic waves whose frequency content was related to the magnitude of the aftershock. Spectral differences in quarry shot recordings that correlate with source duration times are also discussed.

Travel time data, from widely recorded nuclear detonations in the Eniwetok and Bikini atolls of the central Pacific, have been compiled and are presented. Although a number of stations recorded ten or more events from each atoll, the resulting data may be considered as from a single point source, precisely known in time and place. Composite P-wave travel times are presented in a graphical form and, in the distance range from 3 to 102 degrees, are represented as eight near straight-line segments. P-wave speeds in the top of the mantle average about 8.2 km/sec to distances beyond 17 degrees, and a sharp discontinuity at 19.5 degrees is indicated. There is no evidence for or against a low-speed layer in the upper mantle nor for a regional shadow zone. A mantle model consisting of a number of discrete spherical shells has been constructed. A core depth of 2,870 km, 30 km short of the accepted value, is calculated from PcP arrival times at Matsushiro and College, which are 2.5 and 3.5 sec. earlier than are indicated in the Jeffreys-Bullen tables.

Travel times and amplitudes of body waves in lunar models have been computed. The effect of a low-velocity zone upon the travel times and amplitudes of body waves is likely to be small unless the condition for the existence of a shadow zone at short to moderate epicentral distances is nearly satisfied. The PKP phase from a possible central core of the moon is likely to have a large amplitude in the area opposite to the epicenter.

Summary and Conclusions Seismograms recorded at epicentral distances between 4° and 26° are investigated, and revised travel-time curves for P and S are given. Both consist of two branches, the first almost a straight line ending in a shadow zone, the second beginning with relatively large amplitudes and with a delay relative to the first branch. The end of the shadow zone for P seems to be near 15° in most regions; for S this distance seems to vary somewhat and to be usually a few degrees greater. The “20-degree discontinuity” of Lehmann and Jeffreys, following Byerly (1926), as well as observations by Neumann (1933) and others, probably can be referred to the same phenomenon. Differences in distance are partly due to local effects, partly to the difficulty of tracing the first branch of the travel-time curves of P and S across the shadow zone. Huancayo, Peru, seismograms from near-by earthquakes at intermediate depth are used for studying the change of amplitude with focal depth at a given distance in and near the shadow zone. All observations are explained on the assumption that the velocity of P as well as S waves decreases somewhat (between 1/2 and 3 per cent?) at a depth below the Mohorovičić discontinuity to a minimum value at a depth near 80 to 100 km. The data do not permit decision whether the decrease in velocity is gradual over a range of about 50 km. or (almost) sudden at a given depth. The layer with lower velocity extends downward to a depth of about 150 to 180 km.; below, the velocities increase rather rapidly, but Poisson's ratio remains near 0.30, contrasting with a value of slightly less than 1/4 in the upper layers. Correspondingly, the rigidity remains relatively small as compared with the bulk modulus, apparently down to the surface of the core. It is of interest to note that such a low-velocity layer has now been established for the solid earth, the ocean, and the atmosphere, providing shadow zones for elastic (sound) waves in all three. It is also noteworthy that only a relatively small decrease in velocity is required to produce a rather extensive and pronounced shadow zone. The theory of free waves connected with the surface of minimum wave velocity probably will throw some light on the relatively large amplitudes and persistence of surface waves with a velocity of about 4.45km/sec. in seismograms.

Theoretical ray paths through velocity models constructed from numerically calculated thermal models of slabs were computed. The results were in good agreement with observed travel times. First motion amplitudes of P waves at teleseismic distances were measured from long- and short-period WWSSN records of intermediate focus earthquakes in the Tonga, Kermadec, and Kurile regions and of nuclear explosions and shallow earthquakes in the Aleutian region. These amplitudes were corrected for source mechanism. The Aleutian data were sufficient to show that intermediate focus earthquakes in that region occur in the colder regions of the slab. At short periods, for regions other than the Aleutians, shadowing effects which could be associated with the slab were not very marked, less than a factor of 2 reduction for epicentral distances between 30° and 50°. No systematic effects due to plates were found in the long-period data. Some stations in the predicted shadow zone of a Tonga earthquake recorded low amplitude precursors which probably were greatly defocused waves which ran the full length of the slab. Simple diffraction is incapable of explaining the short-period results.