Higher-mode Surface Waves Research Articles

Modal synthesis of high-frequency waves in Scotland

SUMMARY Local recordings on the 1974 LISPB array of a shock from an earthquake series in NW Scotland show a well developed Sg-wavegroup and higher mode coda. Using the results of previous work on the group velocity dispersion of the higher mode surface waves, a synthetic seismogram study is carried out to obtain a revised estimate of the depth of the event and investigate the nature of the rupture process. High-frequency (up to 5Hz) synthetic seismograms are constructed using a modal summation technique. These indicate that a fault model consisting of a single rupture is inconsistent and that a more appropriate description consists of two components. The main component corresponds to an event at a depth of 10 km and the other a weaker 'source' acting at 0.5 km. This result may be interpreted as a double event (both sources occurring on the pre-existing Strathconan fault with a lateral separation of about 2 km) or a consequence of scattering from buried heterogeneities in the upper crust.

Quasi-continental oceanic structure beneath the Arabian Fan sediments from observed surface-wave dispersion studies

AbstractThe fundamental and higher modes of surface waves generated by 31 earthquakes and recorded at seismographic stations along the western margins of India and Pakistan (Trivandrum, Kodaikanal, Goa, Bombay, Poona, New Delhi, Nillore, and Quetta) are used to estimate the crustal structure beneath the Arabian Fan sediments. The sedimentary thickness is determined from the observed higher mode data. The observed dispersion data suggest an increase in crustal thickness northward, from an approximately 16 km crustal thickness at the southern tip of India (Trivandrum) to an approximately 28 km crustal thickness at the regions of 20°N and above latitude, with an overlying 6 km sedimentary thickness. This gradual increase in crustal thickness in the northward direction and the attaining of quasi-continental oceanic (transition from continent to ocean) structure beneath the Arabian Fan sediments suggest that the Mohorovičić discontinuity may have resulted from a change in crystal structure due to increase of pressure and not a phase change. The same material exists beneath the Moho, and it does not represent the boundary between two different materials. The transition has given rise to crustal thickening in the northward direction. Another possible explanation is that the increase in hydrostatic pressure due to the load exerted by a large sedimentary column together with horizontal pressure caused by the collision of Indian and Eurasian plates has given rise to an increase in temperature near the Moho. Because of the thermal blanketing effect of this large sedimentary column, an inferred rise in temperature may have either changed the upper mantle into material with crustal-like velocity or may have given rise to metamorphism of earlier existing sedimentary rocks. An inferred high temperature near the Moho depth beneath the Arabian Fan sediments is in close agreement with the high attenuating zone at the shallow depth (30 to 45 km) as determined by Singh (1987).

Source models of the Harzer explosion from regional observations of fundamental-mode and higher mode surface waves.

Abstract For shallow source depths, the moment-tensor elements with isotropic radiation patterns, M zz and M xx + M yy , are not resolvable in moment-tensor inversions of long-period surface-wave data because their respective Green9s functions have similar frequency dependence. Examination of Green9s functions at higher frequencies shows that, while resolution for some momenttensor elements improves, it is still not possible to resolve the isotropic-radiating moments from fundamental-mode data recorded at regional distances. On the other hand, the addition of higher mode Rayleigh-wave amplitudes can improve the resolution of these moments significantly, since there are appreciable differences between the higher mode Green9s functions. An extension of Romanowicz9s algorithm is presented to invert fundamental-mode and higher mode data for the second-order moment tensor. A source of “noise” in the estimation of the moment tensor for underground explosions is the spallation of geologic strata at ground zero, since this too can be a significant source of higher modes. The inversion proposed in this paper accounts for possible higher mode excitation due to spall using the source model of Day et al . The inversion is applied to regional recordings of the Harzer explosion of 6 June 1981 at the Nevada Test Site. The results of the inversion demonstrate a trade-off between the second-order moment tensor representation and the single, directed force used to represent spall. Observations and numerical simulations of spall provide estimates of spall source parameters, which in turn constrain the moment-tensor representation of Harzer. The results of this study demonstrate the clear need for observations to characterize the spall source associated with underground explosions. Furthermore, they demonstrate the potential benefit of using higher modes to refine estimates of the explosion moment with reduced uncertainties compared to moment determinations from fundamental-mode data alone.

The 3-D shear wave structure in the mantle by overtone waveform inversion-II. Inversion of X-waves, R-waves and G-waves

SUMMARY The 3-D upper-mantle structure from the surface of the Earth to a depth of about 1000 km is obtained by inverting waveforms of fundamental and higher-mode surface waves. Minor- and major-arc waves of R-waves, G-waves and X-waves (higher-mode wave packets) are used as basic data. Two features of the solution seem fairly robust; one is the shallow structure in the upper few hundred kilometres which is strongly correlated with the age of the crust. The second feature is the deep fast-velocity anomaly near the western Pacific (Indonesia, Philippines and Mariana) region and its antipodal region of South America, both of which are subduction zones, which forms a strong l= 2 pattern. Simple slab models with 100 km thicknesses of 10 per cent faster-velocity material do not explain such large-scale fast-velocity anomalies. This may indicate large-scale deformation of the 670 km discontinuity, piling up of slabs in the upper mantle or thickening lithosphere in the lower mantle or large horizontal motions of subducted material. These results are stable whether an earth model 1066A or PREM is used as a starting model.

Three dimensional reconstruction of Pangea

The three dimensional seismic velocity structure from the surface of the Earth to a depth of about 900 km was determined from fundamental and higher mode surface waves. Velocity anomalies near the surface correlate well with the age of the surface rocks. Reconstruction of the ancient continent Pangea connects all fast velocity anomalies near the center of Pangea. Fast velocity anomalies extend to 200‐400 km. Considering the resolving power of long period surface waves, this indicates that Pangea was a continent with a lithospheric thickness of about 200 (±100) km or larger, which broke up right in the middle (Central Atlantic). Examinations of seismic velocity sections with respect to depth show different depth penetration of fast velocity anomalies under various continents such as North America, South America, Eurasia and Africa. We speculate that continents possessed different thicknesses before Pangea was formed and had moved over the surface of the Earth independently.

Upper mantle structure beneath the Canadian Shield derived from higher modes of surface waves.

An analysis of surface waves including the fundamental and first higher modes, and Sa phase was made to determine the upper mantle structure beneath the Canadian Shield. Four earthquakes which occurred beneath the Canadian Shield were used for this purpose. By comparing synthetic and observed seismograms, the shear velocity structure of the upper mantle was determined. The shear velocity structure of the shallower part was determined mainly using the fundamental and first higher modes. The structure in the deeper part was mainly constrained by the Sa phase. Phase of Love type Sa wave was successfully reproduced by a uniform shear velocity structure over the entire area of the Canadian Shield. The average shear velocity of the upper mantle above the depth of 400km obtained in this study is 4.67km/sec, which is higher than velocities of any other models presented before. The low velocity layer of the upper mantle is poorly developed. Since the polarization anomaly of surface waves was not observed for the fundamental and first higher modes and Sa phase, anisotropic velocity structure does not exist in the upper mantle beneath the Canadian Shield.

Higher‐mode surface waves and structure of the Great Basin of Nevada and western Utah

Observed seismograms and dispersion data for crust and mantle higher mode surface waves in the Great Basin are compared with theoretical seismograms and dispersion curves computed for the Great Basin model of Priestley and Brune [1978]. This structure was originally derived from fundamental mode surface wave and refraction data. Phases identified as Sa [T∼13 s] are observed to have a phase velocity of 4.50±0.03 km s−1. Crustal second Rayleigh mode (first shear mode) waves have predominant periods varying from about 5 s on some paths to about 8 s on others. The observed excitation and phase velocity of the Sa phase are in agreement with theoretical seismograms and computed phase velocities for a modified Great Basin model. The agreement provides added support, in an unexpected way, for the existence of a mantle lid of velocity about 4.5 km s−1 in the Great Basin. The crustal higher mode group velocity observations, i.e., the predominant periods of the second Rayleigh mode along various paths, reflect variations in crustal thickness within the Great Basin. Crustal thicknesses of approximately 25 km are indicated for some paths in northwestern Nevada and southeastern Oregon, whereas crustal thicknesses of greater than 35 km are indicated for east central Nevada. The crustal thickness of 35 km in the Great Basin model is probably most appropriate for the central part of the Great Basin.

Seismic anisotropy in the upper mantle

Abstract Seismic wave propagation in anisotropic media is fundamentally different from isotropic propagation, displaying variation of characteristics with direction, and, perhaps more diagnostic, coupling between motion in the sagittal plane and horizontal transverse motion. Such coupling has been observed for higher mode surface waves indicating anisotropy in the upper mantle beneath much of Eurasia. Synthetic seismograms show that the passage of P or SV body waves through an anisotropic upper mantle will write SH signatures on the wavetrains generated at both isotropic/anisotropic and anisotropic/isotropic interfaces. These signatures have not yet been positively identified on seismograms, but once observed, may be interpretated in terms of depth, thickness, orientation, and degree of anisotropy. The widespread anisotropy already demonstrated implies that the interpretation of every seismic wave which penetrates the upper mantle must be modified for anisotropy if the observations are made with sufficient resolution.

A search for the oceanic Lg phase

The Lg phase has been shown previously to be a collection of higher-mode surface waves guided by the continental crust (Knopoff, Schwab & Kausel). A simple scaling between continental and oceanic crustal thicknesses suggests that a search for an oceanic Lg phase should be made in the period range from 1 to 2s. In a search for SH polarized Lg arrivals over oceanic paths, we found that in addition to the fundamental mode, seismo-grams at relatively short ranges in the Pacific showed the presence of only the first higher mode with group velocities on the steep portion of the dispersion curve rather than at the group velocity minimum as expected. Numerical model analysis indicates that, contrary to the continental case, there is no strong confluence of stationary phases of higher-mode crustal waves in the appropriate period range to produce Lg wave packets; this is due to small but significant differences in scaled crustal structures. Further, lateral variations in the thickness of oceanic sediments are sufficient to scatter most of the crustal surface-wave energy within a relatively short distance. Even were this thickness uniform, attenuation in the sediments would be strong enough to absorb the Lg stationary phases in a short distance.

Regional variations of higher Rayleigh-mode phase velocities: a spatial-filtering method

Summary. Application of both spatial filtering and multiple-frequency filtering techniques allows one to isolate a higher-mode surface wave and to find the regional variation of its dispersion. The method is applied to four sets of long-period records across the United States for intermediate earthquakes located in the New Hebrides. The first and second higher Rayleigh modes show lower phase velocities in the western part of the States than in the eastern part. Furthermore, an oceanic phase-velocity curve is determined between 50 and 130 s for the first higher Rayleigh mode on the full path across the Pacific Ocean.

Thrust faulting and crust--upper mantle structure in East Australia

Summary. The mid-crustal earthquake of 1973 March 9 (mb= 5.5, h≤ 20 km) located 60 km south-west of Sydney, Australia, provides unambiguous evidence of contemporary thrust faulting in South-eastern Australia — a region of high heat flow and Cenozoic basaltic volcanism. Aftershock locations suggest a steeply dipping fault in the depth range from 8 to 24 km with a lateral extent of about 8 km. The mechanism solution is consistent with a tectonic stress field that is dominated by east—west horizontal compression. A seismic moment of 5.7 ± 1023± 20 per cent dyne-cm was computed from surface-wave amplitudes. Minimum values of slip and stress drop, 2 cm and 1 bar respectively, were estimated from the moment and a fault size taken’ from aftershock locations. Refinement modelling by a controlled Monte Carlo technique was used to provide unbiased models directly from multimode group velocities. The dispersion of fundamental and higher mode surface waves recorded at the digital high-gain station at Charters Towers, Queensland, and the WWSSN station at Adelaide, South Australia, is satisfied by crust- and upper-mantle models which have neither pronounced S-wave low-velocity zones nor thick high-velocity lids within 140 km of the Earth's surface. These models have subcrustal shear velocities of 4.20–4.32 km/s which are 0.4–0.5 km/s slower than Canadian shield shear velocities (CANSD).

Spatial attenuation of intensities for central U.S. earthquakes

abstract Attenuation of ground motion in the central United States has to be determined principally using the Modified Mercalli (MM) intensity observations because of the absence of instrumental strong ground-motion data. Nuttli's previous studies of Mississippi Valley earthquakes indicate that higher-mode surface waves produce the largest ground motion except possibly in the near-field region. Particle velocity rather than acceleration correlates directly with intensity and the coefficient of anelastic attenuation has an average value of 0.10 per degree. Using data from isoseismals of the November 9, 1968, southern Illinois and the December 16, 1811, New Madrid, Missouri earthquakes and assuming a linear relationship between log(A/T) and MM intensity, attenuation is expressed by the equation, valid for I(R) ≧IV (MM), I ( R ) = I 0 + 3.7 − 0.0011 R − 2.7 log ⁡ R ; for R ≧ 20 k m where R is the epicentral distance in kilometers. This relationship shows fairly good agreement with isoseismals of many large earthquakes in the central United States and may therefore be useful in providing realistic estimates of spatial attenuation and hence of design earthquakes for a given site. It can also be sometimes useful in estimating the epicentral intensity of an earthquake whose maximum intensity is not reliably known.

Array analysis of seismic surface waves: Limits and possibilities

The dispersion of higher modes of surface waves over a region covered by an array of stations can be measured by applying a frequency-wavenumber transform to segments of the signals in these stations, centered at a number of group-velocities. Thus, at a fixed period, modes appear as separate maxima in a display of the power spectrum on a phase-velocity vs. group velocity plane.

Radiation and attenuation of rayleigh waves from the Southeastern Missouri Earthquake of October 21, 1965

The southeastern Missouri earthquake of October 21, 1965, generated fundamental mode and higher-mode surface waves that were widely recorded throughout North America. Amplitude radiation patterns for the fundamental and first higher Rayleigh modes were determined and compared with patterns computed for various fault plane solutions. The favored solution is that of a fault 4 km deep, oriented N70°E, dipping 50°S, and having a slip vector oriented 85° downward from the horizontal on the fault face. A least squares fitting process was devised to determine the source spectrum and the values for the Rayleigh wave attenuation coefficient at each period. The fundamental mode attenuation coefficient is slightly greater than 0.001 km−1 at a period of 4 sec, decreases rapidly to 0.0002 km−1 or less at periods between 17 and 25 sec, and increases slowly to about 0.00017 km−1 at 50 sec. The first higher mode attenuation coefficients parallel and are slightly lower than those of the fundamental mode at periods between 4 and 10 sec. The source spectrum peaks between 5 and 9 sec and appears to attain a lower dc level at periods of greater than 20 sec. The similarity in the shapes and the orientations of the short-period radiation patterns and the area of perceptibility for this earthquake suggests that the size of the ‘felt area’ of an earthquake is related to the nature of the radiation and the attenuation of short-period Rayleigh waves. This observation and the lower short-period Rayleigh wave attenuation coefficient values observed in the eastern United States in comparison with those observed in the western United States indicate that the larger areas of perceptibility of eastern United States earthquakes occur because short-period Rayleigh waves are transmitted more efficiently in that region.

Seismic pulse in a layered sphere: Normal modes and surface waves

An exact solution is obtained for the displacement of the surface of a layered sphere caused by an explosive point source located within the sphere. The solid elastic mantle and the fluid core have densities and elastic constants taken as averages for Bullen's model B. For all modes of periods 4 sec and longer seismograms were computed at several distances from deep and shallow sources. They show Rayleigh waves, higher-mode surface waves, and reflected and diffracted waves. Stoneley waves are found to be due to a source located on the interface. Rayleigh waves are more highly dispersed in the layered sphere than in the homogeneous sphere. Second-mode surface waves have a larger angular component than radial component, and in most cases under consideration they have a larger angular component than any other arrival. The third higher-mode surface waves have a larger radial component. The correspondence between reflected pulses and several modes of surface waves is discussed.

Microseisms: Mode Structure and Sources

Frequency-wave number spectra of microseisms were obtained by use of a set of short-period and long-period seismometers at LASA (Large Aperture Seismic Array, Montana). At times of relatively high microseismic activity short-period (shorter than 5 seconds) microseisms consist of both body waves and higher-mode surface waves. From the phase velocity and direction of body waves, source areas were determined, coinciding with low-pressure regions on the weather map. At longer periods, microseisms consist of fundamental- mode Rayleigh and Love waves, the former being dominant. Most microseismic energy arrives at LASA from the northeast and the west.

The Motion of a Sphere Caused by an Impulsive Force and by an Explosive Point-Source

Summary An exact solution is obtained for the displacement of the surface of a uniform elastic solid sphere of radius a due to an impulsive force applied in radial direction at a point situated at a depth d below the surface. The theoretical seismograms, which were computed for several epicentral distances 9 (Ok9 < 180), show several modes of surface waves in addition to various reflected and diffracted pulses. The higher modes of surface waves are a result of sphericity only and are compared with the observed higher modes and with the higher modes in a plane layered model. A comparison of the present SV-P source with an explosive P-source shows that the Rayleigh-waves RIi from the SV-P source have a larger high-frequency content than R from the P-source, show less dispersion and have larger amplitudes when caused by shallow and medium-depth sources. Higher mode surface waves R2i have larger angular than radial component. They are larger in the results from the P-source, and smaller from the SV-P source. The mode RSi has larger radial than angular component and is found equally from both sources. The GVv surface-waves are the largest guided waves to arrive from the deep SV-P source, they are largest except for the Rayleigh-wave from the shallow and medium depth SV-P sources. The radial component of CV. is 2-3 times larger than its angular component and is similar to the G, guided waves from an SH-torque source. GVv is absent in results from the P-source. The connection between the higher modes of surface waves and groups of certain reflected pulses is given. ' Refracted' pulses, found in results from the shallow SV-P source, have a larger angular than radial component. In several cases the angular component is larger than that of the direct pulse.

An earthquake with exceptionally strong higher-mode surface waves

An earthquake in the Northern Sinkiang Province, China, on November 13th, 1965, produced exceptionally strong higher-mode surface waves recorded at the Swedish seismograph stations, especially by the Galitzin seismographs at Kiruna. Group-velocity dispersion curves are deduced for the second Rayleigh and the second and third Love wave modes. The energy content of the second Rayleigh and Love modes is computed, and it is found that the former amounts to about 70 times as much as in average. Various reasons for this exceptional behaviour are discussed, such as depth extent of focus, focal mechanism and properties of propagation path.

Effect of Depth of a Point Source on the Motion of the Surface of an Elastic Solid Sphere

Summary An exact solution, obtained previously for the displacement of the surface of a uniform elastic solid sphere due to an impulsive compressional pulse from a point-source situated at depth d below the surface of a sphere of radius a is applied here to the problem of propagation from a source at d = a/32 and a/6400 and compared with results for d= a/8. Theoretical seismograms, radial and angular component, are given at distances 0 < θ < π from the source. Rayleigh waves are found due to all sources. In the high frequency limit they have the velocity of Rayleigh waves in a homogeneous half space. There is dispersion towards higher velocities. The Rayleigh waves from the shallow source have amplitudes more than ten times the amplitude of body waves. In the seismograms from the medium and deep sources their amplitude is smaller, they have less high-frequency components and show more dispersion. The amplitude of Rayleigh waves has a minimum at 90|Mo and 270|Mo. At 180|Mo and 360|Mo the radial component has a maximum of ten, seventeen and forty times the radial component at 90|Mo for the deep, medium and shallow sources respectively. The ratio of angular to radial amplitude is largest at 90|Mo and 270|Mo, decreasing to zero at 180|Mo and 360|Mo. The Rayleigh waves show phase shift, almost elliptical retrograde particle motion, change in form of ellipses with depth of source and deviations of the direction of the major axis from the vertical direction similar to results in observed seismograms. Higher modes of surface waves are found and their connection with groups of reflected pulses of mixed types given. As in several observed seismograms the second mode is especially predominant in the angular component. Whereas diffracted pulses connected with μ times reflected Pμ are encountered mainly in deep-focus events, diffraction phenomena connected with the transformed phases PμSv are found here at all depths and have in several cases amplitudes comparable to, or larger than, the reflected pulses.

Higher-mode seismic surface waves from atmospheric nuclear explosions over Novaya Zemlya

The second Rayleigh mode and the second and third Love modes were observed at Uppsala from atmospheric nuclear explosions over Novaya Zemlya. The group velocity dispersion, the energy, and the initial phase of the higher modes are calculated. The Rayleigh modes are generated by the action of the shock wave on the ground, and the energy is most effectively coupled when the apparent velocity of the shock wave is equal to the phase velocity of the surface wave. The Love modes are generated by some form of coupling with the second Rayleigh mode.