The body waves due to a general seismic source in a layered earth model: 1. Formulation of the theory

abstract The radiation field exterior to any kind of volume source in a homogeneous medium can be represented in terms of an expansion in spherical harmonics. Such an expansion then provides an equivalent elastic source representation of quite general character in that nearly any proposed seismic source model, whether obtained using analytical or numerical (finite difference or finite element) methods, can be written in this form. The compatibility of this equivalent source with currently used source models, especially numerical models including detailed computations of the nonlinear processes at the source, is discussed. The equivalent source is then embedded in a stack of plane elastic layers representing the near-source crustal geology, and expressions are derived for computing the steeply emergent body waves exiting the base of the model. These displacements can then be combined with transfer functions representing the effect of the remainder of the travel path to compute theoretical seismograms for the body waves recorded in the far-field.

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An experimental study of source motion synthesis from first arrivals

Bulletin of the Seismological Society of America ◽

10.1785/bssa0530050955 ◽

1963 ◽

Vol 53 (5) ◽

pp. 955-963

Author(s):

Henry N. Pollack

Keyword(s):

Experimental Study ◽

Source Function ◽

Seismic Source ◽

The Body ◽

Body Waves ◽

Fixed Position ◽

Explosive Source ◽

Simple Medium ◽

Surface Ice ◽

Source Motion

Abstract The motion near a seismic source is synthesized from experimentally obtained seismograms of non-dispersed body waves. The body waves were emitted from an explosive source submerged in a lake with a frozen surface. The seismograms were recorded at several distances by moving the source to a greater depth for each record, while the seismometer remained in a fixed position on the surface ice sheet. All syntheses of the waveform one meter from the source yield the impulsive nature of the source. Deviations between the synthesized one-meter record and the observed one-meter motion are thought to reflect primarily the changing character of the shot medium with depth from the ice. These results indicate that over the short propagation distances (about three wavelengths for the higher frequencies recorded) through the simple medium of this experiment, the observed waveforms and their associated spectra retain characteristics of the source function. The records also yield some information regarding the nature and structure of the elastic medium about the source.

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Seismic source functions and magnitude determinations for underground nuclear detonations

Bulletin of the Seismological Society of America ◽

10.1785/bssa0670010135 ◽

1977 ◽

Vol 67 (1) ◽

pp. 135-158

Author(s):

John R. Murphy

Keyword(s):

Body Wave ◽

Broad Band ◽

Seismic Source ◽

Source Model ◽

The Body ◽

P Wave ◽

Cube Root ◽

Motion Data ◽

Surface Wave Data ◽

Body Wave Magnitude

abstract A variety of near-regional, regional, and teleseismic ground-motion data have been used to evaluate proposed models of the nuclear seismic source function for underground detonations in tuff/rhyolite emplacement media. It has been found that both the near-regional broad-band seismic data and the teleseismic body-wave magnitude data are consistent with the modified source model proposed by Mueller and Murphy (1971) but not with the simple cube-root of the yield-scaling source model. In particular, the observed linearity and slopes of the body-wave magnitude-yield curves as well as the observed variation of P-wave period with yield have been found to be fully compatible with the modified source model. On the other hand, it has been concluded that the observed long-period surface-wave data are inconsistent with a simple, spherically symmetric source model. The results of a preliminary analysis have suggested that this discrepancy may be related to the spall closure phenomenon.

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Electromagnetic sounding and crustal electrical conductivity in the region of the Wopmay Orogen, Northwest Territories, Canada

Canadian Journal of Earth Sciences ◽

10.1139/e89-203 ◽

1989 ◽

Vol 26 (11) ◽

pp. 2385-2395 ◽

Cited By ~ 11

Author(s):

P. A. Camfield ◽

J. C. Gupta ◽

A. G. Jones ◽

R. D. Kurtz ◽

D. H. Krentz ◽

...

Keyword(s):

Transfer Functions ◽

Three Dimensional ◽

Temporal Variations ◽

Electric Polarization ◽

Fault Scarp ◽

The Body ◽

Earth Model ◽

Period Range ◽

Group A ◽

A Minor

Temporal variations of the three components of the geomagnetic field were recorded at eight sites along a 240 km profile across the Early Proterozoic Wopmay Orogen. After an empirical separation of these data into normal and anomalous parts, horizontal-to-vertical-field transfer functions in the period range 40–1200 s display evidence for a minor anomaly spatially located near the allochthonous shelf margin at the eastern edge of the Hepburn Batholith. The observations can be partially simulated by a two-dimensional 20 ? m body (30 km wide, 2 km thick) embedded in the surface of a very resistive layered Earth model derived from inversion of magnetotelluric sounding data at a central station. The body correlates spatially with metamorphosed graphitic pelites of the Odjick Formation (Epworth Group), a unit of deep-water facies interpreted as continental slope–rise deposits. Laboratory measurements on samples of the pelite yielded resistivity values of the order of 104 ?∙m, so the enhanced conductivity of the body is more likely caused by water filling cracks associated with the pelites' well-developed cleavage and schistosity, rather than by the graphite. A scalar audiomagnetotelluric survey across the Wopmay fault zone, a prominent structure that bisects the orogen, gave results very much distorted by three-dimensional effects. The electric-polarization apparent resistivities of these data indicate a shallow conductor 2 km east of the fault scarp, 1–2 km wide. Models of the feature suggest that its vertical extent is at least 1–2 km.

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Slithering CSF: Cerebrospinal Fluid Dynamics in the Stationary and Moving Viper Boa, Candoia aspera

Biology ◽

10.3390/biology10070672 ◽

2021 ◽

Vol 10 (7) ◽

pp. 672

Author(s):

Bruce A. Young ◽

Skye Greer ◽

Michael Cramberg

Keyword(s):

Cerebrospinal Fluid ◽

Cardiac Cycle ◽

Low Frequency ◽

Mean Amplitude ◽

The Body ◽

Body Waves ◽

Lower Amplitude ◽

Lateral Undulation ◽

Recovery From Anesthesia ◽

The Relationship

In the viper boa (Candoia aspera), the cerebrospinal fluid (CSF) shows two stable overlapping patterns of pulsations: low-frequency (0.08 Hz) pulses with a mean amplitude of 4.1 mmHg that correspond to the ventilatory cycle, and higher-frequency (0.66 Hz) pulses with a mean amplitude of 1.2 mmHg that correspond to the cardiac cycle. Manual oscillations of anesthetized C. aspera induced propagating sinusoidal body waves. These waves resulted in a different pattern of CSF pulsations with frequencies corresponding to the displacement frequency of the body and with amplitudes greater than those of the cardiac or ventilatory cycles. After recovery from anesthesia, the snakes moved independently using lateral undulation and concertina locomotion. The episodes of lateral undulation produced similar influences on the CSF pressure as were observed during the manual oscillations, though the induced CSF pulsations were of lower amplitude during lateral undulation. No impact on the CSF was found while C. aspera was performing concertina locomotion. The relationship between the propagation of the body and the CSF pulsations suggests that the body movements produce an impulse on the spinal CSF.

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Seismic cone penetration test and seismic tomography in permafrost

Canadian Geotechnical Journal ◽

10.1139/t04-026 ◽

2004 ◽

Vol 41 (5) ◽

pp. 796-813 ◽

Cited By ~ 19

Author(s):

Anne-Marie LeBlanc ◽

Richard Fortier ◽

Michel Allard ◽

Calin Cosma ◽

Sylvie Buteau

Keyword(s):

Seismic Tomography ◽

Dynamic Properties ◽

Cone Penetration Test ◽

The Body ◽

Body Waves ◽

Reconstruction Technique ◽

Seismic Velocities ◽

Penetration Test ◽

Cone Penetration ◽

Seismic Cone Penetration Test

Two high-resolution multi-offset vertical seismic profile (VSP) surveys were carried out in a permafrost mound near Umiujaq in northern Quebec, Canada, while performing seismic cone penetration tests (SCPT) to study the cryostratigraphy and assess the body waves velocities and the dynamic properties of warm permafrost. Penetrometer-mounted triaxial accelerometers were used as the VSP receivers, and a swept impact seismic technique (SIST) source generating both compressional and shear waves was moved near the surface following a cross configuration of 40 seismic shot-point locations surrounding each of the two SCPTs. The inversion of travel times based on a simultaneous iterative reconstruction technique (SIRT) provided tomographic images of the distribution of seismic velocities in permafrost. The Young's and shear moduli at low strains were then calculated from the seismic velocities and the permafrost density measured on core samples. The combination of multi-offset VSP survey, SCPT, SIST, and SIRT for tomographic imaging led to new insights in the dynamic properties of permafrost at temperatures close to 0 °C. The P- and S-wave velocities in permafrost vary from 2400 to 3200 m/s and from 900 to 1750 m/s, respectively, for a temperature range between 0.2 and 2.0 °C. The Young's modulus varies from 2.15 to 13.65 GPa, and the shear modulus varies from 1.00 to 4.75 GPa over the same range of temperature.Key words: permafrost, seismic cone penetration test, vertical seismic profiling, seismic tomography, dynamic properties.

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A theoretical study of the radiation from small strikeslip earthquakes at close distances

Bulletin of the Seismological Society of America ◽

10.1785/bssa0730010083 ◽

1983 ◽

Vol 73 (1) ◽

pp. 83-96 ◽

Cited By ~ 1

Author(s):

Michel Campillo ◽

Michel Bouchon

Keyword(s):

Ground Motion ◽

Epicentral Distance ◽

Homogeneous Medium ◽

Source Model ◽

Strike Slip ◽

Peak Ground Velocity ◽

Corner Frequency ◽

Crack Model ◽

Sharp Change ◽

S Wave

abstract We present a study of the seismic radiation of a physically realistic source model—the circular crack model of Madariaga—at close distance range and for vertically heterogeneous crustal structures. We use this model to represent the source of small strike-slip earthquakes. We show that the characteristics of the radiated seismic spectra, like the corner frequency, are strongly affected by the presence of the free surface and by crustal layering, and that they can be considerably different from the ones of the homogeneous-medium far-field solution. The vertical and radial displacement spectra are the most strongly affected. We use this source model to calculate the decay of peak ground velocity with epicentral distance and source depth for small strike-slip earthquakes in California. For distances between 10 and 80 km, the peak horizontal velocity decay is of the form r−1.25 for a 4-km hypocentral depth and r−1.65 for deeper sources. The predominance of supercritically reflected arrivals beyond epicentral distances of 70 to 80 km produces a sharp change in the rate of decay of the ground motion. For most of the cases considered, the peak ground velocity increases between 80 and 100 km. We also show that the S-wave velocity in the source layer is the lower limit of phase velocities associated with significant ground motion.

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A dynamic model for far-field acceleration

Bulletin of the Seismological Society of America ◽

10.1785/bssa0720041049 ◽

1982 ◽

Vol 72 (4) ◽

pp. 1049-1068

Author(s):

John Boatwright

Keyword(s):

Stress Drop ◽

High Frequency ◽

Dynamic Stress ◽

The Body ◽

Body Waves ◽

Far Field ◽

Rupture Velocity ◽

Frequency Level ◽

Average Change ◽

Dynamic Stress Drop

abstract A model for the far-field acceleration radiated by an incoherent rupture is constructed by combining Madariaga's (1977) theory for the high-frequency radiation from crack models of faulting with a simple statistical source model. By extending Madariaga's results to acceleration pulses with finite durations, the peak acceleration of a pulse radiated by a single stop or start of a crack tip is shown to depend on the dynamic stress drop of the subevent, the total change in rupture velocity, and the ratio of the subevent radius to the acceleration pulse width. An incoherent rupture is approximated by a sample from a self-similar distribution of coherent subevents. Assuming the subevents fit together without overlapping, the high-frequency level of the acceleration spectra depends linearly on the rms dynamic stress drop, the average change in rupture velocity, and the square root of the overall rupture area. The high-frequency level is independent, to first order, of the rupture complexity. Following Hanks (1979), simple approximations are derived for the relation between the rms dynamic stress drop and the rms acceleration, averaged over the pulse duration. This relation necessarily depends on the shape of the body-wave spectra. The body waves radiated by 10 small earthquakes near Monticello Dam, South Carolina, are analyzed to test these results. The average change of rupture velocity of Δv = 0.8β associated with the radiation of the acceleration pulses is estimated by comparing the rms acceleration contained in the P waves to that in the S waves. The rms dynamic stress drops of the 10 events, estimated from the rms accelerations, range from 0.4 to 1.9 bars and are strongly correlated with estimates of the apparent stress.

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NUMERICAL MODELS OF HUGE TSUNAMIS OFF THE SANRIKU COAST

Coastal Engineering Proceedings ◽

10.9753/icce.v15.61 ◽

1976 ◽

Vol 1 (15) ◽

pp. 61

Author(s):

Toshio Iwasaki

Keyword(s):

Numerical Models ◽

Source Model ◽

Wave Source ◽

Sanriku Coast ◽

Wave Approximation ◽

Long Wave ◽

Small Wave ◽

Wave Heights ◽

Deep Region ◽

Long Wave Approximation

Although numerical computations of the generation and propagation of tsunamis are successfully achieved in recent years, modeling of their wave sources is still a big problem. Three kinds of, wave source model, that is statistical, oceanographic and fault model, are studied in this paper. It is found that the first model gives reasonable wave heights as shown in the previous paper, the second one presents roughly one half of those for the first model and the last one produces too small wave heights. Based on the analysis of computed results, nature of undulations off from the shore boundary, directivity of wave propagation and the spindle shaped leading part are discussed. Comparing magnitude of various wave parameters for the leading wave along the minor axis of the wave source, it is shown that the long wave approximation modified by the slope effect illustrates the tsunamis in deep region of the sea and the slope effect is most dominant in shallow region.

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Long-period mechanism of the 8 November 1980 Eureka, California, earthquake

Bulletin of the Seismological Society of America ◽

10.1785/bssa0720020439 ◽

1982 ◽

Vol 72 (2) ◽

pp. 439-456

Author(s):

Thorne Lay ◽

Jeffrey W. Given ◽

Hiroo Kanamori

Keyword(s):

Point Source ◽

Seismic Moment ◽

Moment Tensor ◽

Strike Slip ◽

The Body ◽

Body Waves ◽

Long Period ◽

Amplitude Data ◽

The Moment ◽

Scalar Moment

Abstract The seismic moment and source orientation of the 8 November 1980 Eureka, California, earthquake (Ms = 7.2) are determined using long-period surface and body wave data obtained from the SRO, ASRO, and IDA networks. The favorable azimuthal distribution of the recording stations allows a well-constrained mechanism to be determined by a simultaneous moment tensor inversion of the Love and Rayleigh wave observations. The shallow depth of the event precludes determination of the full moment tensor, but constraining Mzx = Mzy = 0 and using a point source at 16-km depth gives a major double couple for period T = 256 sec with scalar moment M0 = 1.1 · 1027 dyne-cm and a left-lateral vertical strike-slip orientation trending N48.2°E. The choice of fault planes is made on the basis of the aftershock distribution. This solution is insensitive to the depth of the point source for depths less than 33 km. Using the moment tensor solution as a starting model, the Rayleigh and Love wave amplitude data alone are inverted in order to fine-tune the solution. This results in a slightly larger scalar moment of 1.28 · 1027 dyne-cm, but insignificant (<5°) changes in strike and dip. The rake is not well enough resolved to indicate significant variation from the pure strike-slip solution. Additional amplitude inversions of the surface waves at periods ranging from 75 to 512 sec yield a moment estimate of 1.3 ± 0.2 · 1027 dyne-cm, and a similar strike-slip fault orientation. The long-period P and SH waves recorded at SRO and ASRO stations are utilized to determine the seismic moment for 15- to 30-sec periods. A deconvolution algorithm developed by Kikuchi and Kanamori (1982) is used to determine the time function for the first 180 sec of the P and SH signals. The SH data are more stable and indicate a complex bilateral rupture with at least four subevents. The dominant first subevent has a moment of 6.4 · 1026 dyne-cm. Summing the moment of this and the next three subevents, all of which occur in the first 80 sec of rupture, yields a moment of 1.3 · 1027 dyne-cm. Thus, when the multiple source character of the body waves is taken into account, the seismic moment for the Eureka event throughout the period range 15 to 500 sec is 1.3 ± 0.2 · 1027 dyne-cm.

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