scholarly journals A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

2020 ◽  
Vol 222 (1) ◽  
pp. 582-594
Author(s):  
Thomas Forbriger ◽  
Lingli Gao ◽  
Peter Malischewsky ◽  
Matthias Ohrnberger ◽  
Yudi Pan
Keyword(s):  
Phase Velocity ◽  
Rayleigh Wave ◽  
Half Space ◽  
Wave Velocity ◽  
Poisson’S Ratio ◽  
P Wave ◽  
Poisson's Ratio ◽  
Wave Number ◽  
Homogeneous Layer ◽  
Rayleigh Mode

SUMMARY Other than commonly assumed in seismology, the phase velocity of Rayleigh waves is not necessarily a single-valued function of frequency. In fact, a single Rayleigh mode can exist with three different values of phase velocity at one frequency. We demonstrate this for the first higher mode on a realistic shallow seismic structure of a homogeneous layer of unconsolidated sediments on top of a half-space of solid rock (LOH). In the case of LOH a significant contrast to the half-space is required to produce the phenomenon. In a simpler structure of a homogeneous layer with fixed (rigid) bottom (LFB) the phenomenon exists for values of Poisson’s ratio between 0.19 and 0.5 and is most pronounced for P-wave velocity being three times S-wave velocity (Poisson’s ratio of 0.4375). A pavement-like structure (PAV) of two layers on top of a half-space produces the multivaluedness for the fundamental mode. Programs for the computation of synthetic dispersion curves are prone to trouble in such cases. Many of them use mode-follower algorithms which loose track of the dispersion curve and miss the multivalued section. We show results for well established programs. Their inability to properly handle these cases might be one reason why the phenomenon of multivaluedness went unnoticed in seismological Rayleigh wave research for so long. For the very same reason methods of dispersion analysis must fail if they imply wave number kl(ω) for the lth Rayleigh mode to be a single-valued function of frequency ω. This applies in particular to deconvolution methods like phase-matched filters. We demonstrate that a slant-stack analysis fails in the multivalued section, while a Fourier–Bessel transformation captures the complete Rayleigh-wave signal. Waves of finite bandwidth in the multivalued section propagate with positive group-velocity and negative phase-velocity. Their eigenfunctions appear conventional and contain no conspicuous feature.

Some numerical solutions for Lamb's problem

1974 ◽  
Vol 64 (2) ◽  
pp. 473-491
Author(s):  
Harold M. Mooney
Keyword(s):  
Rayleigh Wave ◽  
Poisson’S Ratio ◽  
Pulse Width ◽  
Numerical Solutions ◽  
Pulse Height ◽  
P Wave ◽  
Poisson's Ratio ◽  
Wave Form ◽  
Lamb’S Problem ◽  
Wave Forms

abstract We consider a version of Lamb's Problem in which a vertical time-dependent point force acts on the surface of a uniform half-space. The resulting surface disturbance is computed as vertical and horizontal components of displacement, particle velocity, acceleration, and strain. The goal is to provide numerical solutions appropriate to a comparison with observed wave forms produced by impacts onto granite and onto soil. Solutions for step- and delta-function sources are not physically realistic but represent limiting cases. They show a clear P arrival (larger on horizontal than vertical components) and an obscure S arrival. The Rayleigh pulse includes a singularity at the theoretical arrival time. All of the energy buildup appears on the vertical components and all of the energy decay, on the horizontal components. The effects of Poisson's ratio upon vertical displacements for a step-function source are shown. For fixed shear velocity, an increase of Poisson's ratio produces a P pulse which is larger, faster, and more gradually emergent, an S pulse with more clear-cut beginning, and a much narrower Rayleigh pulse. For a source-time function given by cos2(πt/T), −T/2 ≦ T/2, a × 10 reduction in pulse width at fixed pulse height yields an increase in P and Rayleigh-wave amplitudes by factors of 1, 10, and 100 for displacement, velocity and strain, and acceleration, respectively. The observed wave forms appear somewhat oscillatory, with widths proportional to the source pulse width. The Rayleigh pulse appears as emergent positive on vertical components and as sharp negative on horizontal components. We show a theoretical seismic profile for granite, with source pulse width of 10 µsec and detectors at 10, 20, 30, 40, and 50 cm. Pulse amplitude decays as r−1 for P wave and r−12 for Rayleigh wave. Pulse width broadens slightly with distance but the wave form character remains essentially unchanged.

Seismic wave velocity investigation at The Geysers‐Clear Lake geothermal field, California

Geophysics ◽  
1982 ◽  
Vol 47 (5) ◽  
pp. 819-824 ◽  
Author(s):  
Harsh K. Gupta ◽  
Ronald W. Ward ◽  
Tzeu‐Lie Lin
Keyword(s):  
Wave Velocity ◽  
Poisson’S Ratio ◽  
Poisson Ratio ◽  
Volcanic Field ◽  
P Wave ◽  
Poisson's Ratio ◽  
Clear Lake ◽  
Seismic Wave Velocity ◽  
S Waves ◽  
The Geysers

Analysis of P‐ and S‐waves from shallow microearthquakes in the vicinity of The Geysers geothermal area, California, recorded by a dense, telemetered seismic array operated by the U.S. Geological Survey (USGS) shows that these phases are easily recognized and traced on record sections to distances of 80 km. Regional average velocities for the upper crust are estimated to be [Formula: see text] and [Formula: see text] for P‐ and S‐waves, respectively. Poisson’s ratio is estimated at 23 locations using Wadati diagrams and is found to vary from 0.13 to 0.32. In general, the Poisson’s ratio is found to be lower at the locations close to the steam production zones at The Geysers and Clear Lake volcanic field to the northeast. The low Poisson ratio corresponds to a decrease in P‐wave velocity in areas of high heat flow. The decrease may be caused by fracturing of the rock and saturation with gas or steam.

scholarly journals Unusual, equivocal Rayleigh-dispersion curves for simple models taking into account the special propagation conditions in the valley of Mexico City (CDMX) - Preliminary results

2017 ◽  
Vol 56 (1) ◽  
Author(s):  
Peter G. Malischewsky ◽  
Thomas Forbriger ◽  
Cinna Lomnitz†
Keyword(s):  
Phase Velocity ◽  
Mexico City ◽  
Rayleigh Waves ◽  
Poisson’S Ratio ◽  
Dispersion Analysis ◽  
Poisson's Ratio ◽  
Homogeneous Layer ◽  
Preliminary Results ◽  
Analysis And Synthesis ◽  
Simple Models

Other than commonly assumed in seismology, the phase velocity of Rayleigh waves not necessarily is a single-valued function of frequency. We demonstrate this for the first higher mode in simple models of a homogeneous layer on top of a homogeneous halfspace (LOH), which are used for the subsurface of the Texcoco zone in Mexico City valley in previous studies. In the structure of a homegenous layer with fixed bottom (LFB) the phenomenon exists for values of Poisson’s ratio between 0.19 and 0.5 and is most pronounced for P-velocity being three times S-velocity (Poisson’s ratio of 0.4375). This type of dispersion is demonstrated and a discussion of their possible fatal consequences for methods customarily used in seismology for dispersion analysis and synthesis of dispersion relations is presented.

scholarly journals Experimental Investigation on the Correlation between Dynamic Ultrasonic and Mechanical Properties of Sandstone Subjected to Uniaxial Compression

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Yunjiang Sun ◽  
Jianping Zuo ◽  
Yue Shi ◽  
Zhengdai Li ◽  
Changning Mi ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Ultrasonic Wave ◽  
Uniaxial Compression ◽  
Wave Velocity ◽  
Poisson’S Ratio ◽  
P Wave ◽  
Poisson's Ratio ◽  
Ultrasonic Wave Velocity ◽  
P Wave Velocity

Ultrasonic wave velocity is effective to evaluate anisotropy property and predict rock failure. This paper investigates the correlation between dynamic ultrasonic and mechanical properties of sandstones with different buried depths subjected to uniaxial compression tests. The circumferential anisotropy and axial wave velocity of sandstone are obtained by means of ultrasonic wave velocity measurements. The mechanical properties, including Young’s modulus and uniaxial compressive strength, are positively correlated with the axial P wave velocity. The average angles between the sandstone failure plane and the minimum and maximum wave directions are 35.8° and 63.3°, respectively. The axial P wave velocity almost keeps constant, and the axial S wave velocity has a decreasing trend before the failure of rock specimen. In most rock samples under uniaxial compression, shear failure occurs in the middle and splitting appears near both sides. Additionally, the dynamic Young’s modulus and dynamic Poisson’s ratio during loading are obtained, and the negative values of the Poisson’s ratio occur at the initial compression stage. Distortion and rotation of micro/mesorock structures may be responsible for the negative Poisson’s ratio.

THE REFLECTION OF RAYLEIGH WAVES BY A HIGH IMPEDANCE OBSTACLE ON A HALF‐SPACE

Geophysics ◽  
1960 ◽  
Vol 25 (6) ◽  
pp. 1195-1202 ◽  
Author(s):  
R. W. Fredricks ◽  
L. Knopoff
Keyword(s):  
Reflection Coefficient ◽  
Rayleigh Wave ◽  
Half Space ◽  
Poisson’S Ratio ◽  
Vertical Displacement ◽  
Elastic Half Space ◽  
Poisson's Ratio ◽  
Dual Integral Equations ◽  
High Impedance ◽  
Theoretic Solution

The reflection of a time‐harmonic Rayleigh wave by a high impedance obstacle in shearless contact with an elastic half‐space of lower impedance is examined theoretically. The potentials are found by a function—theoretic solution to dual integral equations. From these potentials, a “reflection coefficient” is defined for the surface vertical displacement in the Rayleigh wave. Results show that the reflected wave is π/2 radians out of phase with the incident wave for arbitrary Poisson’s ratio. The modulus of the “reflection coefficient” depends upon Poisson’s ratio, and is evaluated as [Formula: see text] for σ=0.25.

scholarly journals Evolution and properties of young oceanic crust: constraints from Poisson's ratio

2021 ◽  
Author(s):  
M J Funnell ◽  
A H Robinson ◽  
R W Hobbs ◽  
C Peirce
Keyword(s):  
Oceanic Crust ◽  
Wave Velocity ◽  
Poisson’S Ratio ◽  
Seismic Velocity ◽  
P Wave ◽  
Poisson's Ratio ◽  
Morphological Evidence ◽  
S Wave ◽  
Typical Structure ◽  
Velocity Models

Summary The seismic velocity of the oceanic crust is a function of its physical properties that include its lithology, degree of alteration, and porosity. Variations in these properties are particularly significant in young crust, but also occur with age as it evolves through hydrothermal circulation and is progressively covered with sediment. While such variation may be investigated through P-wave velocity alone, joint analysis with S-wave velocity allows the determination of Poisson's ratio, which provides a more robust insight into the nature of change in these properties. Here we describe the independent modelling of P- and S-wave seismic datasets, acquired along an ∼330 km-long profile traversing new to ∼8 Myr-old oceanic crust formed at the intermediate-spreading Costa Rica Rift (CRR). Despite S-wave data coverage being almost four-times lower than that of the P-wave dataset, both velocity models demonstrate correlations in local variability and a long-wavelength increase in velocity with distance, and thus age, from the ridge axis of up to 0.8 and 0.6 km s−1, respectively. Using the Vp and Vs models to calculate Poisson's ratio (σ), it reveals a typical structure for young oceanic crust, with generally high values in the uppermost crust that decrease to a minimum of 0.24 by 1.0–1.5 km sub-basement, before increasing again throughout the lower crust. The observed upper crustal decrease in σ most likely results from sealing of fractures, which is supported by observations of a significant decrease in porosity with depth (from ∼15 to < 2 per cent) through the dyke sequence in Ocean Drilling Program borehole 504B. High Poisson's ratio (>0.31) is observed throughout the crust of the north flank of the CRR axis and, whilst this falls within the ‘serpentinite’ classification of lithological proxies, morphological evidence of pervasive surface magmatism and limited tectonism suggests, instead, that the cause is porosity in the form of pervasive fracturing and, thus, that this is the dominant control on seismic velocity in the newly formed CRR crust. South of the CRR, the values of Poisson's ratio are representative of more typical oceanic crust, and decrease with increasing distance from the spreading centre, most likely as a result of mineralisation and increased fracture infill. This is supported by borehole observations and modelled 3-D seismic anisotropy. Crustal segments formed during periods of particularly low half-spreading rate (<35 mm yr−1) demonstrate high Poisson's ratio relative to the background, indicating the likely retention of increased porosity and fracturing associated with the greater degrees of tectonism at the time of their formation. Across the south flank of the CRR, we find that the average Poisson's ratio in the upper 1 km of the crust decreases with age by ∼0.0084 Myr−1 prior to the thermal sealing of the crust, suggesting that, to at least ∼7 Myr, advective hydrothermal processes dominate early CRR-generated oceanic crustal evolution, consistent with heat flow measurements.

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