THE MECHANISM OF GENERATION OF LONG WAVES FROM EXPLOSIONS

Geophysics ◽  
1955 ◽  
Vol 20 (1) ◽  
pp. 87-103 ◽  
Author(s):  
C. Hewitt Dix

Cagniard’s method is applied to the numerical calculation of the vertical displacement due to a point source in a semi‐infinite elastic solid medium at three points on a vertical line through the source. The source is a step in the scalar displacement potential. From these calculated responses the response for any physically possible spherically symmetric source can be computed by application of the Duhamel integral. Clear evidence of backward transmission of transverse wave energy is found along the vertical axis through the source. This, together with the energy of the longitudinal waves, also transmitted backwards, accounts for the mechanism by which energy is held near the source and near the free surface long enough to account for the generation of long period surface waves. This mechanism of generation of long period surface waves is not restricted to the free surface case. Any good reflector, which also generates secondary transverse waves from longitudinal primary waves, will serve the purpose. It is suggested that this gives a clue to the mechanism of the formation of “ground roll” in many practical cases.

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Baljeet Singh

The governing equations for generalized thermoelasticity of a mixture of an elastic solid and a Newtonian fluid are formulated in the context of Lord-Shulman and Green-Lindsay theories of generalized thermoelasticity. These equations are solved to show the existence of three coupled longitudinal waves and two coupled transverse waves, which are dispersive in nature. Reflection from a thermally insulated stress-free surface is considered for incidence of coupled longitudinal wave. The speeds and reflection coefficients of plane waves are computed numerically for a particular model.


Geophysics ◽  
1956 ◽  
Vol 21 (1) ◽  
pp. 71-87 ◽  
Author(s):  
T. W. Spencer

The problem treated is concerned with predicting the transient response of a system composed of a liquid layer, bounded above by a vacuum and below by a perfectly elastic solid, when excited by an arbitrary pressure applied uniformly over the surface of a spherical cavity located in the fluid. The Laplace transform of the displacement response is expressed in terms of an integral which is expanded in such a way that each term describes the contribution from one of the image sources. Each term may be evaluated exactly at points located on a vertical axis passing through the source. The final expression for the vertical displacement at axial points is composed of the acoustic, after‐flow, and correction terms. In solids for which Poisson’s ratio is greater than one third the initial variation of the correction is toward positive values (corresponding to motion directed toward the interface). For Poisson’s ratio less than one third the initial variation may be either positive or negative depending on the magnitude of the compressional velocity ratio. A surface wave is shown to exist regardless of the choice of parameters. The surface wave velocity is always less than it would be in the absence of the liquid.


1963 ◽  
Vol 17 (1) ◽  
pp. 75-88 ◽  
Author(s):  
John W. Miles

A semi-infinite body of liquid is in uniform rotation about a vertical axis for t < 0. A concentrated, vertical displacement of the free surface is imposed at t = 0. The motion of the free surface for t > 0 is calculated in linear approximation with the aid of Hankel and Laplace transformations, together with an intermediate transformation to parabolic co-ordinates. The result appears as an integral superposition of dispersive waves that divides naturally into two parts, corresponding to waves of the first and second class, with angular frequencies that are respectively greater or less than twice the angular speed of rotation. The waves of the first class, which are qualitatively similar to those in the classical (Cauchy–Poisson) problem, are found to dominate the asymptotic representation, as obtained through a stationary-phase approximation. The analysis is carried out in such a way as to separate the effects of Coriolis acceleration and free-surface curvature. Attention is focused on concave surfaces, such as would be realized in a laboratory experiment, but it is pointed out that striking differences exist between the dispersion laws for concave and convex surfaces, especially as regards waves of the second class.


2012 ◽  
Vol 707 ◽  
pp. 482-495 ◽  
Author(s):  
Ofer Manor ◽  
Leslie Y. Yeo ◽  
James R. Friend

AbstractThe classical Schlichting boundary layer theory is extended to account for the excitation of generalized surface waves in the frequency and velocity amplitude range commonly used in microfluidic applications, including Rayleigh and Sezawa surface waves and Lamb, flexural and surface-skimming bulk waves. These waves possess longitudinal and transverse displacements of similar magnitude along the boundary, often spatiotemporally out of phase, giving rise to a periodic flow shown to consist of a superposition of classical Schlichting streaming and uniaxial flow that have no net influence on the flow over a long period of time. Correcting the velocity field for weak but significant inertial effects results in a non-vanishing steady component, a drift flow, itself sensitive to both the amplitude and phase (prograde or retrograde) of the surface acoustic wave propagating along the boundary. We validate the proposed theory with experimental observations of colloidal pattern assembly in microchannels filled with dilute particle suspensions to show the complexity of the boundary layer, and suggest an asymptotic slip boundary condition for bulk flow in microfluidic applications that are actuated by surface waves.


Geophysics ◽  
1951 ◽  
Vol 16 (1) ◽  
pp. 63-80 ◽  
Author(s):  
Milton B. Dobrin

A non‐mathematical summary is presented of the published theories and observations on dispersion, i.e., variation of velocity with frequency, in surface waves from earthquakes and in waterborne waves from shallow‐water explosions. Two further instances are cited in which dispersion theory has been used in analyzing seismic data. In the seismic refraction survey of Bikini Atoll, information on the first 400 feet of sediments below the lagoon bottom could not be obtained from ground wave first arrival times because shot‐detector distances were too great. Dispersion in the water waves, however, gave data on speed variations in the bottom sediments which made possible inferences on the recent geological history of the atoll. Recent systematic observations on ground roll from explosions in shot holes have shown dispersion in the surface waves which is similar in many ways to that observed in Rayleigh waves from distant earthquakes. Classical wave theory attributes Rayleigh wave dispersion to the modification of the waves by a surface layer. In the case of earthquakes, this layer is the earth’s crust. In the case of waves from shot‐holes, it is the low‐speed weathered zone. A comparison of observed ground roll dispersion with theory shows qualitative agreement, but it brings out discrepancies attributable to the fact that neither the theory for liquids nor for conventional solids applies exactly to unconsolidated near‐surface rocks. Additional experimental and theoretical study of this type of surface wave dispersion may provide useful information on the properties of the surface zone and add to our knowledge of the mechanism by which ground roll is generated in seismic shooting.


2006 ◽  
Vol 111 (B11) ◽  
pp. n/a-n/a ◽  
Author(s):  
A. M. G. Ferreira ◽  
N. F. d'Oreye ◽  
J. H. Woodhouse ◽  
W. Zürn

Author(s):  
Timothée Jamin ◽  
Leonardo Gordillo ◽  
Gerardo Ruiz-Chavarría ◽  
Michael Berhanu ◽  
Eric Falcon

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.


1995 ◽  
Vol 85 (3) ◽  
pp. 716-735 ◽  
Author(s):  
John F. Cassidy ◽  
Garry C. Rogers

Abstract On 6 April 1992, a magnitude 6.8 (MS) earthquake occurred in the triple-junction region at the northern end of the Cascadia subduction zone. This was the largest earthquake in at least 75 yr to occur along the 110-km-long Revere-Dellwood-Wilson (RDW) transform fault and the first large earthquake in this region recorded by modern broadband digital seismic networks. It thus provides an opportunity to examine the rupture process along a young (&lt;2 Ma) oceanic transform fault and to gain better insight into the tectonics of this triple-junction region. We have investigated the source parameters and the rupture process of this earthquake by modeling broadband body waves and long-period surface waves and by accurately locating the mainshock and the first 10 days of aftershocks using a well-located “calibration” event recorded during an ocean-bottom seismometer survey. Analysis of P and SH waveforms reveals that this was a complex rupture sequence consisting of three strike-slip subevents in 12 sec. The initial rupture occurred 5 to 6 km to the SW of the seafloor trace of the RDW fault at 50.55° N, 130.46° W. The dominant subevent occurred 2 to 3 sec later and 4.3 km beneath the seafloor trace of the RDW fault, and a third subevent occurred 5 sec later, 18 km to the NNW, suggesting a northwestward propagating rupture. The aftershock sequence extended along a 60- to 70-km-long segment of the RDW fault, with the bulk of the activity concentrated ∼30 to 40 km to the NNW of the epicenter, consistent with this interpretation. The well-constrained mechanism of the initial rupture (strike/dip/slip 339°/90°/−168°) and of the largest aftershock (165°/80°/170°) are rotated 15° to 20° clockwise relative to the seafloor trace of the RDW fault but are parallel to the Pacific/North America relative plate motion vector. In contrast, the mechanisms of the dominant subevent (326°/87°/−172°), and the long-period solution derived from surface waves aligns with the RDW fault. This suggests that small earthquakes (M &lt; 6) in this area occur along faults that are optimally aligned with respect to the regional stress field, whereas large earthquakes, involving tens of kilometers of rupture, activate the RDW fault. For the mainshock, we estimate a seismic moment (from surface waves) of 1.0 × 1026 dyne-cm, a stress drop of 60 bars, and an average slip of 1.2 m. This represents only 21 yr of strain accumulation, implying that there is either a significant amount of aseismic slip along the RDW fault or that much of the strain accumulation manifests itself as deformation within the Dellwood and Winona blocks or along the continental margin.


2018 ◽  
Vol 35 (1) ◽  
pp. 15-23
Author(s):  
Zi-Yu Guo ◽  
Xiao-Peng Chen ◽  
Lai-Bing Jia ◽  
Bin Xu

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