Propagation of Elastic Pulses and Acoustic Emission in a Plate—Part 3: General Responses

1981 ◽  
Vol 48 (1) ◽  
pp. 139-147 ◽  
Author(s):  
A. N. Ceranoglu ◽  
Yih-Hsing Pao
Keyword(s):  
Acoustic Emission ◽  
Exact Solutions ◽  
Transient Response ◽  
Numerical Results ◽  
Point Sources ◽  
Concentrated Force ◽  
Center Of Rotation ◽  
Inverse Transform ◽  
Double Couple

In the first part of this paper, the Laplace transformed solutions in terms of the generalized ray integrals for point sources in a plate are presented. The inverse transform and the exact solutions for the epicentral responses together with numerical results were given in Part 2. In this part a modified version of Cagniard’s method is applied to obtain the transient response of the plate at any location due to point sources applied at the surface or the interior of the plate. Numerical results are shown for a concentrated force, a single-couple, a double-force, a double-couple without moment and a center of rotation, at locations up to six plate thicknesses from the source.

Propagation of Elastic Pulses and Acoustic Emission in a Plate—Part 2: Epicentral Responses

1981 ◽  
Vol 48 (1) ◽  
pp. 133-138 ◽  
Author(s):  
A. N. Ceranoglu ◽  
Yih-Hsing Pao
Keyword(s):  
Acoustic Emission ◽  
Transit Time ◽  
Transient Response ◽  
Elastic Plate ◽  
Numerical Results ◽  
P Wave ◽  
Concentrated Force ◽  
Center Of Rotation ◽  
Double Couple ◽  
Time Required

In the first part of this paper expressions for Green’s dyadics in terms of the generalized ray integrals for both unbounded and bounded media were given. In this part Cagniard’s method is applied to obtain the transient response along the epicentral points of an elastic plate. Numerical results are shown for a concentrated force, a single-couple, a double force, a double-couple without moment and a center of rotation up to 10 transit time required for the longitudinal (P)-wave to cross the thickness of the plate.

Propagation of Elastic Pulses and Acoustic Emission in a Plate—Part 1: Theory

1981 ◽  
Vol 48 (1) ◽  
pp. 125-132 ◽  
Author(s):  
A. N. Ceranoglu ◽  
Yih-Hsing Pao
Keyword(s):  
Acoustic Emission ◽  
Elastic Plate ◽  
Dynamic Process ◽  
Ray Theory ◽  
Transient Waves ◽  
Concentrated Force ◽  
Center Of Rotation ◽  
Material Defects ◽  
Double Couple

Transient waves generated by a variety of dynamic nuclei of strains including a concentrated force, a single-couple, a double-force, a double-couple without moment, a center of rotation, and a center of explosion in an elastic plate are analyzed. Some of these sources, or a combination of them, could be used to model the dynamic process of material defects. The analysis is based on the generalized ray theory and Cagniard’s method and the solutions are presented in terms of Green’s dyadics for a plate.

Use of reciprocity theorem for obtaining Rayleigh wave radiation patterns

1966 ◽  
Vol 56 (4) ◽  
pp. 925-936 ◽  
Author(s):  
I. N. Gupta
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Three Dimensional ◽  
Reciprocity Theorem ◽  
Point Sources ◽  
Dimensional Case ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
Homogeneous Half Space ◽  
Double Couple

abstract The reciprocity theorem is used to obtain Rayleigh wave radiation patterns from sources on the surface of or within an elastic semi-infinite medium. Nine elementary line sources first considered are: horizontal and vertical forces, horizontal and vertical double forces without moment, horizontal and vertical single couples, center of dilatation (two dimensional case), center of rotation, and double couple without moment. The results are extended to the three dimensional case of similar point sources in a homogeneous half space. Haskell's results for the radiation patterns of Rayleigh waves from a fault of arbitrary dip and direction of motion are reproduced in a much simpler manner. Numerical results on the effect of the depth of these sources on the Rayleigh wave amplitudes are shown for a solid having Poisson's ratio of 0.25.

Transient Response of an Interface-Crack in a Layered Plate

1986 ◽  
Vol 53 (3) ◽  
pp. 579-586 ◽  
Author(s):  
T. Kundu
Keyword(s):  
Stress Field ◽  
Interface Crack ◽  
Transient Response ◽  
Singular Integrals ◽  
Fortran Program ◽  
Numerical Results ◽  
New Method ◽  
Layered Plate ◽  
Improved Method ◽  
Sample Problem

In this paper, the transient response of an interface crack, in a two layered plate subjected to an antiplane stress field, is analytically computed. The problem is formulated in terms of semi-infinite integrals following the technique developed by Neerhoff (1979). It has been shown that the major steps of Neerhoff’s technique, which was originally developed for layered half-spaces, can also be applied to layered plate problems. An improved method for manipulation of semi-infinite singular integrals is also presented here. Finally, the new method is coded in FORTRAN program and numerical results for a sample problem are presented.

scholarly journals ON NONCOMMUTATIVE SOLITONS

2000 ◽  
Vol 15 (36) ◽  
pp. 2205-2218 ◽  
Author(s):  
A. SOLOVYOV
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Exact Solutions ◽  
Physical Meaning ◽  
Symmetric Solution ◽  
Numerical Results ◽  
Scalar Field Theory ◽  
Radially Symmetric Solution

We consider (2+1)-dimensional classical noncommutative scalar field theory. The general ansatz for a radially symmetric solution is obtained. Some exact solutions are presented. Their possible physical meaning is discussed. The case of finite θ is discussed qualitatively and illustrated by some numerical results.

scholarly journals Monitoring of induced distributed double-couple sources using Marchenko-based virtual receivers

Solid Earth ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1301-1319 ◽  
Author(s):  
Joeri Brackenhoff ◽  
Jan Thorbecke ◽  
Kees Wapenaar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Synthetic Data ◽  
Real Data ◽  
Point Sources ◽  
Reflection Data ◽  
Double Couple ◽  
Source Mechanisms ◽  
Source Signal ◽  
Time Part

Abstract. We aim to monitor and characterize signals in the subsurface by combining these passive signals with recorded reflection data at the surface of the Earth. To achieve this, we propose a method to create virtual receivers from reflection data using the Marchenko method. By applying homogeneous Green’s function retrieval, these virtual receivers are then used to monitor the responses from subsurface sources. We consider monopole point sources with a symmetric source signal, for which the full wave field without artifacts in the subsurface can be obtained. Responses from more complex source mechanisms, such as double-couple sources, can also be used and provide results with comparable quality to the monopole responses. If the source signal is not symmetric in time, our technique based on homogeneous Green’s function retrieval provides an incomplete signal, with additional artifacts. The duration of these artifacts is limited and they are only present when the source of the signal is located above the virtual receiver. For sources along a fault rupture, this limitation is also present and more severe due to the source activating over a longer period of time. Part of the correct signal is still retrieved, as is the source location of the signal. These artifacts do not occur in another method that creates virtual sources as well as receivers from reflection data at the surface. This second method can be used to forecast responses to possible future induced seismicity sources (monopoles, double-couple sources and fault ruptures). This method is applied to field data, and similar results to the ones on synthetic data are achieved, which shows the potential for application on real data signals.

scholarly journals Noise-mediated dynamics in a two-dimensional oscillator: Exact solutions and numerical results

2001 ◽  
Vol 56 (3) ◽  
pp. 354-360 ◽  
Author(s):  
J. A Acebrón ◽  
A. R Bulsara ◽  
M. E Inchiosa ◽  
W.-J Rappel
Keyword(s):  
Exact Solutions ◽  
Numerical Results ◽  
Two Dimensional

Inversion of near-source S polarization for parameters of double-couple point sources

1989 ◽  
Vol 79 (6) ◽  
pp. 1779-1809
Author(s):  
Pascal Bernard ◽  
Aldo Zollo
Keyword(s):  
Frequency Band ◽  
Strike Slip ◽  
Point Sources ◽  
Inversion Method ◽  
Reasonable Assumption ◽  
Good Resolution ◽  
Angular Difference ◽  
Amplitude Data ◽  
Highly Nonlinear ◽  
Double Couple

Abstract We propose an inversion method for retrieving the focal parameters of small to moderate earthquakes by using the near-source S-wave polarizations, which are expected to be less sensitive than amplitude data to source details or propagation effects. We first studied the variability of the polarization vector for complete synthetic records generated in simple media with a shallow low-velocity layer, for various distances (0 to 50 km), source depths (1 to 15 km), and mechanisms. In the frequency band 1 to 2 Hz, a polarization fluctuation of less than 20° is found for sources deeper than 5 km. The mean angular difference between ray theory and complete field polarization is less than 10° when the complete waveform meets the two following criteria: (1) The polarization is nearly stable (less than 30° of variability) and (2) the motion is nearly horizontal (vector dip less than 30°). The inversion method uses a norm related to the angular difference in polarization between the real and synthetic waveforms generated by a point double couple. As the problem is highly nonlinear, the model space (strike, dip, slip, location) should be finely sampled and systematically explored in the whole domain of interest. We tested the inversion resolution with synthetic data for a strike-slip and a dip-slip source at 10 km in depth (no error in location) recorded at eight stations within 30 km, assuming an error of 25° on the synthetic polarization. The dip-slip inversion gives a good resolution in dip (15° of uncertainty), but a strong correlation between strike and slip, because no recording site was close to the near vertical principal axis of the stress tensor in the test. On the contrary, the near horizontal major axis of the tensor is very well constrained. The strike-slip inversion gives a good resolution in the three parameters, with uncertainties of about 10°. A 25° change in the strike, dip, or slip angle statistically results in a 25° rotation of the polarization. With numerous stations, the overdetermination of the problem reduces the model error to values lower than 25°. The absence of records in specific areas introduces additional solutions for the possible mechanisms. Finally, the sensitivity of polarization to 3 km shift in source location is globally smaller than for 25° of rotation of any fault angle. The application of this method to real data requires the evaluation of the reliability in the polarizations computed for simplified media. An uncertainty of 25° is expected to be a reasonable assumption for distances smaller than 30 km in the 1 to 2 Hz frequency band; more generally, the error is expected to increase with distance and frequency.

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