Displacement potentials

2009 ◽  
pp. 157-188
Author(s):  
Andrei Constantinescu ◽  
Alexander Korsunsky
Keyword(s):  
Displacement Potentials

The Elastic Field of an Elliptic Inclusion With a Slipping Interface

1986 ◽  
Vol 53 (1) ◽  
pp. 103-107 ◽  
Author(s):  
E. Tsuchida ◽  
T. Mura ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Infinite Series ◽  
Elastic Field ◽  
Elliptic Inclusion ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Bonded Interface ◽  
The Matrix ◽  
Displacement Potentials ◽  
Uniform Expansion

The paper analyzes the elastic fields caused by an elliptic inclusion which undergoes a uniform expansion. The interface between the inclusion and the matrix cannot sustain shear tractions and is free to slip. Papkovich–Neuber displacement potentials are used to solve the problem. In contrast to the perfectly bonded interface, the solution cannot be expressed in closed form and involves infinite series. The results are illustrated by numerical examples.

GASBUGGY SEISMIC SOURCE MEASUREMENTS

Geophysics ◽  
1972 ◽  
Vol 37 (2) ◽  
pp. 301-312 ◽  
Author(s):  
William R. Perret
Keyword(s):  
Seismic Source ◽  
Gas Production ◽  
Tight Gas ◽  
Near Surface ◽  
Nuclear Explosions ◽  
Vertical Displacements ◽  
Remote Station ◽  
Displacement Potentials ◽  
Gas Bearing ◽  
Peak Value

Gasbuggy, a 29‐kt nuclear experiment, was detonated December 10, 1967, at a depth of 4240 ft in the San Juan Basin in New Mexico. Its purpose was to develop techniques for stimulation of natural gas production from tight gas‐bearing formations. Data from four subsurface instrument stations in a boring 1500 ft from Gasbuggy indicated formation of a spherical cavity of 88 ft radius and a microfracture radius of about 480 ft. The mean peak value of reduced displacement potentials which defined the seismic source was [Formula: see text]. Calculations indicate that about 2 percent of the energy released remained in the seismic source at 1500 ft. Data from surface motion instruments distributed between surface zero and 8400 ft were similar to those observed above any other contained nuclear explosions. Spalling was indicated at all surface stations. Transient vertical displacements indicate a mound about 6.7 inches high near surface zero and extending through the most remote station where uplift was 0.3 inch.

Generalized ray theory for shear dislocations

1974 ◽  
Vol 64 (1) ◽  
pp. 45-64 ◽  
Author(s):  
Donald V. Helmberger
Keyword(s):  
Point Source ◽  
Step Function ◽  
Time Function ◽  
Corner Frequency ◽  
S Wave ◽  
S Waves ◽  
Vertical Fault ◽  
Wave Forms ◽  
Displacement Potentials ◽  
Apparent Shift

abstract Generalized ray expansions of the P, SH, and SV displacement potentials resulting from a point-source dislocation are evaluated at the surface of a layered half-space. The Cagniard-de Hoop technique is used to obtain the transient response. The results of this analysis are used to construct synthetic seismograms for a shear dislocation on a vertical fault plane. Comparisons of synthetic and observed seismograms for the Borrego Mountain earthquake (April 9, 1968) at teleseismic distances indicate an equivalent point-source depth of 9 km with the far-field time function approximated by a step function with an exponential decay. This time function fits both the P and S wave forms. The apparent shift in corner frequency between the P and S waves for shallow events, as reported by some investigators, is explained by surface reflections.

scholarly journals Spectral-method algorithm for modeling dispersion of acoustic modes in elastic cylindrical structures

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. H19-H27 ◽  
Author(s):  
Florian Karpfinger ◽  
Henri-Pierre Valero ◽  
Boris Gurevich ◽  
Andrey Bakulin ◽  
Bikash Sinha
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Method ◽  
Differential Operators ◽  
Generalized Eigenvalue Problem ◽  
Low Frequencies ◽  
Cylindrical Structures ◽  
Generalized Eigenvalue ◽  
Displacement Potentials ◽  
As Stress ◽  
Search Routine

A new spectral-method algorithm can be used to study wave propagation in cylindrically layered fluid and elastic structures. The cylindrical structure is discretized with Chebyshev points in the radial direction, whereas differentiation matrices are used to approximate the differential operators. We express the problem of determining modal dispersions as a generalized eigenvalue problem that can be solved readily for all eigenvalues corresponding to various axial wavenumbers. Modal dispersions of guided modes can then be expressed in terms of axial wavenumbers as a function of frequency. The associated eigenvectors are related to the displacement potentials that can be used to calcu-late radial distributions of modal amplitudes as well as stress components at a given frequency. The workflow includes input parameters and the construction of differentiation matrices and boundary conditions that yield the generalized eigenvalue problem. Results from this algorithm for a fluid-filled borehole surrounded by an elastic formation agree very well with those from a root-finding search routine. Computational efficiency of the algorithm has been demonstrated on a four-layer completion model used in a hydrocarbon-producing well. Even though the algorithm is numerically unstable at very low frequencies, it produces reliable and accurate results for multilayered cylindrical structures at moderate frequencies that are of interest in estimating formation properties using modal dispersions.

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