scholarly journals Displacements and stresses induced by a point source across a plane interface separating two elastic semi-infinite spaces: An analytical solution

1998 ◽  
Vol 103 (B7) ◽  
pp. 15109-15125 ◽  
Author(s):  
Stefano Tinti ◽  
Alberto Armigliato
Keyword(s):  
Analytical Solution ◽  
Point Source ◽  
Plane Interface

Reflection maxima for reflections from single interfaces

Geophysics ◽  
1988 ◽  
Vol 53 (2) ◽  
pp. 271-275 ◽  
Author(s):  
C. A. Rendleman ◽  
F. K. Levin
Keyword(s):  
Plane Wave ◽  
Point Source ◽  
Critical Angle ◽  
Maximum Amplitude ◽  
P Wave ◽  
Plane Interface ◽  
Wide Angle ◽  
Mathematical Expressions ◽  
Shed Light

At a workshop on refraction and wide‐angle reflections, Hilterman (1985) pointed out that, in contrast to the plane‐wave case, when there is a point source, a P-wave reflected from a plane interface attains its maximum amplitude at an offset greater than that corresponding to the critical angle (Figure 1). The same conclusion had been drawn earlier by Červený (1967). However, neither Červený’s results, which were based on very complicated mathematical expressions derived by Brekhovskikh (1960), nor Hilterman’s computer‐generated data shed light on the physics implied by the shifted maximum.

An Analytical Solution of Two-Dimensional Flow and Deformation Coupling Due to a Point Source Within a Finite Poroelastic Media

2011 ◽  
Vol 78 (6) ◽  
Author(s):  
Peichao Li ◽  
Detang Lu
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Point Source ◽  
Transient Behavior ◽  
Finite Domain ◽  
Two Dimensional ◽  
Pressure Derivative ◽  
Poroelastic Media ◽  
Two Dimensional Flow ◽  
Dependent Flow

An analytical solution is derived for the time-dependent flow and deformation coupling of a saturated isotropic homogeneous incompressible poroelastic media within a two-dimensional (2D) finite domain due to a point source at some arbitrary position. In this study, the pore pressure field is assumed to conform to the second type of boundary conditions. Boundary conditions of the displacement field are chosen with care to match the appropriate finite sine and cosine transforms and simplify the resulting solution. It is found that the analytical solution is always independent of the Poisson’s ratio. The detailed solutions are given for the case of a periodic point source with zero pressure derivatives on the boundaries and for an imposed pressure derivative on the lower edge in the absence of a source. The presented analytical solutions are highly applicable for calibrating numerical codes, and meanwhile they can be used to further investigate the transient behavior of flow and deformation coupling induced by fluid withdrawal within a 2D finite poroelastic media.

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