Insights into wave propagation in prestressed porous media are important in geophysical applications, such as monitoring changes in geo-pressure. This can be addressed by poro-acoustoelasticity theory, which extends the classical acoustoelasticity of solids to porous media. The relevant poro-acoustoelasticity equations can be derived from anisotropic poroelasticity equations by replacing the poroelastic stiffness matrix with an acoustoelastic stiffness matrix consisting of second-order 2oeC and third-order 3oeC elastic constants. The theory considers the poroelasticity equations as nonlinear due to the cubic strain energy function with linear strains under ?nite-magnitude prestresses. In this study, a rotated staggered-grid finite-difference (RSG-FD) method with an unsplit convolutional perfectly matched layer (C-PML) absorbing boundary is used to solve a first-order velocity-stress formulation of poro-acoustoelasticity equations for elastic wave propagation in prestressed porous media. Numerical solutions were partially verified by computing the velocities of fast P-wave, slow P-wave and S-wave as a function of hydrostatic prestress and were compared with the exact values. Numerical simulations of wave propagation were carried out for the model of poro-acoustoelastic homogenous space under three states, prestress-confining (hydrostatic), uniaxial, and pure shear; and for the model of two poro-acoustoelastic homogenous half-spaces in the planar contact under confining (hydrostatic) prestress. The resulting wavefield snapshots show fast P-wave, slow P-wave and S-wave propagations in poro-acoustoelastic media under loading prestresses, which illustrates that the stress-induced velocity anisotropy is of orthotropy strongly related to the orientation of prestresses. These examples demonstrate the significant impact of prestressing conditions on seismic responses in both velocity and anisotropy.

Seismic exploration of deep oil/gas reservoirs involves the propagation of seismic waves in high-pressure media. Traditional elastic wave equations are not suitable for describing such media. The theory of acoustoelasticity establishes the dynamic equation of wave propagating in prestressed media through constitutive relation using third-order elastic constants. Many studies have been carried out on numerical simulations for acoustoelastic waves, but mainly are limited to 2D cases. A standard staggered-grid (SSG) finite difference (FD) approach and the perfectly matched layer (PML) absorbing boundary are combined to solve 3D first-order velocity-stress equations of acoustoelasticity to simulate wave propagating in 3D prestressed solid medium. Our numerical results are partially validated by plane wave analytical solution through the comparison of calculated and theoretical P-/S-wave velocities as a function of confining prestress. We perform numerical simulations of acoustoelastic waves under confining, uniaxial, and pure shear prestressed conditions. The results show the stress-induced velocity anisotropy in acoustoelastic media, which is closely related to the direction of prestresses. Comparisons to seismic simulations based on the theory of elasticity illustrate the limitation of conventional elastic simulations for prestressed media. Numerical simulations prove the significant effect of prestressed conditions on seismic responses.

The t h i r d -o r d e r e l a s t i c m o d u l i o f m a r a g i n g s t e e l s a m p l e s w i t h n o m i n a l s t r e n g t h s o f 200 a n d 300 k s i h a v e d e t e r m i n e d , p r i o r a n d a f t e r a g i n g t r e a t m e n t f o r 3 h o u r s a t 900' F , 1 8 N i y i e l d b e e n h e a t f r o m h y d r o s t a t i c p r e s s u r e dependence and s e c o n d h a r m o n i c g e n e r a t i o n e x p e r i m e n t s . The change i n u l t r a s o n i c v e l o c i t y u n d e r h y d r o s t a t i c p r e s s u r e , a s s m a l l a s few p a r t s i n 10' f o r 1 0 p s i , was measured up t o 2 4 0 p s i by t h e p u l s e d -p h a s e -l o c k e d -l o o p t e c h n i q u e a n d t h e a m p l i t u d e s of f u n d a m e n t a l a n d s e c o n d h a r m o n i c waves by a c a p a c i t i v e d e t e c t o r . T h e e f f e c t o f a g e -h a r d e n i n g o n t h e t h i r d -o r d e r e l a s t i c m o d u l i i n c l u d i n g t h e n o n l i n e a r i t y p a r a m e t e r i s d i s c u s s e d . I . INTRODUCTION The 18Ni m a r a g i n g s t e e l s , f i r s t d e v e l o p e d i n e a r l y 1 9 6 0 '~~ h a v e f o u n d n u m e r o u s a p p l i c a t i o n s e s p e c i a l l y i n t h e a e r o s p a c e i n d u s t r y p r i m a r i l y b e c a u s e a n e x t r a o r d i n a r y c o m b i n a t i o n of s t r u c t u r a l s t r e n g t h a n d f r a c t u r e t o u g h n e s s c a n b e a c h i e v e d i n t h i s c l a s s o f a l l o y s by a s i m p l e h e a t t r e a t m e n t p r o c e d u r e c a l l e d " m a r a g i n g " ( m a r t e n s i t e + a g e h a r d e n i n g ) . H o w e v e r , d e s p i t e t r e m e n d o u s i n t e r e s t i n t h e e n g i n e e r i n g p r o p e r t i e s a n d m e t a l l u r g i c a l a s p e c t s o f t h e s e c a r b o n -f r e e a l l o y s c o n t a i n i n g a p p r e c i a b l e a m o u n t s o f molybedenum a n d c o b a l t i n a d d i t i o n t o 1 8 % n i c k e l , t h e s t u d y o f e l a s t i c p r o p e r t i e s h a s b e e n l a c k i n g i n t h e l i t e r a t u r e . I n f a c t , o n l y t h e s e c o n do r d e r e l a s t i c c o n s t a n t s a r e r e p o r t e d 4 f o r a n n e a l e d 1 8 N i ( 3 0 0 ) g r a d e a t room and l o w e r t e m p e r a t u r e s . W e h a v e t h e r e f o r e u n d e r t a k e n t h e i n v e s t i g a t i o n o f t h e e f f e c t o f maraging t r e a t m e n t on t h e s e c o n d -a n d t h i r d -o r d e r e l a s t i c c o n s t a n t s o f 200-a n d 3 0 0 -g r a d e m a r a g i n g s t e e l s . T h i s s t u d y was a l s o i n s p i r e d b y a r e c e n t work5 of o n e o f t h e a u t h o r s ( J . H . C ) who p r o p o s e d t h a t t h e n o n l i n e a r i t y p a r a m e t e r of c u b i c c r y s t a l s , which c a n b e e x p r e s s e d i n t e r m s o f seconda n d t h i r d -o r d e r e l a s t i c c o n s t a n t s , c a n b e 0090-5607/87/0000-1 I3 1 $1 .OO 0 1987 IEEE c o r r e l a t e d w i t h t h e e l a s t i c h a r d n e s s o f t h e m a t e r i a l...

Insights into wave propagation in prestressed media are important in geophysical applications such as monitoring changes in geo-pressure and tectonic stress. This can be addressed by acoustoelasticity theory, which accounts for nonlinear strain responses due to stresses of finite magnitude. In this study, a rotated staggered grid finite-difference (RSG-FD) method with an unsplit convolutional perfectly matched layer absorbing boundary is used to solve the relevant acoustoelastic equations with third-order elastic constants for elastic wave propagation in prestressed media. We partially verify our numerical simulations by the plane-wave theoretical solution. Comparisons of theoretical and calculated wave velocities are conducted for both P-wave and S-wave as a function of hydrostatic prestresses. We discuss several aspects of the numerical implementation. Numerical acoustoelasticity simulations for wave propagation in single- and double-layer models are carried out under four states of prestresses, confining, uniaxial, pure-shear, and simple-shear. The results display the effective anisotropy of elastic wave propagation in acoustoelastic media, illustrating that the prestress-induced velocity anisotropy is of orthotropic features strongly related to the orientation of prestresses. These examples demonstrate the significant impact of prestressed conditions on seismic responses in both phase and amplitude.