Generalized viscoelastic wave equation

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August undefined, 2024

WebABSTRACT During seismic wave propagation, intrinsic attenuation inside the earth gives rise to amplitude loss and phase dispersion. Without appropriate correction strategies in migration, these effects degrade the amplitudes and resolution of migrated images. Based on a new time-domain viscoacoustic wave equation, we have developed a … WebDec 8, 2024 · Using Taylor expansion in terms of β, the phase velocity can be approximated to. vg(ω) = √2c(β) A √A + B ≈ c(β)[1 + (− 1 8β2 + 1 2β)( ω ω0)β]. The linearity between …

Theoretical Model for Nonlinear Long Waves over a Thin Viscoelastic …

WebJan 6, 2024 · Abstract We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. WebFeb 8, 2024 · We study existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to … oxidation number of o in hydroxide ion

ENERGY DECAY FOR VARIABLE COEFFICIENT VISCOELASTIC …

WebFeb 1, 2016 · This paper presents a generalized wave equation which unifies viscoelastic and pure elastic cases into a single wave equation. In the generalized wave equation, the degree of viscoelasticity varies between zero and unity, and is defined by a … WebSep 11, 2024 · The generalized standard-linear-solid model, also called the Zener model, is widely used in viscoacoustic/viscoelastic wavefield forward and inverse modeling, because the wave equations in... WebThis work presents a new constitutive relation and the corresponding time‐domain wave equation to model wave propagation in inhomogeneous anisotropic and dissipative media. The rheological equation includes the generalized Hooke’s law and Boltzmann’s superposition principle to account for anelasticity. The attenuation properties in ... oxidation number of oxygen in hof

A generalized viscoelastic Biot/squirt model for clay …

WebMay 24, 2024 · The modified viscoelastic wave equations The first-order viscoelastic wave equations for a two-dimensional (2D) medium, are given as (Zhu & Carcione 2014) ∂vx ∂t = 1 ρ∂τxx ∂x + 1 ρ∂τxz ∂z, (10) ∂vz ∂t = 1 ρ∂τxz ∂x + 1 ρ∂τzz ∂z, (11) ∂τxx ∂t = MP(∂vx ∂x + ∂vz ∂z) − 2MS∂vz ∂z, (12) ∂τzz ∂t = MP(∂vx ∂x + ∂vz ∂z) − 2MS∂vx ∂x, (13) WebWe theoretically analyzed the interaction between surface water waves and a thin muddy seabed. Wave motion in the inviscid water layer was assumed to be irrotational and the soft mud was modeled as a linear viscoelastic fluid. Under the Boussinesq approximation for nonlinear long waves, we present a set of depth-integrated equations that can be solved … oxidation number of o4Webto expand a frequency-dependent viscoelastic modulus into an nth-order rational function in order to replace the con-volutory integral by n ﬁrst-order differential equations. Em-merich and Korn (1987) improved the approach (in terms of accuracy and efﬁciency) by considering the rheology of the generalized Maxwell body (GMB) whose ... jefferson county co short term rental rules

"WebHere, we study the internal variable approach to viscoelasticity. First, we generalize the classical approach by introducing a fractional derivative into the equation for time evolution of the internal variables. Next, we derive restrictions on the coefficients that follow from the dissipation inequality (entropy inequality under isothermal conditions). In the example of … " - Generalized viscoelastic wave equation

Generalized viscoelastic wave equation

WebApr 4, 2014 · Carcione et al ( 2002) established a visco-acoustic wave equation based on Kjartansson's theory. This equation is expressed as v 0 2 cos 2 π γ 2 ω 0 - 2 γ ∇ 2 P = ∂ t 2 - 2 γ P, 4 where γ = 1 π tan - 1 1 Q ⁠, 0 ≤ γ < 1 2 ⁠. Equation ( 4) … Webconstitutive equations of generalized viscoelasticity and then derive the viscoelastic-wave dynamic equations. With the assumption of a plane-wave solution, we ﬁ nally yield the phase

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WebFeb 1, 2016 · In the generalized viscoelastic wave equation (eq. 1), the three parameters controlling viscosity are: the viscoelastic velocity, … WebDec 1, 2024 · This generalized viscoelastic wave equation is characterized by the viscoelastic parameter and the viscoelastic velocity, but these parameters are not well formulated and therefore unfavorable for ...

WebIn the generalized wave equation, the degree of viscoelasticity varies between zero and unity, and is defined by a controlling parameter. When this viscoelastic controlling parameter equals to 0, the viscous property … http://www.lucabaradello.it/carcione/C95.pdf

WebDec 1, 2024 · Wang (2016) proposed the generalized viscoelastic wave equation, which unifies the pure elastic and viscoelastic property into a single form, and proved it follows the basic power law of ... WebGeneralized viscoelastic wave equation 1217 Thispaperattemptstounifytheviscoelasticandpureelasticcases into a single model. In this …

WebSep 1, 2009 · The viscoelastic modeling in 2-D SEG/EAGE salt dome model is carried out by using the simplified viscoelastic equations. A comparison of the viscoelastic single-shot records derived from acoustic ...

WebThis generalized viscoelastic wave equation is characterized by the viscoelastic parameter and the viscoelastic velocity, but these parameters are not well formulated and therefore unfavourable for seismic implementation. Here, we prove that the generalized wave equation is causal and stable by deriving the rate-of-relaxation function. jefferson county co vehicle sales taxWebThe generalized equation that includes the viscoelasticity appropriately describes the dissipation characteristics of the fast P-wave. Plane-wave analysis and numerical … jefferson county collector\u0027s officeWebApr 12, 2024 · In addition, the viscoelastic property. of the subgrade is modelled as a Kelvin model in. terms of the Prony series （Eq. （18））, but it is. inconsistent with the generalized Maxwell model. built in the ABAQUS general FE software. In order. to achieve the equivalent result on the existing basis, as shown in Fig. 5, an equivalent viscoelastic oxidation number of o in cu2oWebwave equation of variable coe cients u00 Lu+ ˆ(u0) = 0; where Lu= div(A(x)ru) = Xn i;j=1 @ @x i a ij(x) @u @x j : Under suitable conditions on ˆ, he improved his previous result [12] in which he focused on the case A= I, and obtained the general decay result. Liu [18] studied a variable coe cient wave equation with an acoustic undamped ... oxidation number of o in so3WebOct 29, 2024 · Motivated by recently proposed generalizations of the diffusion-wave equation with the Caputo time fractional derivative of order α ∈ (1, 2), in the present survey paper a class of generalized time-fractional diffusion-wave equations is introduced. Its definition is based on the subordination principle for Volterra integral equations and … jefferson county co voting guideWebAn analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic(GH) model. ... equation. This model has application from laboratory to astrophysical plasmas as well as biological systems. pacs: 52.27.Gr, 47.20.Ft, 47.20.Gv I Introduction. oxidation number of of2WebMar 1, 2024 · Wave propagation modeling in viscoelastic media often relies on the use of appropriate relaxation functions. These functions usually approximate the quality factor, Q, in the form of rational... jefferson county codes and regulations