Low-frequency layer-induced anisotropy

Geophysical Prospecting

Roganov

2019

In this paper, we consider wave propagation in a periodically layered medium with orthorhombic symmetry. The weak‐contrast approximation is utilized to derive the low‐frequency dispersion in effective properties for P, S1 and S2 waves. We show that the dispersion term for all effective properties is controlled by the second‐order contrasts in elastic properties from the layers. We also compute the sensitivity matrices for second‐ and fourth‐order coefficients from eigenvalues of frequency‐dependent system matrix associated with kinematic parameters for individual wave modes.

\tilde{boldA} false(ω false)

from equation does not correspond to any physical model (Willis ; Shuvalov et al .…”

Section: Discussionmentioning

confidence: 94%

“…Stovas et al . () propose the method to estimate the low‐frequency anisotropy parameters in a layered transversely isotropic medium with vertical symmetry axis (VTI). This method is based on a general theory of low‐frequency wave propagating in multi‐layered periodic media proposed by Roganov and Stovas ().…”

Section: Introductionmentioning

confidence: 99%

Low‐frequency layer‐induced dispersion in a weak‐contrast vertically heterogeneous orthorhombic medium

Roganov¹,

Geophysical Prospecting

Roganov

2019

“…The equations for the low‐frequency effective medium parameters given in a weak contrast approximation (Stovas et al . ) are

\frac{1}{{\overset{V}{true}}_{P} {((), ω)}^{2}} = \frac{1}{V_{P b}^{2}} + \frac{R_{P}}{V_{P b}^{2}} [{((), normalΔ ρ)}^{2} + 2 Δ ρ Δ v_{P} + {((), normalΔ v_{P})}^{2}] ω^{2},

\frac{1}{{\overset{V}{true}}_{S} {((), ω)}^{2}} = \frac{1}{V_{S b}^{2}} + \frac{R_{S}}{V_{S b}^{2}} [{((), normalΔ ρ)}^{2} + 2 Δ ρ Δ v_{S} + {((), normalΔ v_{S})}^{2}] ω^{2},

\begin{matrix} true \\ right \overset{ε}{true} ((), ω) & = & left ε_{b} + R_{P} ([, 3, (1 + r_{0}^{2} + 2 r_{0}^{4}), Δ, ρ, Δ, v_{S}) \\ left + (\frac{(() 1 + r_{0}^{2} - 2 r_{0}^{4} - 4 r_{0}^{6})}{r_{0}^{2}}, Δ, ρ, Δ, v_{P}) \\ left + (4, (2 - 3 r_{0}^{2} - 2 r_{0}^{4}), Δ, v_{S}, Δ, ...) \end{matrix}

…”

Section: Theorymentioning

confidence: 99%

“…Stovas et al . () compute the equations in weak contrast for the low‐frequency layer‐induced anisotropy in an elastic layered medium.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Low‐frequency anisotropy in fractured and layered media

Pang

Geophysical Prospecting

2019

Computing effective medium properties is very important when upscaling data measured at small scale. In the presence of stratigraphic layering, seismic velocities and anisotropy parameters are scale and frequency dependent. For a porous layer permeated by aligned fractures, wave‐induced fluid flow between pores and fractures can also cause significant dispersion in velocities and anisotropy parameters. In this study, we compare the dispersion of anisotropy parameters due to fracturing and layering at low frequencies. We consider a two‐layer model consisting of an elastic shale layer and an anelastic sand layer. Using Chapman's theory, we introduce anisotropy parameters dispersion due to fractures (meso‐scale) in the sand layer. This intrinsic dispersion is added to anisotropy parameters dispersion induced by layering (macro‐scale) at low frequencies. We derive the series coefficients that control the behaviour of anisotropy parameters at low frequencies. We investigate the influences of fracture length and fracture density on fracturing effect, layering effect and combined effect versus frequency and volume fraction of sand layer. Numerical modelling results indicate that the frequency dependence due to layering is not always the dominant effect of the effective properties of the medium. The intrinsic dispersion is not negligible compared with the layering effect while evaluating the frequency‐dependent properties of the layered medium.

Frequency-dependent anisotropy due to two orthogonal sets of mesoscale fractures in porous media

Shuai

Geophysical Journal International

Wei

et al. 2020

SUMMARY Seismic anisotropy can occur in rocks that have complicated internal structures and thin layering. Wave-induced fluid flow (WIFF) is one of the major causes of elastic wave dispersion and anisotropy. The principle goal of this paper is to combine the effects of WIFF and layer-induced anisotropy in orthorhombic (OTR) models that are often used in the seismic industry nowadays to describe azimuthal and polar anisotropy. We derive the effective frequency-dependent anisotropy parameters based on the Chapman model that accounts for the WIFF mechanism. First, we summarize two major problems to establish the link between the frequency-dependent seismic anisotropy and the multiple sets of fractures with different scales and orientations. Then we specify the multiple mesoscale fractures to be vertical and orthogonal so as to simplify the rock physics model to be an ORT medium. We also give the explicit expressions for the effective stiffness and the Thomsen-style parameters (vP0, vS0, ϵ1, ϵ2, γ1, γ2, δ1, δ2, δ3). Finally, we derive the effective frequency-dependent anisotropy parameters for ORT multiple layers using the Backus averaging under the approximation of weak contrast between layers. We also investigate the influence of frequency, fracture parameters (density and scale), effective porosity and volume fraction on the Thomsen-style parameters.