scholarly journals Elastic-Impedance-Based Fluid/Porosity Term and Fracture Weaknesses Inversion in Transversely Isotropic Media with a Tilted Axis of Symmetry

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Xinpeng Pan ◽  
Lin Li ◽  
Guangzhi Zhang ◽  
Yian Cui
Keyword(s):  
Reflection Coefficient ◽  
Seismic Data ◽  
Wave Reflection ◽  
Transversely Isotropic ◽  
Unknown Parameters ◽  
Fluid Identification ◽  
Pp Wave ◽  
Axis Of Symmetry ◽  
Dip Angle ◽  
Elastic Impedance

The rock containing a set of tilted fractures is equivalent to a transversely isotropic (TTI) medium with a tilted axis of symmetry. To implement fluid identification and tilted fracture detection, we propose an inversion approach of utilizing seismic data to simultaneously estimate parameters that are sensitive to fluids and tilted fractures. We first derive a PP-wave reflection coefficient and elastic impedance (EI) in terms of the dip angle, fluid/porosity term, shear modulus, density, and fracture weaknesses, and we present numerical examples to demonstrate how the PP-wave reflection coefficient and EI vary with the dip angle. Based on the information of dip angle of fractures provided by geologic and well data, we propose a two-step inversion approach of utilizing azimuthal seismic data to estimate unknown parameters involving the fluid/porosity term and fracture weaknesses: (1) the constrained sparse spike inversion (CSSI) for azimuthally anisotropic EI data and (2) the estimation of unknown parameters with the low-frequency constrained regularization term. Synthetic and real data demonstrate that fluid and fracture parameters are reasonably estimated, which may help fluid identification and fracture characterization.

PP-wave reflection coefficients in weakly anisotropic elastic media

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2129-2141 ◽  
Author(s):  
Václav Vavryuk ◽  
Ivan Peník
Keyword(s):  
Reflection Coefficient ◽  
Approximate Formula ◽  
Wave Reflection ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Pp Wave ◽  
Axis Of Symmetry ◽  
Amplitude Versus

Approximate PP-wave reflection coefficients for weak contrast interfaces separating elastic, weakly transversely isotropic media have been derived recently by several authors. Application of these coefficients is limited because the axis of symmetry of transversely isotropic media must be either perpendicular or parallel to the reflector. In this paper, we remove this limitation by deriving a formula for the PP-wave reflection coefficient for weak contrast interfaces separating two weakly but arbitrarily anisotropic media. The formula is obtained by applying the first‐order perturbation theory. The approximate coefficient consists of a sum of the PP-wave reflection coefficient for a weak contrast interface separating two background isotropic half‐spaces and a perturbation attributable to the deviation of anisotropic half‐spaces from their isotropic backgrounds. The coefficient depends linearly on differences of weak anisotropy parameters across the interface. This simplifies studies of sensitivity of such coefficients to the parameters of the surrounding structure, which represent a basic part of the amplitude‐versus‐offset (AVO) or amplitude‐versus‐azimuth (AVA) analysis. The reflection coefficient is reciprocal. In the same way, the formula for the PP-wave transmission coefficient can be derived. The generalization of the procedure presented for the derivation of coefficients of converted waves is also possible although slightly more complicated. Dependence of the reflection coefficient on the angle of incidence is expressed in terms of three factors, as in isotropic media. The first factor alone describes normal incidence reflection. The second yields the low‐order angular variations. All three factors describe the coefficient in the whole region, in which the approximate formula is valid. In symmetry planes of weakly anisotropic media of higher symmetry, the approximate formula reduces to the formulas presented by other authors. The accuracy of the approximate formula for the PP reflection coefficient is illustrated on the model with an interface separating an isotropic half‐space from a half‐space filled by a transversely isotropic material with a horizontal axis of symmetry. The results show a very good fit with results of the exact formula, even in cases of strong anisotropy and strong velocity contrast.

Fracture detection and fluid identification based on anisotropic Gassmann equation and linear-slip model

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R85-R98 ◽  
Author(s):  
Xinpeng Pan ◽  
Guangzhi Zhang
Keyword(s):  
Seismic Data ◽  
Order Approximation ◽  
Low Frequency ◽  
Rock Physics ◽  
Transversely Isotropic ◽  
Slip Model ◽  
Fracture Detection ◽  
Fluid Identification ◽  
Pp Wave ◽  
Linear Slip Model

Detection of fracture and fluid properties from subsurface azimuthal seismic data improves our abilities to characterize the saturated porous reservoirs with aligned fractures. Motivated by the fracture detection and fluid identification in a fractured porous medium, we have developed a feasible approach to perform a rock physics model-based amplitude variation with offset and azimuth (AVOAz) inversion for the fracture and fluid parameters in a horizontal transversely isotropic (HTI) medium using the PP-wave angle gathers along different azimuths. Based on the linear-slip model, we first use anisotropic Gassmann’s equation to derive the expressions of saturated stiffness components and their perturbations of first-order approximation in terms of elastic properties of an isotropic porous background and fracture compliances induced by a single set of rotationally invariant fractures. We then derive a linearized PP-wave reflection coefficient in terms of fluid modulus, dry-rock matrix term, porosity, density, and fracture compliances or quasi-compliances for an interface separating two weakly HTI media based on the Born scattering theory. Finally, we solve the AVOAz inverse problems iteratively constrained by the Cauchy-sparse regularization and the low-frequency regularization in a Bayesian framework. The results demonstrate that the fluid modulus and fracture quasi-compliances are reasonably estimated in the case of synthetic and real seismic data containing moderate noise in a gas-filled fractured porous reservoir.

P‐wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 713-722 ◽  
Author(s):  
Andreas Rüger
Keyword(s):  
Reflection Coefficient ◽  
Wave Reflection ◽  
Numerical Solutions ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Horizontal Axis ◽  
P Wave ◽  
Reflection Coefficients ◽  
Gradient Term ◽  
Axis Of Symmetry

The study of P‐wave reflection coefficients in anisotropic media is important for amplitude variation with offset (AVO) analysis. While numerical evaluation of the reflection coefficient is straightforward, numerical solutions do not provide analytic insight into the influence of anisotropy on the AVO signature. To overcome this difficulty, I present an improved approximation for P‐wave reflection coefficients at a horizontal boundary in transversely isotropic media with vertical axis of symmetry (VTI media). This solution has the same AVO‐gradient term describing the low‐order angular variation of the reflection coefficient as the equations published previously, but is more accurate for large incidence angles. The refined approximation is then extended to transverse isotropy with a horizontal axis of symmetry (HTI), which is caused typically by a system of vertical cracks. Comparison of the approximate reflection coefficients for P‐waves incident in the two vertical symmetry planes of HTI media indicates that the azimuthal variation of the AVO gradient is a function of the shear‐wave splitting parameter γ, and the anisotropy parameter describing P‐wave anisotropy for nearvertical propagation in the vertical plane containing the symmetry axis.

scholarly journals Amplitude Variation with Angle Inversion for New Parameterized Porosity and Fluid Bulk Modulus

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shengjun Li ◽  
Bingyang Liu ◽  
Jianhu Gao ◽  
Huaizhen Chen
Keyword(s):  
Reflection Coefficient ◽  
Bulk Modulus ◽  
Seismic Data ◽  
Reservoir Characterization ◽  
Signal To Noise Ratio ◽  
Empirical Relationship ◽  
Amplitude Variation ◽  
Fluid Identification ◽  
Saturated Rock ◽  
Elastic Impedance

Estimating porosity and fluid bulk modulus is an important goal of reservoir characterization. Based on the model of fluid substitution, we first propose a simplified bulk modulus of a saturated rock as a function of bulk moduli of minerals and fluids, in which we employ an empirical relationship to replace the bulk modulus of dry rock with that of minerals and a new parameterized porosity. Using the simplified bulk modulus, we derive a PP-wave reflection coefficient in terms of the new parameterized porosity and fluid bulk modulus. Focusing on reservoirs embedded in rocks whose lithologies are similar, we further simplify the derived reflection coefficient and present elastic impedance that is related to porosity and fluid bulk modulus. Based on the presented elastic impedance, we establish an approach of employing seismic amplitude variation with offset/angle to estimate density, new parameterized porosity, and fluid bulk modulus. We finally employ noisy synthetic seismic data and real datasets to verify the stability and reliability of the proposed inversion approach. Test on synthetic seismic data illustrates that the proposed inversion approach can produce stable inversion results in the case of signal-to-noise ratio (SNR) of 2, and applying the approach to real datasets, we conclude that reliably results of porosity and fluid bulk modulus are obtained, which is useful for fluid identification and reservoir characterization.

Two-step joint PP- and PS-wave three-term amplitude-variation with offset inversion

2016 ◽  
Vol 4 (4) ◽  
pp. T613-T625 ◽  
Author(s):  
Qizhen Du ◽  
Bo Zhang ◽  
Xianjun Meng ◽  
Chengfeng Guo ◽  
Gang Chen ◽  
...  
Keyword(s):  
Reflection Coefficient ◽  
Wave Reflection ◽  
Coefficient Matrix ◽  
P Wave ◽  
Inversion Method ◽  
S Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Avo Inversion ◽  
Pp Wave

Three-term amplitude-variation with offset (AVO) inversion generally suffers from instability when there is limited prior geologic or petrophysical constraints. Two-term AVO inversion shows higher instability compared with three-term AVO inversion. However, density, which is important in the fluid-type estimation, cannot be recovered from two-term AVO inversion. To reliably predict the P- and S-waves and density, we have developed a robust two-step joint PP- and PS-wave three-term AVO-inversion method. Our inversion workflow consists of two steps. The first step is to estimate the P- and S-wave reflectivities using Stewart’s joint two-term PP- and PS-AVO inversion. The second step is to treat the P-wave reflectivity obtained from the first step as the prior constraint to remove the P-wave velocity related-term from the three-term Aki-Richards PP-wave approximated reflection coefficient equation, and then the reduced PP-wave reflection coefficient equation is combined with the PS-wave reflection coefficient equation to estimate the S-wave and density reflectivities. We determined the effectiveness of our method by first applying it to synthetic models and then to field data. We also analyzed the condition number of the coefficient matrix to illustrate the stability of the proposed method. The estimated results using proposed method are superior to those obtained from three-term AVO inversion.

Seismic inversion for geologic fractures and fractured media

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. C145-C161 ◽  
Author(s):  
Xiaoqin Cui ◽  
Edward S. Krebes ◽  
Laurence R. Lines
Keyword(s):  
Seismic Data ◽  
Wave Reflection ◽  
Rock Properties ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Avo Inversion ◽  
Impedance Contrast ◽  
Fractured Medium ◽  
Pp Wave ◽  
Contact Part

Amplitude variation with offset (AVO) inversion attempts to use the available surface seismic data to estimate the density, P-wave velocity, and S-wave velocity of the earth model. Under linear slip interface theory, synthetic seismograms for models with fractures prove that fractures are also reflection generators. Consequently, observed reflections are not necessarily due to lithologic variations only, but they could be due in part to the effect of fractures. To obtain approximate equations for AVO inversion for fractured media, denoted by AVO with fracture (AVOF), we derived new equations for PP-wave reflection and transmission coefficients that are based on nonwelded contact boundary conditions. In particular, along with the fracture compliances, azimuth has also been taken into account in the equations because the fractures can have any orientation. The new approximate AVOF equations for a horizontally fractured medium with impedance contrast are developed by simplifying the equations for the new PP-wave reflection and transmission coefficients. In the new approximate AVOF equations, the reflection coefficients are divided into a welded contact part (a conventional impedance contrast part) and a nonwelded contact part (a fracture part). This makes the equations flexible enough to separately invert for the rock properties of the fracture and the background medium in the case of a fractured medium with impedance contrast. The new approximate AVOF equations state that fractures could cause the seismic reflectivity to be frequency dependent, and that the fractures not only influence the wave amplitude but also change the wave phase. The linear least-squares and nonlinear conjugate gradient inversion algorithms are applied to estimate the elastic reflectivity using the new approximate AVOF equations. The inverted results for seismic data for a horizontally fractured medium with impedance contrast are evaluated to find a more accurate delineation of the subsurface rock properties.

Moveout approximations for P- and SV-waves in dip-constrained transversely isotropic media

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. C53-C59 ◽  
Author(s):  
Véronique Farra ◽  
Ivan Pšenčík
Keyword(s):  
Transversely Isotropic ◽  
Arbitrary Orientation ◽  
Transversely Isotropic Medium ◽  
Weak Anisotropy ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Axis Of Symmetry ◽  
Dip Angle ◽  
P And Sv Waves ◽  
Axes Of Symmetry

We generalize the P- and SV-wave moveout formulas obtained for transversely isotropic media with vertical axes of symmetry (VTI), based on the weak-anisotropy approximation. We generalize them for 3D dip-constrained transversely isotropic (DTI) media. A DTI medium is a transversely isotropic medium whose axis of symmetry is perpendicular to a dipping reflector. The formulas are derived in the plane defined by the source-receiver line and the normal to the reflector. In this configuration, they can be easily obtained from the corresponding VTI formulas. It is only necessary to replace the expression for the normalized offset by the expression containing the apparent dip angle. The final results apply to general 3D situations, in which the plane reflector may have arbitrary orientation, and the source and the receiver may be situated arbitrarily in the DTI medium. The accuracy of the proposed formulas is tested on models with varying dip of the reflector, and for several orientations of the horizontal source-receiver line with respect to the dipping reflector.

Wave reflection at an anelastic transversely isotropic ocean bottom

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM139-SM146 ◽  
Author(s):  
Rolf Sidler ◽  
José M. Carcione
Keyword(s):  
Reflection Coefficient ◽  
Plane Wave ◽  
Domain Decomposition ◽  
Wave Reflection ◽  
Differential Operators ◽  
Domain Decomposition Method ◽  
Rotational Symmetry ◽  
Transversely Isotropic ◽  
Synthetic Seismograms ◽  
Ocean Bottom

We study the reflection of waves at the ocean bottom, which is modeled as a plane interface separating a viscoacoustic medium (water) and a viscoelastic transversely isotropic solid whose axis of rotational symmetry is perpendicular to the bottom. We compute the plane-wave reflection coefficient (including the phenomenon known as the Rayleigh window) both numerically — by amplitude variation with offset (AVO) analysis of synthetic seismograms generated using a domain decomposition method and analytically. A first simulation considers the water-steel interface, for which experimental data is available. Then, we consider soft sediments and stiff crustal rocks for various values of the anellipticity parameter [Formula: see text]. The domain-decomposition technique relies on one grid for the fluid and another grid for the solid and uses Fourier and Chebyshev differential operators. The ane-lastic and anisotropic stress-strain relation is described by the Zener model. Special attention is given to modeling the boundary conditions at the ocean bottom. For this purpose, we further develop the technique for wave propagation at fluid/anelastic-anisotropic-solid interfaces. AVO slowness-frequency-domain analysis is used to compute the reflection coefficient and phase angle from the synthetic seismograms. This allows us to verify the domain-decomposition algorithm, which is shown to model with high accuracy the Rayleigh window for varying [Formula: see text]. The comparison also verifies the calculation of the analytical plane-wave reflection coefficient because a wrong choice of the sign of the vertical slowness of the reflected wave may cause nonphysical discontinuities in the coefficient. Moreover, the pseudospectral modeling code allows a general material variability and a complete and accurate characterization of the seismic response of an anisotropic ocean bottom.

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