Inversion for asymmetric fracture parameters using synthetic AVOA data

Far, Mehdi E.; Thomsen, Leon; Sayers, Colin M.

doi:10.1190/segam2012-0162.1

Cited by 4 publications

(17 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Far () and Far et al . (, ) showed that simplified assumptions about fracture structure (fractures with rotationally invariant compliances and/or penny‐shaped cracks) can cause major errors in estimation of fracture parameters. However, their analysis using synthetic reflectivity data shows that inversion with an assumption of rotationally invariant fractures is robust, whereas inversion with an assumption of more realistic asymmetric fracture shapes is not robust if we have uncertainty in background unfractured rock parameters.…”

Section: Resultsmentioning

confidence: 99%

“…Far () and Far et al . (, ) extended this work to take into account asymmetric vertical fractures with variable shear compliances. Having variable shear compliances introduces another tensor, i.e., κ.…”

Section: Theorymentioning

confidence: 99%

“…With this more general definition of fracture compliance (shape), the additional fracture compliance can be defined as (Far ; Far et al . , ):

\begin{matrix} true \\ right Δ S_{i j k l} & = & left \frac{1}{4} ((), δ_{3 i} δ_{3 k} κ_{j l} + δ_{3 i} δ_{3 l} κ_{j k} + δ_{3 j} δ_{3 k} κ_{i l} + δ_{3 j} δ_{3 l} κ_{i k}) \\ left + \frac{1}{4} ((), δ_{i k} α_{j l} + δ_{i l} α_{j k} + δ_{j k} α_{i l} + δ_{j l} α_{i k}) + β_{i j k l} \end{matrix}

where

δ_{i j}

is the Krönecker delta and

α_{i j} = \frac{1}{V} \sum_{r} B_{T}^{(r)} n_{i}^{(r)} n_{j}^{(r)} A^{(r)}

κ_{i j} = \frac{1}{V} \sum_{r} (B_{S}^{(r)} - B_{T}^{(r)}) n_{i}^{(r)} n_{j}^{(r)} A^{(r)}

β_{i j k l} = \frac{1}{V} \sum_{r} <...>

…”

Section: Theorymentioning

confidence: 99%

“…Excess compliances

Δ S_{i j k l}

, resulting from the presence of the fractures, are then in the conventional two‐index notation (Far ; Far et al . , ):

Δ S = [\begin{matrix} right α_{11} + β_{1111} & right β_{1122} & right 0 & 0 & 0 & α_{12} + 2 β_{1112} \\ right β_{1122} & right α_{22} + β_{2222} & right 0 & 0 & 0 & α_{12} + 2 β_{1222} \\ right 0 & right 0 & right 0 & 0 & 0 & 0 \\ right 0 & right 0 & right 0 & α_{22} + κ_{22} & α_{12} + κ_{12} & 0 \\ right 0 & right 0 & right 0 & α_{12} + κ_{12} & α_{11} + κ_{11} & 0 \\ right α_{12} + 2 β_{1112} & right α_{12} + 2 β_{1222} & right 0 & 0 & 0 & α_{11} + α_{22} + 4 β_{1122} \end{matrix}] .

…”

Section: Theorymentioning

confidence: 99%

“…The theory of Sayers and Kachanov (, ) was developed for effective medium modelling of media with rotationally invariant fractures. Far (); Far, Thomsen, and Sayers (); and Far et al . () generalized the theory of Sayers and Kachanov (, ) to asymmetric fractures (fractures with variable shear compliance that include rectangular fractures) and, using synthetic data tests, showed that the assumption of rotationally invariant fractures causes major errors in estimation of fracture parameters.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Fracture characterization using converted waves

Far

Hardage

2015

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

A B S T R A C TWe present a method for inversion of fracture compliance matrix components from wide-azimuth noisy synthetic PS reflection data and quantitatively show that reflection amplitude variations with offset and azimuth for converted PS-waves are more informative than P-waves for fracture characterization. We consider monoclinic symmetry for fractured reservoir (parameters chosen from Woodford Shale), which can be formed by two or more sets of vertical fractures embedded in a vertically transverse isotropic background. Components of effective fracture compliance matrices for a medium with monoclinic symmetry are related to the characteristics of the fractured medium. Monte Carlo simulation results show that inversion of PS reflection data is more robust than that of PP reflection data to uncertainties in our a priori knowledge (vertically transverse isotropic parameters of unfractured rock) than PP reflection data. We also show that, while inversion of PP reflections is sensitive to contrasts in elastic properties of upper and lower media, inversion of PS reflections is robust with respect to such contrasts.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

“…With this more general definition of fracture compliance (shape), the additional fracture compliance can be defined as (Far ; Far et al . , ):

\begin{matrix} true \\ right Δ S_{i j k l} & = & left \frac{1}{4} ((), δ_{3 i} δ_{3 k} κ_{j l} + δ_{3 i} δ_{3 l} κ_{j k} + δ_{3 j} δ_{3 k} κ_{i l} + δ_{3 j} δ_{3 l} κ_{i k}) \\ left + \frac{1}{4} ((), δ_{i k} α_{j l} + δ_{i l} α_{j k} + δ_{j k} α_{i l} + δ_{j l} α_{i k}) + β_{i j k l} \end{matrix}

where

δ_{i j}

is the Krönecker delta and

α_{i j} = \frac{1}{V} \sum_{r} B_{T}^{(r)} n_{i}^{(r)} n_{j}^{(r)} A^{(r)}

κ_{i j} = \frac{1}{V} \sum_{r} (B_{S}^{(r)} - B_{T}^{(r)}) n_{i}^{(r)} n_{j}^{(r)} A^{(r)}

β_{i j k l} = \frac{1}{V} \sum_{r} <...>

…”

Section: Theorymentioning

confidence: 99%

“…Excess compliances

Δ S_{i j k l}

, resulting from the presence of the fractures, are then in the conventional two‐index notation (Far ; Far et al . , ):

Δ S = [\begin{matrix} right α_{11} + β_{1111} & right β_{1122} & right 0 & 0 & 0 & α_{12} + 2 β_{1112} \\ right β_{1122} & right α_{22} + β_{2222} & right 0 & 0 & 0 & α_{12} + 2 β_{1222} \\ right 0 & right 0 & right 0 & 0 & 0 & 0 \\ right 0 & right 0 & right 0 & α_{22} + κ_{22} & α_{12} + κ_{12} & 0 \\ right 0 & right 0 & right 0 & α_{12} + κ_{12} & α_{11} + κ_{11} & 0 \\ right α_{12} + 2 β_{1112} & right α_{12} + 2 β_{1222} & right 0 & 0 & 0 & α_{11} + α_{22} + 4 β_{1122} \end{matrix}] .

…”

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fracture characterization using converted waves

Far

Hardage

2015

Geophysical Prospecting

Self Cite

View full text Add to dashboard Cite

show abstract

Seismic characterization of reservoirs with asymmetric fractures

2013

Self Cite

View full text Add to dashboard Cite

Variations of reflection amplitude with offset and azimuth are sensitive to the presence of natural and induced fractures. We tested inversion for fracture compliance matrix components from wide azimuth noisy synthetic PP-reflection data. The model was a fractured reservoir with monoclinic symmetry, formed by two sets of vertical asymmetric fractures embedded in a VTI background. The fractures (joints) were assumed to be vertical, with noncircular shape and/or with asymmetric shear compliance. Results of synthetic inversion showed that an incorrect assumption about fracture shear symmetry (e.g., treating asymmetric fractures as rotationally invariant fractures) can cause considerable error in estimation of the fracture compliance matrix. Components of effective second- and fourth-rank fracture compliance matrices for a medium with monoclinic symmetry (which takes into account layering and multiple fracture sets) can be used as attributes related to the characteristics of the fractured medium. Monte Carlo simulation was used to test the effect of uncertainties in the a priori information (about background VTI parameters of unfractured rock), as they affect inversion for these attributes. According to this analysis, the direction of fast shear-wave polarization was inverted robustly in the Monte Carlo simulation. Although the average values of the components of fracture compliance matrices obtained from Monte Carlo simulation were in agreement with the actual values used for forward modeling, individual values obtained in Monte Carlo simulation were sensitive to uncertainties in the background properties in general. Because the elastic properties of background VTI media without fractures (or other azimuthally variable features) do not cause azimuthal changes in reflection coefficient variation with offset, simultaneous inversion for background properties and fracture tensor components require additional constraints.

show abstract

Fracture parameter inversion for Marcellus Shale

2014

View full text Add to dashboard Cite

We inverted P-wave amplitude variation with offset and azimuth (AVOAz) data from the Marcellus Shale to obtain fracture parameters that can fully describe the elastic behavior of fractured rocks with overall symmetry of orthorhombic or monoclinic. AVOAz data from two interfaces, (1) the upper interface between top Marcellus and Stafford limestone and (2) the lower interface between base Marcellus and Onondaga limestone, were used for inversion. To check the validity of our inversion results, fracture parameters for the Marcellus Shale were inverted for each interface using Monte Carlo simulation to include uncertainty in our a priori information, i.e., elastic properties of unfractured rocks that are assumed to be known from well logs. Inversion results appeared robust with respect to uncertainties and converge to the same values for the two inversions. Our results were also consistent with singular value decomposition analysis (resolution matrix).

show abstract

Inversion for asymmetric fracture parameters using synthetic AVOA data

Cited by 4 publications

References 8 publications

Fracture characterization using converted waves

Fracture characterization using converted waves

Seismic characterization of reservoirs with asymmetric fractures

Fracture parameter inversion for Marcellus Shale

Contact Info

Product

Resources

About