Characterization of heterogeneous fracture compliance using multiple reflections coupled with data-driven Green's function retrieval

2015 ◽  
Author(s):  
Shohei Minato* ◽  
Ranajit Ghose
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Data Driven ◽  
Multiple Reflections

scholarly journals Data-driven wavefield focusing and imaging with multidimensional deconvolution: Numerical examples for reflection data with internal multiples

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA107-WA115 ◽  
Author(s):  
Filippo Broggini ◽  
Roel Snieder ◽  
Kees Wapenaar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Imaging Techniques ◽  
Velocity Model ◽  
Single Scattering ◽  
Data Driven ◽  
Multiple Reflections ◽  
Prestack Migration ◽  
Reflection Data ◽  
Internal Multiples

Standard imaging techniques rely on the single scattering assumption. This requires that the recorded data do not include internal multiples, i.e., waves that have bounced multiple times between reflectors before reaching the receivers at the acquisition surface. When multiple reflections are present in the data, standard imaging algorithms incorrectly image them as ghost reflectors. These artifacts can mislead interpreters in locating potential hydrocarbon reservoirs. Recently, we introduced a new approach for retrieving the Green’s function recorded at the acquisition surface due to a virtual source located at depth. We refer to this approach as data-driven wavefield focusing. Additionally, after applying source-receiver reciprocity, this approach allowed us to decompose the Green’s function at a virtual receiver at depth in its downgoing and upgoing components. These wavefields were then used to create a ghost-free image of the medium with either crosscorrelation or multidimensional deconvolution, presenting an advantage over standard prestack migration. We tested the robustness of our approach when an erroneous background velocity model is used to estimate the first-arriving waves, which are a required input for the data-driven wavefield focusing process. We tested the new method with a numerical example based on a modification of the Amoco model.

Characterization of the Thermal-Wave Field in a Wedge-Shaped Solid Using the Green’s Function Method

2012 ◽  
Vol 34 (8-9) ◽  
pp. 1585-1590
Author(s):  
Jie Zhang ◽  
Rui Tai ◽  
Chinhua Wang ◽  
Andreas Mandelis
Keyword(s):  
Green’S Function ◽  
Wave Field ◽  
Green's Function ◽  
Thermal Wave ◽  
Function Method ◽  
Green’S Function Method

scholarly journals Data-Driven Green's Function Retrieval from Reflection Data - Theory and Example

2013 ◽  
Author(s):  
K. Wapenaar ◽  
E. Slob ◽  
F. Broggini ◽  
R. Snieder ◽  
J. Thorbecke ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Data Driven ◽  
Reflection Data

One‐way versions of the Kirchhoff Integral

Geophysics ◽  
1989 ◽  
Vol 54 (4) ◽  
pp. 460-467 ◽  
Author(s):  
A. J. Berkhout ◽  
C. P. A. Wapenaar
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Wave Field ◽  
Green's Function ◽  
Green's Functions ◽  
Acoustic Pressure ◽  
Green’S Functions ◽  
Absorbing Boundary Conditions ◽  
Multiple Reflections ◽  
Kirchhoff Integral

The conventional Kirchhoff integral, based on the two‐way wave equation, states how the acoustic pressure at a point A inside a closed surface S can be calculated when the acoustic wave field is known on S. In its general form, the integrand consists of two terms: one term contains the gradient of a Green’s function and the acoustic pressure; the other term contains a Green’s function and the gradient of the acoustic pressure. The integrand can be simplified by choosing reflecting boundary conditions for the two‐way Green’s functions in such a way that either the first term or the second term vanishes on S. This conventional approach to deriving Rayleigh‐type integrals has practical value only for media with small contrasts, so that the two‐way Green’s functions do not contain significant multiple reflections. We present a modified approach for simplifying the integrand of the Kirchhoff integral by choosing absorbing boundary conditions for the one‐way Green’s functions. The resulting Rayleigh‐type integrals are the theoretical basis for true amplitude one‐way wave‐field extrapolation techniques in inhomogeneous media with significant contrasts.

Fracture Hits and Hydraulic-Fracture Geometry Characterization Using Low-Frequency Distributed Acoustic Sensing Strain Data

2021 ◽  
Vol 73 (07) ◽  
pp. 39-42
Author(s):  
Kan Wu ◽  
Yongzan Liu ◽  
Ge Jin ◽  
George Moridis
Keyword(s):  
Strain Rate ◽  
Green’S Function ◽  
Green's Function ◽  
Hydraulic Fracture ◽  
Laser Energy ◽  
Low Frequency ◽  
Forward Model ◽  
Hydraulic Fractures ◽  
Fracture Geometry

The propagation process and geometry of hydraulic fractures depend on complex interactions among the induced fractures and the pre-existing rock fabric, the heterogeneous rock properties, and the stress state. Accurate characterization of the resulting complex hydraulic-fracture geometry remains challenging. Fiber-optic-based distributed acoustic sensing (DAS) measurements have been used for monitoring hydraulic fracturing in adjacent treatment wells. DAS requires an optical fiber attached to the wellbore to transmit the laser energy into the reservoir. Each section of the fiber scatters a small portion of the laser energy back to a surface sensing unit, which uses interferometry techniques to determine strain changes along with the fiber. DAS data in offset wells fall in the low-frequency bands, which has been proven to be a powerful attribute for the characterization of the geometry of hydraulic fractures. Numerous recently published field examples demonstrate the potential of low-frequency DAS (LF-DAS) data for the detailed characterization of the hydraulic fracture geometry. Understanding the fracture-induced rock deformation associated with LF-DAS signals would be beneficial for the better interpretation of real-time data. However, interpretation of LF-DAS measurement is challenging due to the complexity of the subsurface conditions, in addition to potential unanticipated completion issues such as perforation failure, stage isolation failure, etc. All current research efforts focus on the qualitative interpretation of field data.In this study, we quantified the hydraulic fracture propagation process and described the fracture geometry by developing a geomechanical forward model and a Green’s function-based inversion model for the LF-DAS data interpretation, substantially enhancing the value of the LF-DAS data in the process. The work has a significant transformative potential, involving a tool package with developed forward and inversion models that can provide crucial insights for the optimization of hydraulic-fracturing treatments and reservoir development. Methodology The tool package can be used directly in the field to interpret LF-DAS data and monitor hydraulic fracture propagation. Raw data from the field measurement can be automatically processed. The geomechanics forward model we developed can quantify and analyze the strain-rate response from the LF-DAS measurements based on the 3D displacement discontinuity method. Fracture hits are detected by calculating three 1D features along the channel (location) axis, i.e., the maximum strain rate, the summation of strain rates, and the summation of strain-rate amplitudes. Channels with fracture hits usually exhibit significant peak values of these three features. We proposed general guide-lines for fracture-hit detection based on the quantitative analysis of strain/strain-rate responses during the multistage fracturing treatment. The details of the forward model can be found in Liu et al. (SPE 202482, 204457, AMRA-2020-1426). Additionally, we developed a novel Green’s function-based inversion model to qualify fracture width and height based on the determined fracture hits. The strain field that is estimated from the integration of the strain rates measured by the LF-DAS data along the offset monitoring well is related to the fracture widths through a geomechanics Green’s function. The resulting linear system of equations is solved by the least-square method. Details can be found in Liu et al. (SPE 204158, 205379, 204225).

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