Experimental study on the effects of fractures on elastic wave propagation in synthetic layered rocks

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. D441-D451 ◽  
Author(s):  
Tianyang Li ◽  
Ruihe Wang ◽  
Zizhen Wang ◽  
Yuzhong Wang
Keyword(s):  
Wave Propagation ◽  
Fractal Dimension ◽  
Power Spectrum ◽  
Elastic Wave ◽  
Power Law ◽  
Layered Media ◽  
Physical Models ◽  
P Wave ◽  
Fracture Density ◽  
S Wave

Fractures greatly increase the difficulty of oil and gas exploration and development in reservoirs consisting of interlayered carbonates and shales and increase the uncertainty of highly efficient development. The presence of fractures or layered media is also widely known to affect the elastic properties of rocks. The combined effects of fractures and layered media are still unknown. We have investigated the effects of fracture structure on wave propagation in interlayered carbonate and shale rocks using physical models based on wave theory and the similarity principle. We have designed and built two sets of layered physical models with randomly embedded predesigned vertically aligned fractures according to the control variate principle. We have measured the P- and S-wave velocities and attenuation and analyzed the effects of fracture porosity and aspect ratio (AR) on velocity, attenuation, and power spectral dimension of the P- and S-waves. The experimental results indicated that under conditions of low porosity ([Formula: see text]), Han’s empirical velocity-porosity relations and Wang’s attenuation-porosity relation combined with Wyllie’s time-average model are a good prediction for layered physical models with randomly embedded fractures. When the porosity is constant, the effect of different ARs on elastic wave properties can be described by a power law function. We have calculated the power spectrum fractal dimension [Formula: see text] of the transmitted signal in the frequency domain, which can supplement the S-wave splitting method for estimating the degree of anisotropy. The simple power law relation between the power spectrum fractal dimension of the P-waveform and fracture density suggests the possible use of P-waves for discriminating fracture density. The high precision and low error of this processing method give new ideas for rock anisotropy evaluation and fracture density prediction when only P-wave data are available.

Approximation of pure acoustic seismic wave propagation in TTI media

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB97-WB107 ◽  
Author(s):  
Chunlei Chu ◽  
Brian K. Macy ◽  
Phil D. Anno
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Elastic Wave ◽  
Wave Equations ◽  
Computational Cost ◽  
P Wave ◽  
Anisotropy Axis ◽  
S Wave ◽  
Time Migration ◽  
Tti Media

Pseudoacoustic anisotropic wave equations are simplified elastic wave equations obtained by setting the S-wave velocity to zero along the anisotropy axis of symmetry. These pseudoacoustic wave equations greatly reduce the computational cost of modeling and imaging compared to the full elastic wave equation while preserving P-wave kinematics very well. For this reason, they are widely used in reverse time migration (RTM) to account for anisotropic effects. One fundamental shortcoming of this pseudoacoustic approximation is that it only prevents S-wave propagation along the symmetry axis and not in other directions. This problem leads to the presence of unwanted S-waves in P-wave simulation results and brings artifacts into P-wave RTM images. More significantly, the pseudoacoustic wave equations become unstable for anisotropy parameters [Formula: see text] and for heterogeneous models with highly varying dip and azimuth angles in tilted transversely isotropic (TTI) media. Pure acoustic anisotropic wave equations completely decouple the P-wave response from the elastic wavefield and naturally solve all the above-mentioned problems of the pseudoacoustic wave equations without significantly increasing the computational cost. In this work, we propose new pure acoustic TTI wave equations and compare them with the conventional coupled pseudoacoustic wave equations. Our equations can be directly solved using either the finite-difference method or the pseudospectral method. We give two approaches to derive these equations. One employs Taylor series expansion to approximate the pseudodifferential operator in the decoupled P-wave equation, and the other uses isotropic and elliptically anisotropic dispersion relations to reduce the temporal frequency order of the P-SV dispersion equation. We use several numerical examples to demonstrate that the newly derived pure acoustic wave equations produce highly accurate P-wave results, very close to results produced by coupled pseudoacoustic wave equations, but completely free from S-wave artifacts and instabilities.

Elastic wave propagation in anisotropic porous layered media

2020 ◽  
pp. 839-844
Author(s):  
Anil K. Vashishth ◽  
Poonam Khurana
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Layered Media ◽  
Elastic Wave Propagation

Elastic wave propagation in randomly disordered layered media

1994 ◽  
Vol 95 (5) ◽  
pp. 2863-2863
Author(s):  
R. Esquivel‐Sirvent ◽  
Cecilia Noguez
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Layered Media ◽  
Elastic Wave Propagation

scholarly journals A new acoustic assumption for orthorhombic media

2020 ◽  
Vol 223 (2) ◽  
pp. 1118-1129
Author(s):  
Mohammad Mahdi Abedi ◽  
Alexey Stovas
Keyword(s):  
Wave Propagation ◽  
Conventional Approach ◽  
P Wave ◽  
Model Parameters ◽  
Governing Equations ◽  
S Wave ◽  
S Waves ◽  
Exploration Seismology ◽  
And Inversion ◽  
Approximate Equations

SUMMARY In exploration seismology, the acquisition, processing and inversion of P-wave data is a routine. However, in orthorhombic anisotropic media, the governing equations that describe the P-wave propagation are coupled with two S waves that are considered as redundant noise. The main approach to free the P-wave signal from the S-wave noise is the acoustic assumption on the wave propagation. The conventional acoustic assumption for orthorhombic media zeros out the S-wave velocities along three orthogonal axes, but leaves significant S-wave artefacts in all other directions. The new acoustic assumption that we propose mitigates the S-wave artefacts by zeroing out their velocities along the three orthogonal symmetry planes of orthorhombic media. Similar to the conventional approach, our method reduces the number of required model parameters from nine to six. As numerical experiments on multiple orthorhombic models show, the accuracy of the new acoustic assumption also compares well to the conventional approach. On the other hand, while the conventional acoustic assumption simplifies the governing equations, the new acoustic assumption further complicates them—an issue that emphasizes the necessity of simple approximate equations. Accordingly, we also propose simpler rational approximate phase-velocity and eikonal equations for the new acoustic orthorhombic media. We show a simple ray tracing example and find out that the proposed approximate equations are still highly accurate.

Synthetic full‐waveform acoustic logs in cased boreholes, II—Poorly bonded casing

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 902-913 ◽  
Author(s):  
Kenneth M. Tubman ◽  
C. H. Cheng ◽  
S. P. Cole ◽  
M. Nafi Toksöz
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Theoretical Study ◽  
Fluid Layer ◽  
Body Wave ◽  
P Wave ◽  
Full Waveform ◽  
Fluid Layers ◽  
First Arrival ◽  
Wave Arrival

A generalization of the technique of Tubman et al. (1984) allows the inclusion of intermediate fluid layers in the theoretical study of elastic wave propagation in a layered borehole. The number and location of fluid layers are arbitrary. The only restrictions are that the central cylinder is fluid and the outermost formation is solid. Synthetic full‐waveform microseismograms in poorly bonded cased holes can be generated, allowing investigation of free pipe and cement sheathed pipe with no bond to the formation. If there is a fluid layer between the steel and the cement, the steel is free to ring. The first arrival in this situation is from the casing, even with an extremely thin fluid layer or microannulus. The amplitude and duration of the pipe signal depend upon the thickness of the fluid layer. While the first arrival is from the casing, the formation body‐wave energy is present. The character of the waveform will vary as the formation parameters vary. If the duration of the steel arrival is small, it is possible to distinguish the formation P-wave arrival. If the fluid layer is between the cement and the formation, then the steel is well bonded to the cement but the cement is not bonded to the formation. In this case the thicknesses of the fluid and cement layers are important in determining the nature of the first arrival. If there is a large amount of cement bonded to the steel, the cement can damp out the ringing of the pipe and make it possible to distinguish formation arrivals. If there is less cement bonded to the steel, the cement does not damp out the steel ringing but the cement rings along with the steel and the first arrival is from the combination of the steel and the cement. The velocity of this wave depends upon the velocities and thicknesses of the steel and cement layers.

P-wave and S-wave azimuthal anisotropy at a naturally fractured gas reservoir, Bluebell‐Altamont Field, Utah

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1312-1328 ◽  
Author(s):  
Heloise B. Lynn ◽  
Wallace E. Beckham ◽  
K. Michele Simon ◽  
C. Richard Bates ◽  
M. Layman ◽  
...  
Keyword(s):  
Azimuthal Anisotropy ◽  
P Wave ◽  
Fracture Density ◽  
Wave Reflections ◽  
S Wave ◽  
Gas Reservoir ◽  
Green River ◽  
Wave Data ◽  
Reflection Data ◽  
Naturally Fractured

Reflection P- and S-wave data were used in an investigation to determine the relative merits and strengths of these two data sets to characterize a naturally fractured gas reservoir in the Tertiary Upper Green River formation. The objective is to evaluate the viability of P-wave seismic to detect the presence of gas‐filled fractures, estimate fracture density and orientation, and compare the results with estimates obtained from the S-wave data. The P-wave response to vertical fractures must be evaluated at different source‐receiver azimuths (travelpaths) relative to fracture strike. Two perpendicular lines of multicomponent reflection data were acquired approximately parallel and normal to the dominant strike of Upper Green River fractures as obtained from outcrop, core analysis, and borehole image logs. The P-wave amplitude response is extracted from prestack amplitude variation with offset (AVO) analysis, which is compared to isotropic‐model AVO responses of gas sand versus brine sand in the Upper Green River. A nine‐component vertical seismic profile (VSP) was also obtained for calibration of S-wave reflections with P-wave reflections, and support of reflection S-wave results. The direction of the fast (S1) shear‐wave component from the reflection data and the VSP coincides with the northwest orientation of Upper Green River fractures, and the direction of maximum horizontal in‐situ stress as determined from borehole ellipticity logs. Significant differences were observed in the P-wave AVO gradient measured parallel and perpendicular to the orientation of Upper Green River fractures. Positive AVO gradients were associated with gas‐producing fractured intervals for propagation normal to fractures. AVO gradients measured normal to fractures at known waterwet zones were near zero or negative. A proportional relationship was observed between the azimuthal variation of the P-wave AVO gradient as measured at the tops of fractured intervals, and the fractional difference between the vertical traveltimes of split S-waves (the “S-wave anisotropy”) of the intervals.

Elastic-wave evaluation of downhole hydraulic fracturing: Modeling and field applications

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. D1-D8 ◽  
Author(s):  
Yuan-Da Su ◽  
Zhen Li ◽  
Song Xu ◽  
Chun-Xi Zhuang ◽  
Xiao-Ming Tang
Keyword(s):  
Wave Propagation ◽  
Hydraulic Fracturing ◽  
Elastic Wave ◽  
Fracture Network ◽  
Velocity Variation ◽  
Fracture Aperture ◽  
Filling Material ◽  
S Wave ◽  
Velocity Change ◽  
Main Fracture

We numerically simulate elastic-wave propagation along a fluid-filled borehole with a hydraulically fractured formation. The numerical model is based on the results of hydraulic fracturing on laboratory specimens. Two typical models are simulated: a main fracture crossing the borehole and a fracture network extending from the borehole. In addition, both models contain small, secondary fractures surrounding the borehole. Our result indicates that wave propagation in the main-fracture model is characterized by significant S-wave anisotropy for polarization along and normal to the fracture orientation, with the magnitude of anisotropy depending on the fracture aperture and filling material. In contrast, no significant anisotropy is observed for the fracture network model. In both models, wave propagation is significantly affected by small-fracture-induced near-borehole velocity variation. Our modeling results provide a theoretical foundation for evaluating hydraulic fracturing using the borehole acoustic logging. The hydraulic fracture-induced S-wave anisotropy can be evaluated with the cross-dipole S-wave logging, and the fracturing-induced velocity change can be detected by acoustic traveltime tomography. We used field data examples to demonstrate the effectiveness and practicality of using the borehole acoustic techniques for hydraulic fracturing evaluation.

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