Seismic reflectivity of hydraulic fractures approximated by thin fluid layers

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. T79-T87 ◽  
Author(s):  
A. Oelke ◽  
D. Alexandrov ◽  
I. Abakumov ◽  
S. Glubokovskikh ◽  
R. Shigapov ◽  
...  
Keyword(s):  
Analytical Solutions ◽  
Fluid Layer ◽  
Synthetic Data ◽  
P Wave ◽  
Hydraulic Fractures ◽  
Reflection Coefficients ◽  
S Wave ◽  
Reservoir Properties ◽  
Thin Fluid ◽  
Theoretical Results

We have analyzed the angle-dependent reflectivity of microseismic wavefields at a hydraulic fracture, which we modeled as an ideal thin fluid layer embedded in an elastic, isotropic solid rock. We derived full analytical solutions for the reflections of an incident P-wave, the P-P and P-S reflection coefficients, as well as for an incident S-wave, and the S-S and S-P reflection coefficients. The rather complex analytical solutions were then approximated and we found that these zero-thickness limit approximations are in good agreement with the linear slip model, representing a fracture at slip contact. We compared the analytical solutions for the P-P reflections with synthetic data that were derived using finite-difference modeling and found that the modeling confirmed our theoretical results. For typical parameters of microseismic monitoring by hydraulic fracturing, e.g., a layer thickness of [Formula: see text] and frequencies of [Formula: see text], the reflection coefficients depend on the Poisson’s ratio. Furthermore, the reflection coefficients of an incident S-wave are remarkably high. Theoretical results suggested that it is feasible to image hydraulic fractures using microseismic events as a source and to solve the inverse problem, that is, to interpret reflection coefficients extracted from microseismic data in terms of reservoir properties.

An exact anelastic model for the free-surface relfection of P and S-I waves

1989 ◽  
Vol 79 (3) ◽  
pp. 842-859
Author(s):  
R. D. Borcherdt ◽  
G. Glassmoyer
Keyword(s):  
Free Surface ◽  
Volumetric Strain ◽  
Major Axis ◽  
P Wave ◽  
Reflection Coefficients ◽  
S Wave ◽  
Low Loss ◽  
Surface Reflection ◽  
Pierre Shale ◽  
Homogeneous Wave

Abstract Exact anelastic solutions incorporating inhomogeneous waves are used to model numerically S-I and P waves incident on the free surface of a low-loss anelastic half-space. Anelastic free-surface reflection coefficients are computed for the volumetric strain and displacement components of inhomogeneous wave fields. For the problem of an incident homogeneous S-I wave in Pierre shale, the largest strain and displacement amplitudes for the reflected P wave occur at angles of incidence for which the particle motion for the reflected inhomogeneous P wave is elliptical (minor/major axis = 0.6), the specific absorption (QP−1) is greater (300 per cent) and the velocity is less (25 per cent) than those for a corresponding homogeneous P wave, the direction of phase propagation is not parallel to the free surface, and the amplitude of the wave shows a significant increase with depth (6 per cent in one wavelength). Energy reflection coefficients computed for this low-loss anelastic model show that energy flow due to interaction of the incident and reflected waves reach maxima (30 per cent of the incident energy) near large but nongrazing angles of incidence. For the problem of an incident homogeneous P wave in Pierre shale, the inhomogeneity of the reflected S wave is shown not to contribute to significant variations in wave field characteristics over those that would be expected for a homogeneous wave.

scholarly journals Microseismic monitoring using a fibre-optic Distributed Acoustic Sensor (DAS) array

Geophysics ◽  
2020 ◽  
pp. 1-48
Author(s):  
James P. Verdon ◽  
Steve A. Horne ◽  
Andrew Clarke ◽  
Anna L. Stork ◽  
Alan F. Baird ◽  
...  
Keyword(s):  
Time Windows ◽  
Microseismic Monitoring ◽  
P Wave ◽  
Hydraulic Fractures ◽  
Fibre Optic ◽  
S Wave ◽  
Simple Method ◽  
Waveform Data ◽  
Zero Offset ◽  
Optic Array

We present a case study demonstrating the use of an “L”-shaped downhole fibre-optic array to monitor microseismicity. We use a relatively simple method to detect events from continuous waveform data, and develop a workflow for manual event location. Locations are defined with a cylindrical coordinate system, with the horizontal axis of the DAS cable being the axis of symmetry. Events are located using three manual “picks”, constraining (1) the zero-offset “broadside” channel to the event (2) the P-S wave arrival time difference at the broadside channel, and (3) the angle, ? of the event from the array. Because the one-component DAS array is unable to record P-wave energy on the broadside channel, the P-wave pick is made indirectly by ensuring that the modeled P- and S-wave moveout curves match the observed data. The ? angle requires that signal is observed on the vertical part of the array, in our case this is possible because an engineered fiber, rather than standard telecommunications fiber, provided a significant reduction in the noise level. Because only three picks need to be made, our manual approach is significantly more efficient than equivalent manual processing of downhole geophone data, where picks for P- and S-waves must be made for each receiver. We find that the located events define a tight cluster around the injection interval, indicating that this approach provides relatively precise and accurate event locations. A surface microseismic array was also used at this site, which detected significantly fewer events, the locations of which had significantly greater scatter than the DAS array locations. We conclude by examining some other aspects of the DAS microseismic data, including the presence of multiple events within very short time windows, and the presence of converted phases that appear to represent scattering of energy from the hydraulic fractures themselves.

Near-surface scattering phenomena and implications for tunnel detection

2015 ◽  
Vol 3 (1) ◽  
pp. SF43-SF54 ◽  
Author(s):  
Shelby L. Peterie ◽  
Richard D. Miller
Keyword(s):  
Synthetic Data ◽  
P Wave ◽  
S Wave ◽  
Seismic Line ◽  
Data Set ◽  
Near Surface ◽  
Tunnel Detection ◽  
Impedance Contrast ◽  
Diffraction Imaging ◽  
Imaging Algorithms

Tunnel locations are accurately interpreted from diffraction sections of focused mode converted P- to S-wave diffractions from a perpendicular tunnel and P-wave diffractions from a nonperpendicular (oblique) tunnel. Near-surface tunnels are ideal candidates for diffraction imaging due to their small size relative to the seismic wavelength and large acoustic impedance contrast at the tunnel interface. Diffraction imaging algorithms generally assume that the velocities of the primary wave and the diffracted wave are approximately equal, and that the diffraction apex is recorded directly above the scatterpoint. Scattering phenomena from shallow tunnels with kinematic properties that violate these assumptions were observed in one field data set and one synthetic data set. We developed the traveltime equations for mode-converted and oblique diffractions and demonstrated a diffraction imaging algorithm designed for the roll-along style of acquisition. Potential processing and interpretation pitfalls specific to these diffraction types were identified. Based on our observations, recommendations were made to recognize and image mode-converted and oblique diffractions and accurately interpret tunnel depth, horizontal location, and azimuth with respect to the seismic line.

Petrophysical properties variation of bitumen-bearing carbonates at increasing temperatures from laboratory to model

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. MR297-MR308
Author(s):  
Roberta Ruggieri ◽  
Fabio Trippetta
Keyword(s):  
Central Italy ◽  
Carbonate Reservoir ◽  
P Wave ◽  
Petrophysical Properties ◽  
S Wave ◽  
Reservoir Properties ◽  
Velocity Change ◽  
Seismic Properties ◽  
Wave Velocities ◽  
Velocity Changes

Variations in reservoir seismic properties can be correlated to changes in saturated-fluid properties. Thus, the determination of variation in petrophysical properties of carbonate-bearing rocks is of interest to the oil exploration industry because unconventional oils, such as bitumen (HHC), are emerging as an alternative hydrocarbon reserve. We have investigated the temperature effects on laboratory seismic wave velocities of HHC-bearing carbonate rocks belonging to the Bolognano Formation (Majella Mountain, central Italy), which can be defined as a natural laboratory to study carbonate reservoir properties. We conduct an initial characterization in terms of porosity and density for the carbonate-bearing samples and then density and viscosity measurements for the residual HHC, extracted by HCl dissolution of the hosting rock. Acoustic wave velocities are recorded from ambient temperature to 90°C. Our acoustic velocity data point out an inverse relationship with temperature, and compressional (P) and shear (S) wave velocities show a distinct trend with increasing temperature depending on the amount of HHC content. Indeed, samples with the highest HHC content show a larger gradient of velocity changes in the temperature range of approximately 50°C–60°C, suggesting that the bitumen can be in a fluid state. Conversely, below approximately 50°C, the velocity gradient is lower because, at this temperature, bitumen can change its phase in a solid state. We also propose a theoretical model to predict the P-wave velocity change at different initial porosities for HHC-saturated samples suggesting that the velocity change mainly is related to the absolute volume of HHC.

Extraction of P‐ and S‐waves from the vertical component of the particle velocity at the sea floor

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 231-240 ◽  
Author(s):  
Lasse Amundsen ◽  
Arne Reitan
Keyword(s):  
Particle Velocity ◽  
Synthetic Data ◽  
Vertical Component ◽  
Transversely Isotropic ◽  
Vertical Axis ◽  
Elastic Stiffness ◽  
P Wave ◽  
S Wave ◽  
Sea Floor ◽  
S Waves

At the boundary between two solid media in welded contact, all three components of particle velocity and vertical traction are continuous through the boundary. Across the boundary between a fluid and a solid, however, only the vertical component of particle velocity is continuous while the horizontal components can be discontinuous. Furthermore, the pressure in the fluid is the negative of the vertical component of traction in the solid, while the horizontal components of traction vanish at the interface. Taking advantage of this latter fact, we show that total P‐ and S‐waves can be computed from the vertical component of the particle velocity recorded by single component geophones planted on the sea floor. In the case when the sea floor is transversely isotropic with a vertical axis of symmetry, the computation requires the five independent elastic stiffness components and the density. However, when the sea floor material is fully isotropic, the only material parameter needed is the local shear wave velocity. The analysis of the extraction problem is done in the slowness domain. We show, however, that the S‐wave section can be obtained by a filtering operation in the space‐frequency domain. The P‐wave section is then the difference between the vertical component of the particle velocity and the S‐wave component. A synthetic data example demonstrates the performance of the algorithm.

Determination of formation shear attenuation from dipole sonic log data

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. D73-D79 ◽  
Author(s):  
Qiaomu Qi ◽  
Arthur C. H. Cheng ◽  
Yunyue Elita Li
Keyword(s):  
Reservoir Characterization ◽  
Wave Attenuation ◽  
Synthetic Data ◽  
Low Frequency ◽  
P Wave ◽  
Flexural Wave ◽  
S Wave ◽  
Additional Energy ◽  
Log Data ◽  
Sonic Log

ABSTRACT Formation S-wave attenuation, when combined with compressional attenuation, serves as a potential hydrocarbon indicator for seismic reservoir characterization. Sonic flexural wave measurements provide a direct means for obtaining the in situ S-wave attenuation at log scale. The key characteristic of the flexural wave is that it propagates at the formation shear slowness and experiences shear attenuation at low frequency. However, in a fast formation, the dipole log consists of refracted P- and S-waves in addition to the flexural wave. The refracted P-wave arrives early and can be removed from the dipole waveforms through time windowing. However, the refracted S-wave, which is often embedded in the flexural wave packet, is difficult to separate from the dipole waveforms. The additional energy loss associated with the refracted S-wave results in the estimated dipole attenuation being higher than the shear attenuation at low frequency. To address this issue, we have developed a new method for accurately determining the formation shear attenuation from the dipole sonic log data. The method uses a multifrequency inversion of the frequency-dependent flexural wave attenuation based on energy partitioning. We first developed our method using synthetic data. Application to field data results in a shear attenuation log that is consistent with lithologic interpretation of other available logs.

Frequency‐wavenumber elastic inversion of marine seismic data

Geophysics ◽  
1994 ◽  
Vol 59 (12) ◽  
pp. 1868-1881 ◽  
Author(s):  
Huasheng Zhao ◽  
Bjørn Ursin ◽  
Lasse Amundsen
Keyword(s):  
Wave Velocity ◽  
Reference Data ◽  
Jacobian Matrix ◽  
Synthetic Data ◽  
Velocity Model ◽  
P Wave ◽  
Stratified Medium ◽  
Inversion Method ◽  
S Wave ◽  
Time Space

We present an inversion method for determining the velocities, densities, and layer thicknesses of a horizontally stratified medium with an acoustic layer at the top and a stack of elastic layers below. The multioffset reflection response of the medium generated by a compressional point source is transformed from the time‐space domain into the frequency‐wavenumber domain where the inversion is performed by minimizing the difference between the reference data and the modeled data using a least‐squares technique. The forward modeling is based on the reflectivity method where the solution for each frequency‐wavenumber component is found by computing the generalized reflection and transmission matrices recursively. The gradient of the objective function is computed from analytical expressions of the Jacobian matrix derived directly from the recursive modeling equations. The partial derivatives of the reflection response of the stratified medium are then computed simultaneously with the reflection response by layer‐recursive formulas. The limited‐aperture and discretization effects in time and space of the reference data are included by applying a pair of frequency and wavenumber dependent filters to the predicted data and to the Jacobian matrix at each iteration. Numerical experiments performed with noise‐free synthetic data prove that the proposed inversion method satisfactorily reconstructs the elastic parameters of a stratified medium. The low‐frequency trends of the S‐wave velocity and density are found when the initial P‐wave velocity model gives approximately correct traveltimes. The convergence of the iterative minimization algorithm is fast.

ON NONLEPTONIC DECAYS OF THE Λ0-HYPERON IN THE EFFECTIVE QUARK MODEL WITH CHIRAL U(3)×U(3) SYMMETRY

2007 ◽  
Vol 22 (10) ◽  
pp. 1835-1847 ◽  
Author(s):  
A. YA. BERDNIKOV ◽  
YA. A. BERDNIKOV ◽  
M. FABER ◽  
A. N. IVANOV ◽  
V. A. IVANOVA ◽  
...  
Keyword(s):  
Experimental Data ◽  
Quark Model ◽  
Rest Frame ◽  
Laboratory Frame ◽  
Decay Rates ◽  
P Wave ◽  
Angular Distributions ◽  
S Wave ◽  
Nonleptonic Decays ◽  
Theoretical Results

Within the effective quark model with chiral U (3) × U (3) symmetry we calculate the S-wave and P-wave amplitudes and the partial widths of the nonleptonic decays of the Λ0-hyperon, Λ0 → pπ- and Λ0 → nπ0. The theoretical results agree well with the experimental data. The angular distributions of the decay rates in dependence on the polarizations of baryons are analyzed both in the laboratory frame and in the rest frame of the Λ0-hyperon.

Modeling sensitivity of 3D, 9-C wide azimuth data to changes in fluid content and crack density in cracked reservoirs

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. T155-T165 ◽  
Author(s):  
Herurisa Rusmanugroho ◽  
George A. McMechan
Keyword(s):  
Practical Importance ◽  
Crack Density ◽  
Maximum Amplitude ◽  
P Wave ◽  
Staggered Grid ◽  
Wave Reflections ◽  
S Wave ◽  
Reservoir Properties ◽  
Fluid Content ◽  
Isotropic Media

The volume density of cracks and the fluids contained in them are salient aspects of characterization of cracked reservoirs. Thus, it is of practical importance to investigate whether variations in these reservoir properties are detectable in seismic observations. Eighth-order staggered-grid, 3D finite-difference simulations generate nine-component amplitude variations with offset and azimuth (AVOAZ) for reflections from the top of a vertically cracked zone embedded in an isotropic host. The T-matrix method is used to calculate elastic stiffness tensors. Responses for various crack densities and fluid contents show sensitivity to the spatial orientation of, and variation in, anisotropy. In isotropic media, when source and receiver components have the same orientation (such as XX and YY), reflection amplitude contours align approximately perpendicular to the particle motion. Mixed components (such as XY and YX) have amplitude patterns thatare symmetrical pairs of the same, or opposite, polarity on either side of the diagonal of the 9-C response matrix. In anisotropic media, AVOAZ data show the same basic patterns and symmetries as for isotropic media but with a superimposed tendency for alignment parallel to the strike of the vertical cracks. The data contain combined effects related to the source, receiver, and crack orientations. The sensitivity of data to changes in fluid content is quantified by comparing the differences between responses to various fluid conditions, to the maximum amplitude of oil-filled crack responses. For a crack density of 0.1, amplitude differences are [Formula: see text] for oil-dry and [Formula: see text] for oil-brine. The corresponding values for S-wave reflections are [Formula: see text] for oil-dry and [Formula: see text] for oil-brine. Amplitude changes caused by changing the oil-filled crack density from 0.1 to 0.2 are [Formula: see text] for P-wave reflections and [Formula: see text] for S-wave reflections. These differences are visible in AVOAZ data and are potentially diagnostic for reservoir characterization.

Sign in / Sign up

Export Citation Format

Share Document