Low-frequency reflections from a thin layer with high attenuation caused by interlayer flow

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. N15-N23 ◽  
Author(s):  
Beatriz Quintal ◽  
Stefan M. Schmalholz ◽  
Yuri Y. Podladchikov
Keyword(s):  
Reflection Coefficient ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Incident Wavelength ◽  
High Attenuation ◽  
Partially Saturated ◽  
Fluid Saturation ◽  
Wide Range ◽  
Wave Induced ◽  
Approximate Equations

The 1D interlayer-flow (or White’s) model is based on Biot’s theory of poroelasticity and explains low-frequency seismic wave attenuation in partially saturated rocks by wave-induced fluid flow between two alternating poroelastic layers, each saturated with a different fluid. We have developed approximate equations for both the minimum possible value of the quality factor, [Formula: see text], and the corresponding fluid saturation for which [Formula: see text] is minimal. The simple approximate equations provide a better insight into the dependence of [Formula: see text] on basic petrophysical parameters and allow for a fast assessment of the minimal value of [Formula: see text]. The approximation is valid for a wide range of realistic petrophysical parameter values for sandstones partially saturated with gas and water, and shows that values of [Formula: see text] can be as small as two. We ap-plied the interlayer-flow model to study the reflection coefficient of a thin (i.e., between 6 and 11 times smaller than the incident wavelength) layer that is partially saturated with gas and water. The reflection coefficient of the layer, caused only by a contrast in attenuation between the layer and the nonattenuating background medium, can be larger than 10% for [Formula: see text] within the layer. The reflection coefficient was calculated with finite difference simulations of wave propagation in heterogeneous, poroelastic solids and in equivalent viscoelastic solids. The reflection coefficient of the layer is also estimated with an analytical solution using a complex velocity for the layer. The numerical and analytical results agree well. Our results indicate that reflection coefficients of gas reservoirs can be significantly increased and frequency dependent in the low-frequency range because of attenuation within the reservoir caused by wave-induced flow.

Impact of fluid saturation on the reflection coefficient of a poroelastic layer

Geophysics ◽  
2011 ◽  
Vol 76 (2) ◽  
pp. N1-N12 ◽  
Author(s):  
Beatriz Quintal ◽  
Stefan M. Schmalholz ◽  
Yuri Y. Podladchikov
Keyword(s):  
Fluid Flow ◽  
Reflection Coefficient ◽  
Analytical Solution ◽  
Quality Factor ◽  
Velocity Dispersion ◽  
Normal Incidence ◽  
Sand Layer ◽  
Partially Saturated ◽  
Fluid Saturation ◽  
Wave Induced

The impact of changes in saturation on the frequency-dependent reflection coefficient of a partially saturated layer was studied. Seismic attenuation and velocity dispersion in partially saturated (i.e., patchy saturated) poroelastic media were accounted for by using the analytical solution of the 1D White’s model for wave-induced fluid flow. White’s solution was applied in combination with an analytical solution for the normal-incidence reflection coefficient of an attenuating layer embedded in an elastic or attenuating background medium to investigate the effects of attenuation, velocity dispersion, and tuning on the reflection coefficient. Approximations for the frequency-dependent quality factor, its minimum value, and the frequency at which the minimum value of the quality factor occurs were derived. The approximations are valid for any two alternating sets of petrophysical parameters. An approximation for the normal-incidence reflection coefficient of an attenuating thin (compared to the wavelength) layer was also derived. This approximation gives insight into the influence of contrasts in acoustic impedance and/or attenuation on the reflectivity of a thin layer. Laboratory data for reflections from a water-saturated sand layer and from a dry sand layer were further fit with petrophysical parameters for unconsolidated sand partially saturated with water and air. The results showed that wave-induced fluid flow can explain low-frequency reflection anomalies, which are related to fluid saturation and can be observed in seismic field data. The results further indicate that reflection coefficients of partially saturated layers (e.g., hydrocarbon reservoirs) can vary significantly with frequency, especially at low seismic frequencies where partial saturation may often cause high attenuation.

Numerical modeling and laboratory measurements of seismic attenuation in partially saturated rock

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. L13-L20 ◽  
Author(s):  
Maria Kuteynikova ◽  
Nicola Tisato ◽  
Ralf Jänicke ◽  
Beatriz Quintal
Keyword(s):  
Numerical Modeling ◽  
Seismic Attenuation ◽  
Laboratory Measurements ◽  
Berea Sandstone ◽  
Mesoscopic Scale ◽  
Partially Saturated ◽  
Saturated Rock ◽  
Fluid Saturation ◽  
The Matrix ◽  
Wave Induced

To better understand the effects of fluid saturation on seismic attenuation, we combined numerical modeling in poroelastic media and laboratory measurements of seismic attenuation in partially saturated Berea sandstone samples. Although in laboratory experiments many physical mechanisms for seismic attenuation take place simultaneously, with numerical modeling we separately studied the effect of a single physical mechanism: wave-induced fluid flow on the mesoscopic scale. Using the finite-element method, we solved Biot’s equations of consolidation by performing a quasistatic creep test on a 3D poroelastic model. This model represents a partially saturated rock sample. We obtained the stress-strain relation, from which we calculated frequency-dependent attenuation. In the laboratory, we measured attenuation in extensional mode for dry and partially water-saturated Berea sandstone samples in the frequency range from 0.1 to 100 Hz. All the measurements were performed at room pressure and temperature conditions. From numerical simulations, we found that attenuation varies significantly with fluid distribution within the model. In addition to binary distributions, we used spatially continuous distributions of fluid saturation for the numerical models. Such continuous saturation distribution was implemented using properties of an effective single-phase fluid. By taking into account the matrix anelasticity, we found that wave-induced fluid flow on the mesoscopic scale due to a continuous distribution of fluid saturation can reproduce seismic attenuation data measured in a partially saturated sample. The matrix anelasticity was the attenuation measured in the room-condition dry sample.

scholarly journals Statistical characterization of gas-patch distributions in partially saturated rocks

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA51-WA64 ◽  
Author(s):  
Julianna Toms-Stewart ◽  
Tobias M. Müller ◽  
Boris Gurevich ◽  
Lincoln Paterson
Keyword(s):  
Correlation Function ◽  
Autocorrelation Function ◽  
Correlation Length ◽  
Wave Attenuation ◽  
Length Scales ◽  
Gas Saturation ◽  
Partially Saturated ◽  
Statistical Measures ◽  
Fluid Saturation ◽  
Limestone Sample

Reservoir rocks are often saturated by two or more fluid phases forming complex patterns on all length scales. The objective of this work is to quantify the geometry of fluid phase distribution in partially saturated porous rocks using statistical methods and to model the associated acoustic signatures. Based on X-ray tomographic images at submillimeter resolution obtained during a gas-injection experiment, the spatial distribution of the gas phase in initially water-saturated limestone samples are constructed. Maps of the continuous variation of the percentage of gas saturation are computed and associated binary maps obtained through a global thresholding technique. The autocorrelation function is derived via the two-point probability function computed from the binary gas-distribution maps using Monte Carlo simulations.The autocorrelation function can be approximated well by a single Debye correlation function or a superposition of two such functions. The characteristic length scales and show sensitivity (and hence significance) with respect to the percentage of gas saturation. An almost linear decrease of the Debye correlation length occurs with increasing gas saturation. It is concluded that correlation function and correlation length provide useful statistical information to quantify fluid-saturation patterns and changes in these patterns at the mesoscale. These spatial statistical measures are linked to a model that predicts compressional wave attenuation and dispersion from local, wave-induced fluid flow in randomly heterogeneous poroelastic solids. In particular, for a limestone sample, with flow permeability of 5 darcies and an average gas saturation of [Formula: see text], significant [Formula: see text]-wave attenuation is predicted at ultrasonic frequencies.

Fluid distribution effect on sonic attenuation in partially saturated limestones

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 154-160 ◽  
Author(s):  
Thierry Cadoret ◽  
Gary Mavko ◽  
Bernard Zinszner
Keyword(s):  
Wave Attenuation ◽  
Water Saturation ◽  
High Water ◽  
Fluid Distribution ◽  
Computer Assisted ◽  
Fluid Content ◽  
Partially Saturated ◽  
Fluid Saturation ◽  
Distribution Effect ◽  
Saturation Method

Extensional and torsional wave‐attenuation measurements are obtained at a sonic frequency around 1 kHz on partially saturated limestones using large resonant bars, 1 m long. To study the influence of the fluid distribution, we use two different saturation methods: drying and depressurization. When water saturation (Sw) is higher than 70%, the extensional wave attenuation is found to depend on whether the resonant bar is jacketed. This can be interpreted as the Biot‐Gardner‐White effect. The experimental results obtained on jacketed samples show that, during a drying experiment, extensional wave attenuation is influenced strongly by the fluid content when Sw is between approximately 60% and 100%. This sensitivity to fluid saturation vanishes when saturation is obtained through depressurization. Using a computer‐assisted tomographic (CT) scan, we found that, during depressurization, the fluid distribution is homogeneous at the millimetric scale at all saturations. In contrast, during drying, heterogeneous saturation was observed at high water‐saturation levels. Thus, we interpret the dependence of the extensional wave attenuation upon the saturation method as principally caused by a fluid distribution effect. Torsional attenuation shows no sensitivity to fluid saturation for Sw between 5% and 100%.

scholarly journals Effect of grain-scale gas patches on the seismic properties of double porosity rocks

2016 ◽  
Vol 208 (1) ◽  
pp. 432-436 ◽  
Author(s):  
Stanislav Glubokovskikh ◽  
Boris Gurevich
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Rock Physics ◽  
Time Lapse ◽  
Double Porosity ◽  
Ultrasonic Velocities ◽  
Seismic Properties ◽  
Partially Saturated ◽  
Frequency Regime ◽  
Wave Induced

Time-lapse ultrasonic measurements constitute a tool to establish and calibrate rock physics models for surface seismic monitoring of partially saturated rocks. This workflow requires one to take into account seismic dispersion caused by frequency-dependent wave-induced fluid flow. We develop a theory of squirt flow in rocks saturated with a viscoelastic material containing isolated gas patches between compliant intergranular contacts. This model is valid for the entire frequency range, from seismic to ultrasonic. In the limit of full saturation the derived equations reduce to the Gassmann equations in the low-frequency regime and traditional squirt theory in the high-frequency regime. The model prediction of ultrasonic velocities versus saturation matches with experimental observations.

scholarly journals Attenuation of Seismic Waves in Partially Saturated Berea Sandstone as a Function of Frequency and Confining Pressure

2021 ◽  
Vol 9 ◽  
Author(s):  
Nicola Tisato ◽  
Claudio Madonna ◽  
Erik H. Saenger
Keyword(s):  
Fluid Flow ◽  
Wave Attenuation ◽  
Confining Pressure ◽  
Berea Sandstone ◽  
Experimental Conditions ◽  
Frequency Dependent ◽  
Near Surface ◽  
Partially Saturated ◽  
Near Surface Geophysics ◽  
Wave Induced

Frequency-dependent attenuation (1/Q) should be used as a seismic attribute to improve the accuracy of seismic methods and imaging of the subsurface. In rocks, 1/Q is highly sensitive to the presence of saturating fluids. Thus, 1/Q could be crucial to monitor volcanic and hydrothermal domains and to explore hydrocarbon and water reservoirs. The experimental determination of seismic and teleseismic attenuation (i.e., for frequencies < 100 Hz) is challenging, and as a consequence, 1/Q is still uncertain for a broad range of lithologies and experimental conditions. Moreover, the physics of elastic energy absorption (i.e., 1/Q) is often poorly constrained and understood. Here, we provide a series of measurements of seismic wave attenuation and dynamic Young’s modulus for dry and partially saturated Berea sandstone in the 1–100 Hz bandwidth and for confining pressure ranging between 0 and 20 MPa. We present systematic relationships between the frequency-dependent 1/Q and the liquid saturation, and the confining pressure. Data in the seismic bandwidth are compared to phenomenological models, ultrasonic elastic properties and theoretical models for wave-induced-fluid-flow (i.e., squirt-flow and patchy-saturation). The analysis suggests that the observed frequency-dependent attenuation is caused by wave-induced-fluid-flow but also that the physics behind this attenuation mechanism is not yet fully determined. We also show, that as predicted by wave-induced-fluid-flow theories, attenuation is strongly dependent on confining pressure. Our results can help to interpret data for near-surface geophysics to improve the imaging of the subsurface.

scholarly journals Field Evidence of Inverse Energy Cascades in the Surfzone

2020 ◽  
Vol 50 (8) ◽  
pp. 2315-2321 ◽  
Author(s):  
Steve Elgar ◽  
Britt Raubenheimer
Keyword(s):  
Low Frequency ◽  
Breaking Waves ◽  
Transport Processes ◽  
Energy Cascade ◽  
Inverse Energy Cascade ◽  
Energy Cascades ◽  
Field Evidence ◽  
Wide Range ◽  
Alongshore Current ◽  
Wave Induced

AbstractLow-frequency currents and eddies transport sediment, pathogens, larvae, and heat along the coast and between the shoreline and deeper water. Here, low-frequency currents (between 0.1 and 4.0 mHz) observed in shallow surfzone waters for 120 days during a wide range of wave conditions are compared with theories for generation by instabilities of alongshore currents, by ocean-wave-induced sea surface modulations, and by a nonlinear transfer of energy from breaking waves to low-frequency motions via a two-dimensional inverse energy cascade. For these data, the low-frequency currents are not strongly correlated with shear of the alongshore current, with the strength of the alongshore current, or with wave-group statistics. In contrast, on many occasions, the low-frequency currents are consistent with an inverse energy cascade from breaking waves. The energy of the low-frequency surfzone currents increases with the directional spread of the wave field, consistent with vorticity injection by short-crested breaking waves, and structure functions increase with spatial lags, consistent with a cascade of energy from few-meter-scale vortices to larger-scale motions. These results include the first field evidence for the inverse energy cascade in the surfzone and suggest that breaking waves and nonlinear energy transfers should be considered when estimating nearshore transport processes across and along the coast.

A corrugated-core sandwich beam with local resonators for low-frequency broadband elastic wave attenuation

2021 ◽  
pp. 107754632110349
Author(s):  
Chenyang Xi ◽  
Xiaosong Zhu ◽  
Hui Zheng
Keyword(s):  
Vibration Suppression ◽  
Wave Attenuation ◽  
Dynamic Stiffness ◽  
Sandwich Beam ◽  
Low Frequency ◽  
Spectral Element ◽  
Experimental Investigations ◽  
High Attenuation ◽  
Low Frequency Vibration ◽  
Resonant Effect

This article attempts to enhance the low-frequency vibration suppression performance of corrugated-core sandwich beams. Multiple local resonators are introduced into the corrugated-core sandwich beam to acquire low-frequency bandgaps with broader bandwidth and higher wave attenuation capability. The governing equations for vibration analysis of the local resonator–attached corrugated-core sandwich beam are established based on the spectral element method, which incorporates the locally resonant effect by adding the dynamic stiffness term of one specific resonator to the degree of freedom that it attaches to. The bandgaps of the proposed periodic structure are further derived by imposing the Bloch boundary conditions. After validating the numerical model through finite element simulations as well as experimental investigations, the bandgaps and vibration transmissibility of the corrugated-core sandwich beam are carried out, both with and without attached local resonators. It is found that the vibration reduction capability of the corrugated-core sandwich beam is greatly enhanced, bringing two low-frequency bandgaps with high attenuation factors and wide bandwidths. Meantime, the first bandgap of resonator-free corrugated-core sandwich beam is broadened apparently. An interesting result is that the bandgap with higher frequency is split by a newly generated passband. Furthermore, parametric studies are performed, and it is found that the regulating characteristics of the bandgaps obtained through varying the attachment location of local resonators are similar to those through tuning their inherent parameters.

Numerical simulation of ambient seismic wavefield modification caused by pore-fluid effects in an oil reservoir

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. T41-T52 ◽  
Author(s):  
Marc-André Lambert ◽  
Erik H. Saenger ◽  
Beatriz Quintal ◽  
Stefan M. Schmalholz
Keyword(s):  
Wave Propagation ◽  
Fluid Flow ◽  
Viscoelastic Behavior ◽  
Oil Reservoir ◽  
Noise Mitigation ◽  
Mesoscopic Scale ◽  
High Attenuation ◽  
Fluid Saturation ◽  
Wave Induced ◽  
The Impact

We have modeled numerically the seismic response of a poroelastic inclusion with properties applicable to an oil reservoir that interacts with an ambient wavefield. The model includes wave-induced fluid flow caused by pressure differences between mesoscopic-scale (i.e., in the order of centimeters to meters) heterogeneities. We used a viscoelastic approximation on the macroscopic scale to implement the attenuation and dispersion resulting from this mesoscopic-scale theory in numerical simulations of wave propagation on the kilometer scale. This upscaling method includes finite-element modeling of wave-induced fluid flow to determine effective seismic properties of the poroelastic media, such as attenuation of P- and S-waves. The fitted, equivalent, viscoelastic behavior is implemented in finite-difference wave propagation simulations. With this two-stage process, we model numerically the quasi-poroelastic wave-propagation on the kilometer scale and study the impact of fluid properties and fluid saturation on the modeled seismic amplitudes. In particular, we addressed the question of whether poroelastic effects within an oil reservoir may be a plausible explanation for low-frequency ambient wavefield modifications observed at oil fields in recent years. Our results indicate that ambient wavefield modification is expected to occur for oil reservoirs exhibiting high attenuation. Whether or not such modifications can be detected in surface recordings, however, will depend on acquisition design and noise mitigation processing as well as site-specific conditions, such as the geologic complexity of the subsurface, the nature of the ambient wavefield, and the amount of surface noise.

The Attenuation of Very Low Frequency Brain Oscillations in Transitions from a Rest State to Active Attention

2009 ◽  
Vol 23 (4) ◽  
pp. 191-198 ◽  
Author(s):  
Suzannah K. Helps ◽  
Samantha J. Broyd ◽  
Christopher J. James ◽  
Anke Karl ◽  
Edmund J. S. Sonuga-Barke
Keyword(s):  
Brain Activity ◽  
Sampling Rate ◽  
Low Frequency ◽  
Future Research ◽  
Adhd Symptoms ◽  
Default Mode ◽  
Very Low Frequency ◽  
Wide Range ◽  
Interference Hypothesis ◽  
Mode Interference

Background: The default mode interference hypothesis ( Sonuga-Barke & Castellanos, 2007 ) predicts (1) the attenuation of very low frequency oscillations (VLFO; e.g., .05 Hz) in brain activity within the default mode network during the transition from rest to task, and (2) that failures to attenuate in this way will lead to an increased likelihood of periodic attention lapses that are synchronized to the VLFO pattern. Here, we tested these predictions using DC-EEG recordings within and outside of a previously identified network of electrode locations hypothesized to reflect DMN activity (i.e., S3 network; Helps et al., 2008 ). Method: 24 young adults (mean age 22.3 years; 8 male), sampled to include a wide range of ADHD symptoms, took part in a study of rest to task transitions. Two conditions were compared: 5 min of rest (eyes open) and a 10-min simple 2-choice RT task with a relatively high sampling rate (ISI 1 s). DC-EEG was recorded during both conditions, and the low-frequency spectrum was decomposed and measures of the power within specific bands extracted. Results: Shift from rest to task led to an attenuation of VLFO activity within the S3 network which was inversely associated with ADHD symptoms. RT during task also showed a VLFO signature. During task there was a small but significant degree of synchronization between EEG and RT in the VLFO band. Attenuators showed a lower degree of synchrony than nonattenuators. Discussion: The results provide some initial EEG-based support for the default mode interference hypothesis and suggest that failure to attenuate VLFO in the S3 network is associated with higher synchrony between low-frequency brain activity and RT fluctuations during a simple RT task. Although significant, the effects were small and future research should employ tasks with a higher sampling rate to increase the possibility of extracting robust and stable signals.

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