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 Greybody Factors for Schwarzschild Black Holes: Path-Ordered Exponentials and Product Integrals

Universe ◽  
2018 ◽  
Vol 4 (9) ◽  
pp. 93 ◽  
Author(s):  
Finnian Gray ◽  
Matt Visser
Keyword(s):  
Black Holes ◽  
High Frequency ◽  
Low Frequency ◽  
Intermediate Frequency ◽  
General Context ◽  
Matrix Formalism ◽  
Barrier Penetration ◽  
Frequency Regime ◽  
Transfer Matrix Formalism ◽  
Numerical Approaches

In earlier work concerning the sparsity of the Hawking flux, we found it necessary to re-examine what is known regarding the greybody factors of black holes, with a view to extending and expanding on some old results from the 1970s. Focusing specifically on Schwarzschild black holes, we have re-calculated and re-assessed the greybody factors using a path-ordered-exponential approach, a technique which has the virtue of providing a pedagogically useful semi-explicit formula for the relevant Bogoliubov coefficients. These path-ordered-exponentials, being based on a variant of the “transfer matrix” formalism, are closely related to so-called “product integrals”, leading to quite straightforward and direct numerical evaluation, while side-stepping any need for numerically solving the relevant ordinary differential equations. Furthermore, while considerable analytic information is already available regarding both the high-frequency and low-frequency asymptotics of these greybody factors, numerical approaches seem better adapted to finding suitable “global models” for these greybody factors in the intermediate frequency regime, where most of the Hawking flux is actually concentrated. Working in a more general context, these path-ordered-exponential techniques are also likely to be of interest for generic barrier-penetration problems.

scholarly journals Precorrected-FFT Accelerated Singular Boundary Method for High-Frequency Acoustic Radiation and Scattering

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 238
Author(s):  
Weiwei Li ◽  
Fajie Wang
Keyword(s):  
High Frequency ◽  
Acoustic Radiation ◽  
Low Frequency ◽  
Singular Boundary ◽  
Cpu Time ◽  
Interpolation Matrix ◽  
Collocation Points ◽  
Boundary Method ◽  
Frequency Regime ◽  
Singular Boundary Method

This paper presents a precorrected-FFT (pFFT) accelerated singular boundary method (SBM) for acoustic radiation and scattering in the high-frequency regime. The SBM is a boundary-type collocation method, which is truly free of mesh and integration and easy to program. However, due to the expensive CPU time and memory requirement in solving a fully-populated interpolation matrix equation, this method is usually limited to low-frequency acoustic problems. A new pFFT scheme is introduced to overcome this drawback. Since the models with lots of collocation points can be calculated by the new pFFT accelerated SBM (pFFT-SBM), high-frequency acoustic problems can be simulated. The results of numerical examples show that the new pFFT-SBM possesses an obvious advantage for high-frequency acoustic problems.

scholarly journals On the Effectiveness of Low Frequency Perturbations

2019 ◽  
Author(s):  
Yash Sharma ◽  
Gavin Weiguang Ding ◽  
Marcus A. Brubaker
Keyword(s):  
High Frequency ◽  
State Of The Art ◽  
Low Frequency ◽  
Human Perception ◽  
Search Space ◽  
Frequency Space ◽  
Performance Improvements ◽  
Frequency Regime ◽  
Frequency Components ◽  
Norm Constraint

Carefully crafted, often imperceptible, adversarial perturbations have been shown to cause state-of-the-art models to yield extremely inaccurate outputs, rendering them unsuitable for safety-critical application domains. In addition, recent work has shown that constraining the attack space to a low frequency regime is particularly effective. Yet, it remains unclear whether this is due to generally constraining the attack search space or specifically removing high frequency components from consideration. By systematically controlling the frequency components of the perturbation, evaluating against the top-placing defense submissions in the NeurIPS 2017 competition, we empirically show that performance improvements in both the white-box and black-box transfer settings are yielded only when low frequency components are preserved. In fact, the defended models based on adversarial training are roughly as vulnerable to low frequency perturbations as undefended models, suggesting that the purported robustness of state-of-the-art ImageNet defenses is reliant upon adversarial perturbations being high frequency in nature. We do find that under L-inf-norm constraint 16/255, the competition distortion bound, low frequency perturbations are indeed perceptible. This questions the use of the L-inf-norm, in particular, as a distortion metric, and, in turn, suggests that explicitly considering the frequency space is promising for learning robust models which better align with human perception.

Seismic low-frequency shadows and their application to detect CO2 anomalies on time-lapse seismic data: a case study from Sleipner field, North sea

Geophysics ◽  
2021 ◽  
pp. 1-45
Author(s):  
Emmanuel Anthony ◽  
Nimisha Vedanti
Keyword(s):  
North Sea ◽  
Seismic Data ◽  
High Frequency ◽  
Seismic Waves ◽  
Decomposition Analysis ◽  
Low Frequency ◽  
Time Lapse ◽  
Underlying Mechanism ◽  
Real Field ◽  
Saturated Medium

The detection and underlying mechanism of prospect-scale seismic low-frequency shadows (LFS) has been an issue of debate. Even though the concept of LFS is widely accepted, the practical applicability of the method remains limited due to few real field case studies and little understanding of the underlying attenuation mechanism. To characterize the attenuation phenomenon responsible for the occurrence of LFS in CO2 saturated formations, we use the diffusivity and viscosity of the fluid saturated medium to derive a complex velocity function that characterizes a high-frequency attenuation phenomenon responsible for the occurrence of LFS in a CO2 saturated formation. Synthetic seismic data sets representing pre- and post- CO2 injection scenarios were generated using 2D diffusive viscous equations to model the LFS and understand its occurrence mechanism. Furthermore, to demonstrate the applicability of LFS in a real field, a spectral decomposition analysis of time-lapse 3D seismic data of the Sleipner field, North Sea, was carried out using the continuous wavelet transform. LFSs were clearly detected below the reservoir base at frequencies lower than 30 Hz in the post- CO2 injection surveys. It is shown that the seismic low-frequency shadows are not artefacts but occur due to attenuation of the high frequency components of the propagating seismic waves in the CO2 saturated Utsira Formation. The attenuation of these frequencies is a result of the diffusivity and viscosity of the fluid saturated medium. The low-frequency shadows are localized anomalies at the base of the formation; hence with the present approach, these anomalies cannot be related to the migration of the CO2 plume in the Utsira Formation.

AVO attribute inversion for finely layered reservoirs

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. C25-C36 ◽  
Author(s):  
Alexey Stovas ◽  
Martin Landrø ◽  
Per Avseth
Keyword(s):  
Seismic Data ◽  
Rock Physics ◽  
Time Lapse ◽  
Oil Saturation ◽  
Seismic Properties ◽  
Seismic Input ◽  
Fluid Properties ◽  
Random Variability ◽  
Net To Gross ◽  
Avo Attributes

Assuming that a turbidite reservoir can be approximated by a stack of thin shale-sand layers, we use standard amplitude variaiton with offset (AVO) attributes to estimate net-to-gross (N/G) and oil saturation. Necessary input is Gassmann rock-physics properties for sand and shale, as well as the fluid properties for hydrocarbons. Required seismic input is AVO intercept and gradient. The method is based upon thin-layer reflectivity modeling. It is shown that random variability in thickness and seismic properties of the thin sand and shale layers does not change significantly the AVO attributes at the top and base of the turbidite-reservoir sequence. The method is tested on seismic data from offshore Brazil. The results show reasonable agreement between estimated and observed N/G and oil saturation. The methodology can be developed further for estimating changes in pay thickness from time-lapse seismic data.

scholarly journals Modeling the Epidemic Growth of Preprints on COVID-19 and SARS-CoV-2

2021 ◽  
Vol 9 ◽  
Author(s):  
Giovani L. Vasconcelos ◽  
Luan P. Cordeiro ◽  
Gerson C. Duarte-Filho ◽  
Arthur A. Brum
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Growth Dynamics ◽  
Low Rank ◽  
Cumulative Number ◽  
High Frequency Region ◽  
Short Period ◽  
Frequency Regime ◽  
Near Future ◽  
Current Stage

The response of the scientific community to the global health emergency caused by the COVID-19 pandemic has produced an unprecedented number of manuscripts in a short period of time, the vast majority of which have been shared in the form of preprints posted on online preprint repositories before peer review. This surge in preprint publications has in itself attracted considerable attention, although mostly in the bibliometrics literature. In the present study we apply a mathematical growth model, known as the generalized Richards model, to describe the time evolution of the cumulative number of COVID-19 related preprints. This mathematical approach allows us to infer several important aspects concerning the underlying growth dynamics, such as its current stage and its possible evolution in the near future. We also analyze the rank-frequency distribution of preprints servers, ordered by the number of COVID-19 preprints they host, and find that it follows a power law in the low rank (high frequency) region, with the high rank (low frequency) tail being better described by a q-exponential function. The Zipf-like law in the high frequency regime indicates the presence of a cumulative advantage effect, whereby servers that already have more preprints receive more submissions.

Rock physics analysis and time-lapse rock imaging of geochemical effects due to the injection of CO2 into reservoir rocks

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. O23-O33 ◽  
Author(s):  
Tiziana Vanorio ◽  
Amos Nur ◽  
Yael Ebert
Keyword(s):  
Seismic Velocity ◽  
Fluid Pressure ◽  
Rock Physics ◽  
Time Lapse ◽  
Seismic Monitoring ◽  
Physical Parameters ◽  
Salt Precipitation ◽  
S Wave ◽  
Seismic Properties ◽  
Small Pore

The fundamental concept of time-lapse seismic monitoring is that changes in physical parameters—such as saturation, pore fluid pressure, temperature, and stress—affect rock and fluid properties, which in turn alter the seismic velocity and density. Increasingly, however, time-lapse seismic monitoring is called upon to quantify subsurface changes due in part to chemical reactions between injected fluids and the host rocks. This study springs from a series of laboratory experiments and high-resolution images assessing the changes in microstructure, transport, and seismic properties of fluid-saturated sandstones and carbonates injected with [Formula: see text]. Results show that injecting [Formula: see text] into a brine-rock system induces chemo-mechanical mechanisms that permanently change the rock frame. Injecting [Formula: see text] into brine-saturated-sandstones induces salt precipitation primarily at grain contacts and within small pore throats. In rocks with porosity lower than 10%, salt precipitation reduces permeability and increases P- and S-wave velocities of the dry rock frame. On the other hand, injecting [Formula: see text]-rich water into micritic carbonates induces dissolution of the microcrystalline matrix, leading to porosity enhancement and chemo-mechanical compaction under pressure. In this situation, the elastic moduli of the dry rock frame decrease. The results in these two scenarios illustrate that the time-lapse seismic response of chemically stimulated systems cannot be modeled as a pure fluid-substitution problem. A first set of empirical relationships links the time-variant effects of injection to the elastic properties of the rock frame using laboratory velocity measurements and advanced imaging.

scholarly journals Geomechanical modeling of distributed fiber-optic sensor measurements

2019 ◽  
Vol 7 (1) ◽  
pp. SA21-SA27 ◽  
Author(s):  
Christopher Sherman ◽  
Robert Mellors ◽  
Joseph Morris ◽  
Frederick Ryerson
Keyword(s):  
High Frequency ◽  
Fiber Optic ◽  
New Technology ◽  
Low Frequency ◽  
Rock Physics ◽  
Fiber Optic Sensor ◽  
Acoustic Sensors ◽  
Optic Sensor ◽  
Distributed Fiber Optic Sensor ◽  
Fracture Height

Fiber-optic-based distributed acoustic sensors (DAS) are a new technology that can be deployed in a well and are continuously interrogated during operations. These sensors measure the strain (or strain rate) at all points along the fiber and have been used extensively to monitor hydraulic stimulations. The data from these sensors indicate that they are sensitive to high-frequency signals associated with microseismicity and low-frequency signals associated with fracture growth. We have developed a set of idealized models to simulate these signals and to identify interpretation methods that may be used to estimate fracture location, geometry, and extent. We use a multiphysics code that includes rock physics, fluid flow, and elastic-wave propagation to generate synthetic DAS measurements from a set of simple models that mimic hydraulic fracturing. We then relate the signals observed in the synthetic DAS to specific features in the model such as fracture height, width, and aperture. Our results demonstrate that the synthetic DAS measurements may be used to interpret field DAS measurements and to optimize the design of future sensor deployments for sensitivity to fracture attributes.

scholarly journals Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics

2021 ◽  
Author(s):  
Yu Deng ◽  
Christian Zillinger
Keyword(s):  
Euler Equations ◽  
High Frequency ◽  
Low Frequency ◽  
Linear Instability ◽  
Instability Mechanism ◽  
Resonance Mechanism ◽  
Gevrey Regularity ◽  
Precise Analysis ◽  
Frequency Regime ◽  
Type Spaces

AbstractIn this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to be a (secondary) linear instability mechanism. Furthermore, we develop a more precise analysis of cancellations in the resonance mechanism, which yields a modified exponent in the high frequency regime. This allows us, in addition, to remove a logarithmic constraint on the perturbations present in prior works by Bedrossian, Deng and Masmoudi, and to construct solutions which are initially in a Gevrey class for which the velocity asymptotically converges in Sobolev regularity but diverges in Gevrey regularity.

Microparticle Trapping in Streaming Flows in Open Rectangular Chambers Undergoing Low Frequency Vertical Vibrations

2014 ◽  
Author(s):  
Prashant Agrawal ◽  
Prasanna S. Gandhi ◽  
Adrian Neild
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Mode Switching ◽  
Small Particles ◽  
Low Frequencies ◽  
Different Types ◽  
Frequency Regime ◽  
Vertical Vibrations ◽  
Rectangular Chamber ◽  
Streaming Flows

Microparticle collection in microfluidic systems via mechanical vibrations has been demonstrated in both low frequency systems (in the range of 100Hz) and in the high frequency regime (in the range of 1MHz). However, in most systems, collection of particles with lower inertia is hindered by second order time-averaged streaming flows. In our approach, we experimentally demonstrate collection of small particles (about 3 μm in diameter) by trapping them in streaming flows in a liquid filled open rectangular chamber undergoing vertical vibrations at low frequencies. The proposed method is then utilized to separate two different types of particles in distinct patterns through mode-switching.

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