Estimating grain‐scale fluid effects on velocity dispersion in rocks

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 1940-1949 ◽  
Author(s):  
Gary Mavko ◽  
Diane Jizba
Keyword(s):  
High Frequency ◽  
Velocity Dispersion ◽  
Rock Properties ◽  
S Wave ◽  
Unknown Parameters ◽  
Local Flow ◽  
Essential Information ◽  
Flow Effect ◽  
Total Dispersion ◽  
Aspect Ratios

The magnitude of the grain‐scale local flow effect on velocity dispersion in saturated rocks is quantified, by estimating the high‐frequency unrelaxed shear and bulk frame moduli, which are then combined with the Biot formulation to predict total dispersion. The method is relatively independent of assumptions about idealized pore geometries and unknown parameters such as pore aspect ratios. The local flow effect depends on the heterogeneity of pore stiffness, in particular the presence of compliant cracks and grain contacts; the pressure dependence of the dry rock properties is shown to contain the essential information about the distribution of pore stiffnesses needed to estimate the high‐frequency saturated behavior. To first order, the unrelaxed wet frame compressibility at any given pressure is shown to be approximately the dry frame compressibility at very high pressure; second order corrections add the additional compressibility gained by replacing an amount of mineral equal to the compliant pore volume with fluid. The method predicts that the difference between relaxed and unrelaxed shear compliance is simply proportional to that in bulk. The results for total dispersion (local flow plus Biot) explain quite well the measured P- and S-wave dispersion for a variety of saturated rocks.

The relation between seismic P‐ and S‐wave velocity dispersion in saturated rocks

Geophysics ◽  
1994 ◽  
Vol 59 (1) ◽  
pp. 87-92 ◽  
Author(s):  
Gary Mavko ◽  
Diane Jizba
Keyword(s):  
Wave Velocity ◽  
Large Scale ◽  
Velocity Dispersion ◽  
Seismic Velocity ◽  
Ultrasonic Velocities ◽  
S Wave ◽  
Local Flow ◽  
Wave Velocities ◽  
Shear Compliance

Seismic velocity dispersionin fluid-saturated rocks appears to be dominated by tow mecahnisms: the large scale mechanism modeled by Biot, and the local flow or squirt mecahnism. The tow mechanisms can be distuinguished by the ratio of P-to S-wave dispersions, or more conbeniently, by the ratio of dynamic bulk to shear compliance dispersions derived from the wave velocities. Our formulation suggests that when local flow denominates, the dispersion of the shear compliance will be approximately 4/15 the dispersion of the compressibility. When the Biot mechanism dominates, the constant of proportionality is much smaller. Our examination of ultrasonic velocities from 40 sandstones and granites shows that most, but not all, of the samples were dominated by local flow dispersion, particularly at effective pressures below 40 MPa.

A dynamic elastic model for squirt-flow effect and its application on fluid-viscosity-associated velocity dispersion in reservoir sandstones

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. MR201-MR212
Author(s):  
Zhi-Qiang Yang ◽  
Tao He ◽  
Chang-Chun Zou
Keyword(s):  
Velocity Dispersion ◽  
Pore Space ◽  
Pore Fluid ◽  
Quantitative Prediction ◽  
Elastic Model ◽  
Fluid Viscosity ◽  
Porous Rocks ◽  
S Wave ◽  
Flow Effect ◽  
Reservoir Sandstones

Velocity dispersion is a common phenomenon for fluid-charged porous rocks and carries important information on the pore structure and fluid in reservoir rocks. Previous ultrasonic experiments had measured more significant non-Biot velocity dispersion on saturated reservoir sandstones with increasing pore-fluid viscosity. Although wave-induced local squirt-flow effect could in theory cause most of the non-Biot velocity dispersion, its quantitative prediction remains a challenge. Several popular models were tested to predict the measured velocities under undrained conditions, but they either underestimated the squirt-flow effect or failed to simultaneously satisfy P- and S-wave velocity dispersions (especially for higher viscosity fluids). Based on the classic double-porosity theory that pore space is comprised of mainly stiff/Biot’s porosity and minor compliant porosity, an effective “wet frame” was hypothesized to account for the squirt-flow effect, whose compliant pores are filled with a hypothesized fluid with dynamic modulus. A new dynamic elastic model was then introduced by extending Biot theory to include the squirt-flow effect, after replacing the dry-frame bulk/shear moduli with their wet-frame counterparts. In addition to yielding better velocity predictions for P- and S-wave measurements of different fluid viscosities, the new model is also more applicable because its two key tuning parameters (i.e., the effective aspect ratio and porosity of compliant pores) at in situ reservoir pressure could be constrained with laboratory velocity measurements associated with pore-fluid viscosities.

Estimates of velocity dispersion between seismic and ultrasonic frequencies

Geophysics ◽  
1986 ◽  
Vol 51 (1) ◽  
pp. 183-189 ◽  
Author(s):  
Kenneth W. Winkler
Keyword(s):  
Velocity Dispersion ◽  
Low Frequency ◽  
Degree Of Saturation ◽  
Fluid Viscosity ◽  
Seismic Velocities ◽  
S Wave ◽  
Local Flow ◽  
Saturated Rock ◽  
Analysis Technique ◽  
Zero Frequency

It is generally accepted that acoustic velocities in fluid‐saturated rocks vary with frequency. Evidence comes from experimental measurements and from theoretical causality arguments. We have developed a simple analysis technique that gives estimates of total velocity dispersion between zero frequency and any measurement frequency. The technique requires compressional (P) and shear (S) wave velocity measurements on dry and fully saturated rock. Assuming that the dry velocities are independent of frequency, the Biot‐Gassmann equations are used to calculate the zero‐frequency velocities in the fully saturated rock. Any difference between the measured velocities and the calculated zero‐frequency velocities is interpreted as evidence of dispersion. Application of this analysis technique to a variety c ultrasonic data sets gives consistent results. In many rocks, dispersion between zero frequency and ultrasonic frequencies is on the order of 10 percent at low effective stress, and it decreases to only a few percent at higher stresses. Dispersion varies with degree of saturation and with fluid viscosity in the same way as do low‐frequency attenuation measurements. The results are readily interpreted in terms of the same local‐flow absorption/dispersion mechanism that has been used to explain recent laboratory attenuation measurements. This apparent dispersion places upper bounds on seismic‐to‐sonic velocity differences. It also points out possible discrepancies between seismic velocities and ultrasonic laboratory measurements.

P- and S-wave attenuation logs from monopole sonic data

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 755-765 ◽  
Author(s):  
Xinhua Sun ◽  
Xiaoming Tang ◽  
C. H. (Arthur) Cheng ◽  
L. Neil Frazer
Keyword(s):  
Wave Attenuation ◽  
Fluid Velocity ◽  
P Wave ◽  
Reservoir Rock ◽  
Rock Properties ◽  
S Wave ◽  
Intrinsic Attenuation ◽  
Modified Method ◽  
Receiver Array ◽  
Attenuation Profiles

In this paper, a modification of an existing method for estimating relative P-wave attenuation is proposed. By generating synthetic waveforms without attenuation, the variation of geometrical spreading related to changes in formation properties with depth can be accounted for. With the modified method, reliable P- and S-wave attenuation logs can be extracted from monopole array acoustic waveform log data. Synthetic tests show that the P- and S-wave attenuation values estimated from synthetic waveforms agree well with their respective model values. In‐situ P- and S-wave attenuation profiles provide valuable information about reservoir rock properties. Field data processing results show that this method gives robust estimates of intrinsic attenuation. The attenuation profiles calculated independently from each waveform of an eight‐receiver array are consistent with one another. In fast formations where S-wave velocity exceeds the borehole fluid velocity, both P-wave attenuation ([Formula: see text]) and S-wave attenuation ([Formula: see text]) profiles can be obtained. P- and S-wave attenuation profiles and their comparisons are presented for three reservoirs. Their correlations with formation lithology, permeability, and fractures are also presented.

Relating Acoustic Anisotropy to Kerogen Content in Unconventional Formations - A Case Study in A Kerogen-Rich Unconventional Carbonate

2021 ◽  
Author(s):  
Yair Gordin ◽  
Thomas Bradley ◽  
Yoav O. Rosenberg ◽  
Anat Canning ◽  
Yossef H. Hatzor ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Water Saturation ◽  
Well Logs ◽  
Rock Properties ◽  
Thermal Maturity ◽  
Burial Diagenesis ◽  
S Wave ◽  
Velocity Anisotropy ◽  
Thermal Maturation ◽  
Wide Range

Abstract The mechanical and petrophysical behavior of organic-rich carbonates (ORC) is affected significantly by burial diagenesis and the thermal maturation of their organic matter. Therefore, establishing Rock Physics (RP) relations and appropriate models can be valuable in delineating the spatial distribution of key rock properties such as the total organic carbon (TOC), porosity, water saturation, and thermal maturity in the petroleum system. These key rock properties are of most importance to evaluate during hydrocarbon exploration and production operations when establishing a detailed subsurface model is critical. High-resolution reservoir models are typically based on the inversion of seismic data to calculate the seismic layer properties such as P- and S-wave impedances (or velocities), density, Poisson's ratio, Vp/Vs ratio, etc. If velocity anisotropy data are also available, then another layer of data can be used as input for the subsurface model leading to a better understanding of the geological section. The challenge is to establish reliable geostatistical relations between these seismic layer measurements and petrophysical/geomechanical properties using well logs and laboratory measurements. In this study, we developed RP models to predict the organic richness (TOC of 1-15 wt%), porosity (7-35 %), water saturation, and thermal maturity (Tmax of 420-435⁰C) of the organic-rich carbonate sections using well logs and laboratory core measurements derived from the Ness 5 well drilled in the Golan Basin (950-1350 m). The RP models are based primarily on the modified lower Hashin-Shtrikman bounds (MLHS) and Gassmann's fluid substitution equations. These organic-rich carbonate sections are unique in their relatively low burial diagenetic stage characterized by a wide range of porosity which decreases with depth, and thermal maturation which increases with depth (from immature up to the oil window). As confirmation of the method, the levels of organic content and maturity were confirmed using Rock-Eval pyrolysis data. Following the RP analysis, horizontal (HTI) and vertical (VTI) S-wave velocity anisotropy were analyzed using cross-dipole shear well logs (based on Stoneley waves response). It was found that anisotropy, in addition to the RP analysis, can assist in delineating the organic-rich sections, microfractures, and changes in gas saturation due to thermal maturation. Specifically, increasing thermal maturation enhances VTI and azimuthal HTI S-wave velocity anisotropies, in the ductile and brittle sections, respectively. The observed relationships are quite robust based on the high-quality laboratory and log data. However, our conclusions may be limited to the early stages of maturation and burial diagenesis, as at higher maturation and diagenesis the changes in physical properties can vary significantly.

Output regulation of output feedback systems with unknown exosystem and unknown high-frequency gain sign

2016 ◽  
Vol 40 (1) ◽  
pp. 171-178 ◽  
Author(s):  
Meichen Guo ◽  
Lu Liu
Keyword(s):  
Output Feedback ◽  
High Frequency ◽  
Adaptive Controller ◽  
Output Regulation ◽  
Design Approach ◽  
Feedback Systems ◽  
Unknown Parameters ◽  
Robust Output Regulation ◽  
Matching Design ◽  
Output Regulation Problem

This paper discusses the global robust output regulation problem for a class of nonlinear output feedback systems. It is assumed that the exosystem and the high-frequency gain sign are unknown and that the unknown parameters can be arbitrarily large. To solve this problem, two major challenges are to be overcome. First, the concurrence of the unknown exosystem and the unknown high-frequency gain sign cannot be handled merely by designing estimators for the two unknown parameters respectively. Second, the conventional extended matching design approach cannot be directly implemented, owing to the arbitrarily large unknown parameters. To cope with these difficulties, a new estimator is developed, and the extended matching design approach is modified to obtain a suitable update law for the estimator. The effectiveness of the proposed adaptive controller is illustrated by an example.

Spatial distribution of high-frequency energy radiation on the fault of the 1995 Hyogo-Ken Nanbu, Japan, earthquake (MW 6.9) on the basis of the seismogram envelope inversion

1999 ◽  
Vol 89 (1) ◽  
pp. 22-35 ◽  
Author(s):  
Hisashi Nakahara ◽  
Haruo Sato ◽  
Masakazu Ohtake ◽  
Takeshi Nishimura
Keyword(s):  
Spatial Distribution ◽  
Wave Energy ◽  
High Frequency ◽  
Fault Plane ◽  
Time Window ◽  
Source Region ◽  
Inversion Method ◽  
S Wave ◽  
Energy Radiation ◽  
Initial Rupture

Abstract We studied the generation and propagation of high-frequency (above 1 Hz) S-wave energy from the 1995 Hyogo-Ken Nanbu (Kobe), Japan, earthquake (MW 6.9) by analyzing seismogram envelopes of the mainshock and aftershocks. We first investigated the propagation characteristics of high-frequency S-wave energy in the heterogeneous lithosphere around the source region. By applying the multiple lapse time window analysis method to aftershock records, we estimated two parameters that quantitatively characterize the heterogeneity of the medium: the total scattering coefficient and the intrinsic absorption of the medium for S waves. Observed envelopes of aftershocks were well reproduced by the envelope Green functions synthesized based on the radiative transfer theory with the obtained parameters. Next, we applied the envelope inversion method to 13 strong-motion records of the mainshock. We divided the mainshock fault plane of 49 × 21 km into 21 subfaults of 7 × 7 km square and estimated the spatial distribution of the high-frequency energy radiation on that plane. The average constant rupture velocity and the duration of energy radiation for each subfault were determined by grid searching to be 3.0 km/sec and 5.0 sec, respectively. Energy radiated from the whole fault plane was estimated as 4.9 × 1014 J for 1 to 2 Hz, 3.3 × 1014 J for 2 to 4 Hz, 1.5 × 1014 J for 4 to 8 Hz, 8.9 × 1012 J for 8 to 16 Hz, and 9.8 × 1014 J in all four frequency bands. We found that strong energy was mainly radiated from three regions on the mainshock fault plane: around the initial rupture point, near the surface at Awaji Island, and a shallow portion beneath Kobe. We interpret that energetic portions were associated with rupture acceleration, a fault surface break, and rupture termination, respectively.

Application of structural interpretation and simultaneous inversion to reservoir characterization of the Duvernay Formation, Fox Creek, Alberta, Canada

2019 ◽  
Vol 38 (2) ◽  
pp. 151-160 ◽  
Author(s):  
Ronald Weir ◽  
Don Lawton ◽  
Laurence Lines ◽  
Thomas Eyre ◽  
David Eaton
Keyword(s):  
Reservoir Characterization ◽  
Lateral Displacement ◽  
Rock Properties ◽  
S Wave ◽  
Amplitude Variation With Offset ◽  
Structural Interpretation ◽  
Simultaneous Inversion ◽  
Prestack Inversion ◽  
Unconventional Resource ◽  
Depth Relationship

Simultaneous prestack inversion of multicomponent 3D seismic data integrated with structural interpretation can provide an effective workflow to maximize value for unconventional plays. We outline an integrated workflow for characterizing the Duvernay play in western Canada, an emerging world-class low-permeability unconventional resource fairway. This workflow includes the determination of a time-depth relationship using synthetic seismograms, generation of seismic-derived time- and depth-converted structural maps, and calculation of inversion-based parameters of density and P- and S-wave velocity. The model-based procedure includes poststack (acoustic) inversion, amplitude variation with offset prestack inversion, and joint PP-PS inversion. With these rock properties determined, calculations are made to determine Young's modulus, Poisson's ratio, and brittleness. Faults are mapped based on time slices, isochrons, and correlatable vertical displacements of stratigraphic marker reflections. Significant strike-slip movements are identified by lateral displacement on interpreted geologic features, such as channels and reef edges. Seismic-derived attributes, combined with structural mapping, highlight zones that are conducive to hydraulic fracturing as well as areas unfavorable for development. Mapping of structural discontinuities provides a framework for understanding zones of preexisting weakness and induced-seismicity hazards.

scholarly journals Capturing Regional Variations of Hard‐Rock Attenuation in Europe

2019 ◽  
Vol 109 (4) ◽  
pp. 1401-1418 ◽  
Author(s):  
Marco Pilz ◽  
Fabrice Cotton ◽  
Riccardo Zaccarelli ◽  
Dino Bindi
Keyword(s):  
High Frequency ◽  
Hard Rock ◽  
Epistemic Uncertainty ◽  
Ground Motions ◽  
Soft Soil ◽  
Coda Waves ◽  
Corner Frequency ◽  
S Wave ◽  
Empirical Parameter ◽  
Regional Variations

Abstract A proper assessment of seismic reference site conditions has important applications as they represent the basis on which ground motions and amplifications are generally computed. Besides accounting for the average S‐wave velocity over the uppermost 30 m (VS30), the parameterization of high‐frequency ground motions beyond source‐corner frequency received significant attention. κ, an empirical parameter introduced by Anderson and Hough (1984), is often used to represent the spectral decay of the acceleration spectrum at high frequencies. The lack of hard‐rock records and the poor understanding of the physics of κ introduced significant epistemic uncertainty in the final seismic hazard of recent projects. Thus, determining precise and accurate regional hard‐rock κ0 values is critical. We propose an alternative procedure for capturing the reference κ0 on regional scales by linking the well‐known high‐frequency attenuation parameter κ and the properties of multiple‐scattered coda waves. Using geological and geophysical data around more than 1300 stations for separating reference and soft soil sites and based on more than 10,000 crustal earthquake recordings, we observe that κ0 from multiple‐scattered coda waves seems to be independent of the soil type but correlated with the hard‐rock κ0, showing significant regional variations across Europe. The values range between 0.004 s for northern Europe and 0.020 s for the southern and southeastern parts. On the other hand, measuring κ (and correspondingly κ0) on the S‐wave window (as classically proposed), the results are strongly affected by transmitted (reflected, refracted, and scattered) waves included in the analyzed window biasing the proper assessment of κ0. This effect is more pronounced for soft soil sites. In this way, κ0coda can serve as a proxy for the regional hard‐rock κ0 at the reference sites.

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