scholarly journals The relationships between large-scale variations in shear velocity, density, and compressional velocity in the Earth's mantle

2016 ◽  
Vol 121 (4) ◽  
pp. 2737-2771 ◽  
Author(s):  
P. Moulik ◽  
G. Ekström
Keyword(s):  
Large Scale ◽  
Shear Velocity ◽  
Earth’S Mantle ◽  
Compressional Velocity

scholarly journals Effective buoyancy ratio: a new parameter to characterize thermo-chemical mixing in the Earth's mantle

2014 ◽  
Vol 6 (2) ◽  
pp. 2675-2697
Author(s):  
A. Galsa ◽  
M. Herein ◽  
L. Lenkey ◽  
M. P. Farkas ◽  
G. Taller
Keyword(s):  
Mixing Time ◽  
Initial Density ◽  
Shear Velocity ◽  
Dense Layer ◽  
Earth’S Mantle ◽  
A Value ◽  
Short Time ◽  
Chemical Mixing ◽  
Buoyancy Ratio ◽  
Low Shear

Abstract. Numerical modeling has been carried out in a 2-D cylindrical shell domain to quantify the evolution of a primordial dense layer around the core mantle boundary. Effective buoyancy ratio, Beff was introduced to characterize the evolution of the two-layer thermo-chemical convection in the Earth's mantle. Beff decreases with time due to (1) warming the compositionally dense layer, (2) cooling the overlying mantle, (3) eroding the dense layer by thermal convection in the overlying mantle, and (4) diluting the dense layer by inner convection. When Beff reaches the instability point, Beff = 1, effective thermo-chemical convection starts, and the mantle will be mixed (Beff = 0) during a short time. A parabolic relation was revealed between the initial density difference of the layers and the mixing time. Morphology of large low shear velocity provinces as well as results from seismic tomography and normal mode data suggest a value of Beff ≥ 1 for the mantle.

The large-scale structure of convection in the Earth's mantle

Nature ◽  
1990 ◽  
Vol 344 (6263) ◽  
pp. 209-215 ◽  
Author(s):  
Peter Olson ◽  
Paul G. Silver ◽  
Richard W. Carlson
Keyword(s):  
Large Scale ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Earth’S Mantle

Finite amplitude convective cells and continental drift

1967 ◽  
Vol 28 (1) ◽  
pp. 29-42 ◽  
Author(s):  
D. L. Turcotte ◽  
E. R. Oxburgh
Keyword(s):  
Rayleigh Number ◽  
Large Scale ◽  
Continental Drift ◽  
Finite Amplitude ◽  
Thermal Plumes ◽  
The Core ◽  
Earth’S Mantle ◽  
Convective Cells ◽  
Dimensional Cell ◽  
Good Agreement

A solution is obtained for steady, cellular convection when the Rayleigh number and the Prandtl number are large. The core of each two-dimensional cell contains a highly viscous, isothermal flow. Adjacent to the horizontal boundaries are thin thermal boundary layers. On the vertical boundaries between cells thin thermal plumes drive the viscous flow. The non-dimensional velocities and heat transfer between the horizontal boundaries are found to be functions only of the Rayleigh number. The theory is used to test the hypothesis of large scale convective cells in the earth's mantle. Using accepted values of the Rayleigh number for the earth's mantle the theory predicts the generally accepted velocity associated with continental drift. The theory also predicts values for the heat flux to the earth's surface which are in good agreement with measurements carried out on the ocean floors.

Ambiguities in AVO inversion of reflections from a gas‐sand

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 134-141 ◽  
Author(s):  
Giuseppe Drufuca ◽  
Alfredo Mazzotti
Keyword(s):  
Unique Solution ◽  
Incidence Angle ◽  
Synthetic Data ◽  
Real Data ◽  
Shear Velocity ◽  
Sand Layer ◽  
Borehole Data ◽  
Starting Point ◽  
Wide Range ◽  
Compressional Velocity

We examine the reflections from a thick sand layer embedded in shales deposited in an open marine environment of Miocene age. Borehole data indicate that the sand bed is gas saturated. Making the assumptions of single interface reflections, plane‐wave propagation in elastic and isotropic media, and correct amplitude recovery of the actual seismic data, we try to invert the amplitude variation with offset (AVO) response for the compressional velocity [Formula: see text], shear velocity [Formula: see text], and density [Formula: see text] of the gas‐sand layer, knowing the parameters of the upper layer and the calibration constant. The actual reflections reach incidence angles up to 54 degrees at the farthest offset. Notwithstanding the large range of incidence angles, the outcomes of the inversion are ambiguous for we find many solutions that fit equally well, in a least‐squares sense, the observed AVO response. We present the locus of the solutions as curves in compressional velocity [Formula: see text], shear velocity [Formula: see text], and density [Formula: see text] space. To gain a better understanding of the results, we also perform the same inversion experiment on synthetic AVO data derived from the borehole information. We find that when inverting the AVO response in the same range of incidence angles as in the real data case, the exact solution is found whichever starting point we choose; that is, we have no ambiguity. However, if we limit the incidence angle range, e.g., to 15 degrees, the invention is no longer able to find a unique solution and the set of admissible solutions defines regular curves in [Formula: see text], [Formula: see text], [Formula: see text] space. We infer that residual noise in the recorded data is responsible for the ambiguities of the solutions, and that because of numerical noise, a wide range of incidence angle is required to obtain a unique solution even in noise‐free synthetic data.

Vortex-Excited Response of Large-Scale Cylinders in Sheared Flow

1988 ◽  
Vol 110 (3) ◽  
pp. 272-277 ◽  
Author(s):  
J. A. Humphries ◽  
D. H. Walker
Keyword(s):  
Large Scale ◽  
Shear Velocity ◽  
Reynolds Numbers ◽  
Hydrodynamic Drag ◽  
Flow Induced Vibration ◽  
Sheared Flow ◽  
Drag Forces ◽  
Linear Shear ◽  
Series Of Experiments ◽  
The Mean

A series of experiments were performed to measure the vortex-excited response of a 0.168-m-dia slender circular cylinder in a range of linear shear velocity profiles. Reynolds numbers of up to 2.5 × 105 were achieved. The results clearly showed that regular large-amplitude cylinder vibrations occurred well within the critical drag transition region. It was found that increasing the linear shear profile decreased the peak amplitude response but broadened the range of lock-on over which large oscillations occurred. The flow-induced vibration of the cylinder caused amplification of the mean hydrodynamic drag forces acting on the cylinder when compared with those expected for a similar rigid cylinder.

Shear velocity logging in slow formations using the Stoneley wave

Geophysics ◽  
1986 ◽  
Vol 51 (1) ◽  
pp. 137-147 ◽  
Author(s):  
Jeffry L. Stevens ◽  
Steven M. Day
Keyword(s):  
Error Estimates ◽  
Shear Velocity ◽  
Low Noise ◽  
Head Wave ◽  
Inversion Method ◽  
Stoneley Wave ◽  
Fluid Viscosity ◽  
High Quality ◽  
Stoneley Waves ◽  
Compressional Velocity

We apply an iterative, linearized inversion method to Stoneley waves recorded on acoustic logs in a borehole. Our objective is to assess inversion of Stoneley wave phase and group velocity as a practical technique for shear velocity logging in slow formations. Indirect techniques for shear logging are of particular importance in this case because there is no shear head wave arrival. Acoustic logs from a long‐spaced sonic tool provided high‐quality, low‐noise data in the 1 to 10 kHz band for this experiment. A shear velocity profile estimated by inversion of a 60 ft (18 ⋅ 3 m) section of full‐wave acoustic data correlates well with the P‐wave log for the section. The inferred shear velocity ranges from 60 to 90 percent of the sound velocity of the fluid. Formal error estimates on the shear velocity are everywhere less than 5 percent. Moreover, application of the same inversion method to synthetic waveforms corroborates these error estimates. Finally, a synthetic acoustic waveform computed from inversion results is an excellent match to the observed waveform. On the basis of these results, we conclude that Stoneley‐wave inversion constitutes a practical, indirect, shear‐logging technique for slow formations. Success of the shear‐logging method depends upon availability of high‐quality, low‐noise waveform data in the 1 to 4 kHz band. Given good prior estimates of compressional velocity and density of the borehole fluid, only rough estimates of borehole radius and formation density and compressional velocity are required. The existing inversion procedure also yields estimates of formation Q inferred from spectral amplitudes of Stoneley waves. This extension of the method is promising, since amplitudes of Stoneley waves in a slow formation are highly sensitive to formation Q. Attenuation caused by formation Q dominates over attenuation caused by fluid viscosity if the viscosity is less than about [Formula: see text]. However, Stoneley‐wave amplitudes are also sensitive to gradients in shear velocity in the direction of propagation. In some cases, correction for the effects of shear‐velocity gradients is required to obtain the formation Q from Stoneley‐wave attenuation.

scholarly journals Lunar-forming impacts: processes and alternatives

2014 ◽  
Vol 372 (2024) ◽  
pp. 20130175 ◽  
Author(s):  
R. M. Canup
Keyword(s):  
Angular Momentum ◽  
Large Scale ◽  
Early Earth ◽  
The Sun ◽  
Initial Composition ◽  
High Angular Momentum ◽  
Giant Impact ◽  
Earth’S Mantle ◽  
Momentum Loss ◽  
Angular Momentum Loss

The formation of a protolunar disc by a giant impact with the early Earth is discussed, focusing on two classes of impacts: (i) canonical impacts, in which a Mars-sized impactor produces a planet–disc system whose angular momentum is comparable to that in the current Earth and Moon, and (ii) high-angular-momentum impacts, which produce a system whose angular momentum is approximately a factor of 2 larger than that in the current Earth and Moon. In (i), the disc originates primarily from impactor-derived material and thus is expected to have an initial composition distinct from that of the Earth's mantle. In (ii), a hotter, more compact initial disc is produced with a silicate composition that can be nearly identical to that of the silicate Earth. Both scenarios require subsequent processes for consistency with the current Earth and Moon: disc–planet compositional equilibration in the case of (i), or large-scale angular momentum loss during capture of the newly formed Moon into the evection resonance with the Sun in the case of (ii).

Sequential Measurement of Compressional and Shear Velocities of Rock Samples Under Triaxial Pressure

1969 ◽  
Vol 9 (04) ◽  
pp. 378-394 ◽  
Author(s):  
K.P. Desai ◽  
D.P. Helander
Keyword(s):  
Acoustic Wave ◽  
Resonant Frequency ◽  
Wave Velocity ◽  
Resonance Method ◽  
Shear Velocity ◽  
Berea Sandstone ◽  
Rock Samples ◽  
Wave Velocities ◽  
Compressional Velocity ◽  
Wave Properties

Abstract A laboratory measuring system was designed that can precisely and sequential measure both compressional and shear velocities of rock samples under identical conditions of stress distribution and stress history. This is required if accurate and realistic dynamic elastic properties of rocks are to be determined. The hysteresis effect on velocity pressure characteristics of rock was determined to pressure characteristics of rock was determined to illustrate this point. Lead titanate zirconate transducers were used for measuring compressional wave velocity, and AC-cut quartz transducers were used for measuring shear wave velocity. The system was tested using samples of standard material such as aluminum, steel, brass and lucite. Measurements obtained were accurate within 1 percent. percent. Compressional and shear velocities were measured sequentially on 10 samples of Berea sandstone and two samples of Bartlesville sandstone. It was found that 1. Both compressional and shear velocities increased with an increase in applied external pressure. pressure. 2. Compressional velocity depends upon both external (Pe) and internal (Pi) pressure. 3. Shear velocity depends only upon the differential pressure (Pne-Pe-Pi). 4. The nature of the fluid saturant had little effect on compressional velocity. 5. Shear velocity decreased with an increase in the density of the saturant. 6. The Berea sandstone indicated very little anisotropy. 7. The Bartlesville sandstone showed definite anisotropy. Introduction The various properties of an acoustic wave trainvelocity, amplitude, frequency, etc. may be modified, sometimes quite severely by the media through which the wave has traveled. This suggests the use of wave properties to determine, at least in part, the nature of the material through which the part, the nature of the material through which the wave has passed. To accomplish this successfully requires a reliable technique to for obtaining accurate values of all acoustic wave properties. One purpose of this paper is to describe a recently developed system that can precisely and sequentially record acoustic compressional and shear energies as functions both of time and of frequency. One example of the utility of this system is the accurate measurement of compressional and shear velocities through rock samples subjected to triaxial, i.e., simultaneous but independent vertical, circumferential and pore pressure. Since acoustic velocity and elasticity are closely interrelated, such a system would help to determine realistically the elastic properties of rock samples in the laboratory. METHODS FOR THE INDEPENDENT MEASUREMENT OF COMPRESSIONAL AND SHEAR WAVE VELOCITIES Currently there are two suitable nondestructive laboratory techniques for measuring wave velocity through a rock sample under pressure. One is by the resonance method and the other is by the pulse technique. In the resonance method a sample, in the form of a thin wire, rod, or plate, is make to vibrate in the longitudinal, torsional or flexural mode. Resonant frequency is determined by recording the amplitude of vibration as a function of applied frequency; the amplitude is maximum at resonant frequency. For isotropic materials the relationships between resonance frequencies, elastic moduli and acoustic wave velocities are well known. SPEJ p. 378

scholarly journals Effective buoyancy ratio: a new parameter for characterizing thermo-chemical mixing in the Earth's mantle

Solid Earth ◽  
2015 ◽  
Vol 6 (1) ◽  
pp. 93-102 ◽  
Author(s):  
A. Galsa ◽  
M. Herein ◽  
L. Lenkey ◽  
M. P. Farkas ◽  
G. Taller
Keyword(s):  
Mixing Time ◽  
Initial Density ◽  
Shear Velocity ◽  
Dense Layer ◽  
Earth’S Mantle ◽  
A Value ◽  
Time Period ◽  
Short Time ◽  
Chemical Mixing ◽  
Buoyancy Ratio

Abstract. Numerical modeling has been carried out in a 2-D cylindrical shell domain to quantify the evolution of a primordial dense layer around the core–mantle boundary. Effective buoyancy ratio, Beff was introduced to characterize the evolution of the two-layer thermo-chemical convection in the Earth's mantle. Beff decreases with time due to (1) warming of the compositionally dense layer, (2) cooling of the overlying mantle, (3) eroding of the dense layer through thermal convection in the overlying mantle and (4) diluting of the dense layer through inner convection. When Beff reaches the instability point, Beff = 1, effective thermo-chemical convection starts, and the mantle will be mixed (Beff = 0) over a short time period. A parabolic relationship was revealed between the initial density difference of the layers and the mixing time. Morphology of large low-shear-velocity provinces and results from seismic tomography and normal mode data suggest a value of Beff ≥ 1 for the mantle.

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