Quasi-solitary multiscale cross-diffusion waves as a precursor to Earth instabilities

2021 ◽  
Author(s):  
Klaus Regenauer-Lieb ◽  
Manman Hu ◽  
Qinpei Sun ◽  
Christoph Schrank
Keyword(s):  
Wave Energy ◽  
Fluid Pressure ◽  
Reaction Diffusion ◽  
High Energy ◽  
P Wave ◽  
S Wave ◽  
Cross Diffusion ◽  
Diffusion Waves ◽  
The Cross ◽  
Meso Scale

<p>We propose a mesoscopic thermodynamics approach for coupling multiphysics processes across scales in porous or multiphase media. In this multiscale reaction-diffusion formalism interactions of discrete phenomena at the local scale are seen as being subject to a larger scale Thermo-Hydro-Mechano-Chemical (THMC) thermodynamic force. When local interactions are incompatible with the large-scale thermodynamic stress field incompatibilities can arise which trigger accelerations resulting in meso-scale generalized thermodynamic fluxes of another (THMC) kind. The classical acoustic tensor localization criterion in plasticity theory is here understood as a standing wave solution of such acceleration waves. These classical zero-speed acceleration wave solutions are solitary waves, also known as solitons, and are interpreted in the reaction-diffusion formalism as self-diffusion dominated by harvesting all available energy from the cross-diffusional tails.</p><p>The more general case of non-zero traveling wave speed solutions is related to the cross-diffusion coefficients between different macro- and meso-scale thermodynamic THMC forces and fluxes. These cross-diffusion terms in the 4 x 4 THMC diffusion matrix are shown to lead to multiple diffusional P- and S-wave equations as THMC coupled, time-resolved dynamic solutions of the equation of motion. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves also known as cross-diffusion waves or quasi-solitons. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a soliton wave focus.</p><p>Mathematically these solutions can be compared to events in ocean waves and optical fibers known as 'rogue waves' or 'high energy pulses of light' in lasers. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike on the future fault plane. This hydromechanically coupled fluid pressure P-wave instability is here interpreted as a trigger for the S-wave seismic moment release of a double couple dominated earthquake event. The proposed multiscale cascade of wave energy may apply to many other material instabilities.</p><p> </p><p> </p>

scholarly journals Cross-Diffusion Waves as a trigger for Multiscale, Multi-Physics Instabilities: Theory

2020 ◽  
Author(s):  
Klaus Regenauer-Lieb ◽  
Manman Hu ◽  
Christoph Schrank ◽  
Xiao Chen ◽  
Santiago Peña Clavijo ◽  
...  
Keyword(s):  
Wave Equations ◽  
Reaction Cross ◽  
S Wave ◽  
Cross Diffusion ◽  
Diffusion Waves ◽  
Complex Interactions ◽  
Time Space ◽  
Acceleration Waves ◽  
Non Local ◽  
Meso Scale

Abstract. We propose a non-local, meso-scale approach for coupling multiphysics processes across scale. The physics is based on discrete phenomena, triggered by local Thermo-Hydro-Mechano-Chemical (THMC) instabilities, that cause cross-diffusion (quasi-soliton) acceleration waves. These waves nucleate when the overall stress field is incompatible with accelerations from local feedbacks of generalized THMC thermodynamic forces that trigger generalized thermodynamic fluxes of another kind. Cross-diffusion terms in the 4 × 4 THMC diffusion matrix are shown to lead to multiple diffusional P- and S-wave equations as coupled THMC solutions. Uncertainties in the location of meso-scale material instabilities are captured by a wave-scale correlation of probability amplitudes. Cross-diffusional waves have unusual dispersion patterns and, although they assume a solitary state, do not behave like solitons but show complex interactions when they collide. Their characteristic wavenumber and constant speed define mesoscopic internal material time-space relations entirely defined by the coefficients of the coupled THMC reaction-cross-diffusion equations. For extreme conditions, cross-diffusion waves can lead to an energy cascade connecting large and small-scales and cause solid-state turbulence.

scholarly journals The Interaction of Neutrons with 7Be at BBN Temperatures: Lack of Standard Nuclear Solution to the “Primordial 7Li Problem”

2020 ◽  
Vol 227 ◽  
pp. 01007 ◽  
Author(s):  
M. Gai ◽  
E.E. Kading ◽  
M. Hass ◽  
K.M. Nollett ◽  
S.R. Stern ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
High Energy ◽  
Big Bang ◽  
Alpha Particles ◽  
P Wave ◽  
Recent Measurement ◽  
S Wave ◽  
Big Bang Nucleosynthesis ◽  
The Cross

We report the first measurement of alpha-particles from the interaction of neutrons with 7Be at “temperatures” of Big Bang Nucleosynthesis (BBN). We measured the Maxwellian averaged cross sections (MACS), with neutron beams produced by the LiLiT at the SARAF in Israel (with kT = 49.5 keV hence 0.57 GK). In addition, we measured the cross section of the 7Be(n,p) reaction, which is in excellent agreement with the recent measurement of the n_TOF collaboration, further substantiating our method as a demonstration of “proof of principle”. The cross section for the 7Be(n,ga) and the 7Be(n,a) reaction measured in the “BBN window” is considerably smaller than compiled by Wagoner in 1969 and used today in Big Bang Nucleosynthesis (BBN). We also rule out a hitherto unknown resonance in 8Be at the BBN window, that was conjectured as a possible standard nuclear physics solution to the “Primordial 7Li Problem”. Together with previous results, we deduce a new Wagoner-like Rate for the destruction of 7Be by neutrons which is based on all current measured data. We conclude the lack of a standard nuclear solution to the “Primordial 7Li Problem”. Our upper limit on the cross sections for the high energy alpha-particles is in agreement with recent measurement of the n_TOF collaboration, but it is considerably smaller than the p-wave extrapolation of the Kyoto collaboration. We measured the alpha-particles from the 7Be(n,gi)8Be*(3.03 MeV) reaction, which is considerably larger than a previous s-wave estimate. Hence, in contrast, we conclude s-wave dominance at BBN energies, as would be expected due to the broad (122 keV) low lying 2” state at En = 10 keV.

scholarly journals Cross-diffusion waves resulting from multiscale, multiphysics instabilities: application to earthquakes

Solid Earth ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 1829-1849
Author(s):  
Klaus Regenauer-Lieb ◽  
Manman Hu ◽  
Christoph Schrank ◽  
Xiao Chen ◽  
Santiago Peña Clavijo ◽  
...  
Keyword(s):  
Wave Energy ◽  
Ocean Waves ◽  
High Energy ◽  
Reaction Diffusion Equations ◽  
Shear Instability ◽  
Small Scale ◽  
Cross Diffusion ◽  
New Class ◽  
Diffusion Waves ◽  
Theoretical Approaches

Abstract. Theoretical approaches to earthquake instabilities propose shear-dominated source mechanisms. Here we take a fresh look at the role of possible volumetric instabilities preceding a shear instability. We investigate the phenomena that may prepare earthquake instabilities using the coupling of thermo-hydro-mechano-chemical reaction–diffusion equations in a THMC diffusion matrix. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves known as cross-diffusion or quasi-soliton waves. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a stationary wave focus from large to small scale. We show that the rich solution space of the reaction–cross-diffusion approach to earthquake instabilities can recover classical Turing instabilities (periodic in space instabilities), Hopf bifurcations (spring-slider-like earthquake models), and a new class of quasi-soliton waves. Only the quasi-soliton waves can lead to extreme focussing of the wave energy into short-wavelength instabilities of short duration. The equivalent extreme event in ocean waves and optical fibres leads to the appearance of “rogue waves” and high energy pulses of light in photonics. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike. This spike is likely to cause unstable slip on a pre-existing (near-critically stressed) fault acting as a trigger for the ultimate (shear) seismic moment release.

scholarly journals Cross-Diffusion Waves as a trigger for multiscale, multiphysics Instabilities: Application to earthquakes

2020 ◽  
Author(s):  
Klaus Regenauer-Lieb ◽  
Manman Hu ◽  
Christoph Schrank ◽  
Xiao Chen ◽  
Santiago Peña Clavijo ◽  
...  
Keyword(s):  
Fluid Pressure ◽  
Ocean Waves ◽  
High Energy ◽  
Reaction Diffusion Equations ◽  
Shear Instability ◽  
Critical Conditions ◽  
Small Scale ◽  
Cross Diffusion ◽  
Diffusion Waves ◽  
Theoretical Approaches

Abstract. Theoretical approaches to earthquake instabilities propose shear-dominated instabilities as a source mechanism. Here we take a fresh look at the role of possible volumetric instabilities preceding a shear instability. We investigate the phenomena that may prepare earthquake instabilities using the coupling of Thermo-Hydro-Mechano-Chemical reaction-diffusion equations in a THMC diffusion matrix. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves known as cross-diffusion waves. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a quasi-stationary wave focus from large to small-scale. The equivalent extreme event in ocean waves and optical fibres leads to the appearance of rogue waves and high energy pulses of light in lasers. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike on the future fault plane. This is here interpreted as a trigger for the ultimate (shear) seismic moment release.

scholarly journals Discussion on the Theoretical Basis for Cross-Over Method Applied to Downhole Wave Velocity Test

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Qing Dong ◽  
Zheng-hua Zhou ◽  
Su Jie ◽  
Bing Hao ◽  
Yuan-dong Li
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Wave Velocity ◽  
Theoretical Basis ◽  
Influence Factors ◽  
P Wave ◽  
Engineering Practice ◽  
S Wave ◽  
Simulation Results ◽  
The Cross

At engineering practice, the theoretical basis for the cross-over method, used to obtain shear wave arrival time in the downhole method of the wave velocity test by surface forward and backward strike, is that the polarity of P-wave keeps the same, while the polarity of S-wave transforms when the direction of strike inverted. However, the characteristics of signals recorded in tests are often found to conflict with this theoretical basis for the cross-over method, namely, the polarity of the P-wave also transforms under the action of surface forward and backward strike. Therefore, 3D finite element numerical simulations were conducted to study the validity of the theoretical basis for the cross-over method. The results show that both shear and compression waves are observed to be in 180° phase difference between horizontal signal traces, consistent with the direction of excitation generated by reversed impulse. Furthermore, numerical simulation results prove to be reliable by the analytic solution; it shows that the theoretical basis for the cross-over method applied to the downhole wave velocity test is improper. In meanwhile, numerical simulations reveal the factors (inclining excitation, geophone deflection, inclination, and background noise) that may cause the polarity of the P-wave not to reverse under surface forward and backward strike. Then, as to reduce the influence factors, we propose a method for the downhole wave velocity test under surface strike, the time difference of arrival is based between source peak and response peak, and numerical simulation results show that the S-wave velocity by this method is close to the theoretical S-wave velocity of soil.

Joint microseismic event location and anisotropic velocity inversion with the cross double-difference method using downhole microseismic data

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. KS63-KS73
Author(s):  
Yangyang Ma ◽  
Congcong Yuan ◽  
Jie Zhang
Keyword(s):  
Arrival Time ◽  
Velocity Model ◽  
P Wave ◽  
Double Difference ◽  
S Wave ◽  
Arrival Times ◽  
Monitoring Well ◽  
The Cross ◽  
Microseismic Event ◽  
Wave Arrival

We have applied the cross double-difference (CDD) method to simultaneously determine the microseismic event locations and five Thomsen parameters in vertically layered transversely isotropic media using data from a single vertical monitoring well. Different from the double-difference (DD) method, the CDD method uses the cross-traveltime difference between the S-wave arrival time of one event and the P-wave arrival time of another event. The CDD method can improve the accuracy of the absolute locations and maintain the accuracy of the relative locations because it contains more absolute information than the DD method. We calculate the arrival times of the qP, qSV, and SH waves with a horizontal slowness shooting algorithm. The sensitivities of the arrival times with respect to the five Thomsen parameters are derived using the slowness components. The derivations are analytical, without any weak anisotropic approximation. The input data include the cross-differential traveltimes and absolute arrival times, providing better constraints on the anisotropic parameters and event locations. The synthetic example indicates that the method can produce better event locations and anisotropic velocity model. We apply this method to the field data set acquired from a single vertical monitoring well during a hydraulic fracturing process. We further validate the anisotropic velocity model and microseismic event locations by comparing the modeled and observed waveforms. The observed S-wave splitting also supports the inverted anisotropic results.

Mode Conversion Technique Employed in Shear Wave Velocity Studies of Rock Samples Under Axial and Uniform Compression

1967 ◽  
Vol 7 (02) ◽  
pp. 136-148 ◽  
Author(s):  
A.R. Gregory
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Wave Energy ◽  
Pressure Range ◽  
Mode Conversion ◽  
P Wave ◽  
S Wave ◽  
Rock Samples ◽  
Mode Converters

Abstract A shear wave velocity laboratory apparatus and techniques for testing rock samples under simulated subsurface conditions have been developed. In the apparatus, two electromechanical transducers operating in the frequency range 0.5 to 5.0 megahertz (MHz: megacycles per second) are mounted in contact with each end of the sample. Liquid-solid interfaces of Drakeol-aluminum are used as mode converters. In the generator transducer, there is total mode conversion from P-wave energy to plain S-wave energy, S-wave energy is converted back to P-wave energy in the motor transducer. Similar transducers without mode converters are used to measure P-wave velocities. The apparatus is designed for testing rock samples under axial or uniform loading in the pressure range 0 to 12,000 psi. The transducers have certain advantages over those used by King,1 and the measurement techniques are influenced less by subjective elements than other methods previously reported. An electronic counter-timer having a resolution of 10 nanoseconds measures the transit time of ultrasonic pulses through the sample; elastic wave velocities of most homogeneous materials can be measured with errors of less than 1 percent. S- and P-wave velocity measurements on Bandera sandstone and Solenhofen limestone are reported for the axial pressure range 0 to 6,000 psi and for the uniform pressure range 0 to 10,000 psi. The influence of liquid pore saturants on P- and S-wave velocity is investigated and found to be in broad agreement with Biot's theory. In specific areas, the measurements do not conform to theory. Velocities of samples measured under axial and uniform loading are compared and, in general, velocities measured under uniform stress are higher than those measured under axial stress. Liquid pore fluids cause increases in Poisson's ratio and the bulk modulus but reduce the rigidity modulus, Young's modulus and the bulk compressibility. INTRODUCTION Ultrasonic pulse methods for measuring the shear wave velocity of rock samples in the laboratory have been gradually improved during the last few years. Early experimental pulse techniques reported by Hughes et al.2, and by Gregory3 were beset by uncertainties in determining the first arrival of the shear wave (S-wave) energy. Much of this ambiguity was caused by the multiple modes propagated by piezoelectric crystals and by boundary conversions in the rock specimens. Shear wave velocity data obtained from the critical angle method, described by Schneider and Burton4 and used later by King and Fatt5 and by Gregory,3,6 are of limited accuracy, and interpreting results is too complicated for routine laboratory work. The mode conversion method described by Jamieson and Hoskins7 was recently used by King1 for measuring the S-wave velocities of dry and liquid-saturated rock samples. Glass-air interfaces acted as mode converters in the apparatus, and much of the compressional (P-wave) energy apparently was eliminated from the desired pure shear mode. A more detailed discussion of the current status of laboratory pulse methods applied to geological specimens is given in a review by Simmons.8

scholarly journals Downhole distributed acoustic seismic profiling at Skytrain Ice Rise, West Antarctica

2021 ◽  
Author(s):  
Alex Brisbourne ◽  
Mike Kendall ◽  
Sofia Kufner ◽  
Thomas Hudson ◽  
Andrew Smith
Keyword(s):  
Wave Energy ◽  
Drilling Fluid ◽  
Ice Sheet ◽  
Seismic Profile ◽  
Seismic Attenuation ◽  
Weddell Sea ◽  
P Wave ◽  
West Antarctica ◽  
S Wave ◽  
Ice Flow

<p>Antarctic ice sheet history is imprinted in the structure and fabric of the ice column. At ice rises, the signature of ice flow history is preserved due to the low strain rates inherent at these independent ice flow centres. We present results from a distributed acoustic sensing (DAS) experiment at Skytrain Ice Rise in the Weddell Sea Sector of West Antarctica, aimed at delineating the englacial fabric to improve our understanding of ice sheet history in the region. This pilot experiment demonstrates the feasibility of an innovative technique to delineate ice rise structure. Both direct and reflected P- and S-wave energy, as well as surface wave energy, are observed using a range of source offsets, i.e., a walkaway vertical seismic profile (VSP), recorded using fibre optic cable. Significant noise, which results from the cable hanging untethered in the borehole, is modelled and suppressed at the processing stage. At greater depth, where the cable is suspended in drilling fluid, seismic interval velocities and attenuation are measured. Vertical P-wave velocities are high (V<sub>INT</sub> = 4029 ± 244 m s<sup>-1</sup>) and consistent with a strong vertical cluster fabric. Seismic attenuation is high (Q<sub>INT </sub>= 75 ± 12) and contrary to observations in ice sheets over this temperature range. The signal level is too low, and the noise level too high, to undertake analysis of englacial fabric variability. However, modelling of P- and S-wave traveltimes and amplitudes with a range of fabric geometries, combined with these measurements, demonstrates the capacity of the DAS method to discriminate englacial fabric distribution. From this pilot study we make a number of recommendations for future experiments aimed at quantifying englacial fabric to improve our understanding of recent ice sheet history.</p><p> </p>

The partition of radiated energy between P and S waves

1984 ◽  
Vol 74 (2) ◽  
pp. 361-376
Author(s):  
John Boatwright ◽  
Jon B. Fletcher
Keyword(s):  
Wave Energy ◽  
Body Wave ◽  
Focal Mechanisms ◽  
The Body ◽  
Body Waves ◽  
P Wave ◽  
Corner Frequency ◽  
S Wave ◽  
S Waves ◽  
Radiated Energy

Abstract Seventy-three digitally recorded body waves from nine multiply recorded small earthquakes in Monticello, South Carolina, are analyzed to estimate the energy radiated in P and S waves. Assuming Qα = Qβ = 300, the body-wave spectra are corrected for attenuation in the frequency domain, and the velocity power spectra are integrated over frequency to estimate the radiated energy flux. Focal mechanisms determined for the events by fitting the observed displacement pulse areas are used to correct for the radiation patterns. Averaging the results from the nine events gives 27.3 ± 3.3 for the ratio of the S-wave energy to the P-wave energy using 0.5 〈Fi〉 as a lower bound for the radiation pattern corrections, and 23.7 ± 3.0 using no correction for the focal mechanisms. The average shift between the P-wave corner frequency and the S-wave corner frequency, 1.24 ± 0.22, gives the ratio 13.7 ± 7.3. The substantially higher values obtained from the integral technique implies that the P waves in this data set are depleted in energy relative to the S waves. Cursory inspection of the body-wave arrivals suggests that this enervation results from an anomalous site response at two of the stations. Using the ratio of the P-wave moments to the S-wave moments to correct the two integral estimates gives 16.7 and 14.4 for the ratio of the S-wave energy to the P-wave energy.

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