scholarly journals A computationally efficient elastic wave model for media with power-law absorption

Author(s):  
Bradley E. Treeby ◽  
B. T. Cox
2019 ◽  
Author(s):  
Christopher Horvat ◽  
Lettie Roach ◽  
Rachel Tilling ◽  
Cecilia Bitz ◽  
Baylor Fox-Kemper ◽  
...  

Abstract. In sea-ice-covered areas, the sea ice floe size distribution (FSD) plays an important role in many processes affecting the coupled sea-ice-ocean-atmosphere system. Observations of the FSD are spare – traditionally taken via a pain-staking analysis of ice surface photography – and the seasonal and inter-annual evolution of floe size regionally and globally is largely unknown. Frequently, measured FSDs are assessed using a single number, the scaling exponent of the closest power law fit to the observed floe size data, although in the absence of adequate datasets there have been limited tests of this power-law hypothesis. Here we derive and explain a mathematical technique for deriving statistics of the sea ice FSD from polar-orbiting altimeters, satellites with sub-daily return times to polar regions with high along-track resolutions. Applied to the CryoSat-2 radio altimetric record, covering the period from 2010–2018, and incorporating 11 million individual floe samples, we produce the first climatology and seasonal cycle of sea ice floe size statistics. We then perform the first pan-Arctic test of the power law hypothesis, finding limited support in the range of floe sizes typically analyzed in photographic observational studies. We compare the seasonal variability in observed floe size to fully coupled climate model simulations including a prognostic floe size and thickness distribution and coupled wave model, finding good agreement in regions where modeled ocean surface waves cause sea ice fracture.


2013 ◽  
Vol 2013.19 (0) ◽  
pp. 565-566
Author(s):  
Ryouta Numaguchi ◽  
Akira Chiba ◽  
Souta Matsusaka ◽  
Hirofumi Hidai ◽  
Noboru Morita

2001 ◽  
Author(s):  
Sung-Jin Song ◽  
Hyeon Jae Shin ◽  
Jeong-Rock Kwon

Abstract Flaw characterization with ultrasonic phased array technique involves to key issues, such as obtaining the high quality flaw images and determining the quantitative flaw information (such as location, type and size). This paper deals with these two key issues. For obtaining the high quality images, it is necessary to optimize the parameters of array transducers. To address such a need, a very computationally efficient radiation beam model is developed based on the boundary diffraction wave model, and the 3-D radiation beam fields from array transducers were simulated to investigate their characteristics in detail. From the sectorial images provided by the ultrasonic phased array technique, flaw size can be determined very successfully, if the type of the scatters is identified in advance. For the determination of the type of scatters, an intelligent signal interpretation scheme based on ultrasonic pattern recognition approach is studied, and the variation of features according to the steering angle is found to be a very sensitive feature for this purpose. The performance of the proposed approach is demonstrated with the initial experiments.


Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. D441-D451 ◽  
Author(s):  
Tianyang Li ◽  
Ruihe Wang ◽  
Zizhen Wang ◽  
Yuzhong Wang

Fractures greatly increase the difficulty of oil and gas exploration and development in reservoirs consisting of interlayered carbonates and shales and increase the uncertainty of highly efficient development. The presence of fractures or layered media is also widely known to affect the elastic properties of rocks. The combined effects of fractures and layered media are still unknown. We have investigated the effects of fracture structure on wave propagation in interlayered carbonate and shale rocks using physical models based on wave theory and the similarity principle. We have designed and built two sets of layered physical models with randomly embedded predesigned vertically aligned fractures according to the control variate principle. We have measured the P- and S-wave velocities and attenuation and analyzed the effects of fracture porosity and aspect ratio (AR) on velocity, attenuation, and power spectral dimension of the P- and S-waves. The experimental results indicated that under conditions of low porosity ([Formula: see text]), Han’s empirical velocity-porosity relations and Wang’s attenuation-porosity relation combined with Wyllie’s time-average model are a good prediction for layered physical models with randomly embedded fractures. When the porosity is constant, the effect of different ARs on elastic wave properties can be described by a power law function. We have calculated the power spectrum fractal dimension [Formula: see text] of the transmitted signal in the frequency domain, which can supplement the S-wave splitting method for estimating the degree of anisotropy. The simple power law relation between the power spectrum fractal dimension of the P-waveform and fracture density suggests the possible use of P-waves for discriminating fracture density. The high precision and low error of this processing method give new ideas for rock anisotropy evaluation and fracture density prediction when only P-wave data are available.


2019 ◽  
Vol 49 (2) ◽  
pp. 489-517 ◽  
Author(s):  
Qingxiang Liu ◽  
W. Erick Rogers ◽  
Alexander V. Babanin ◽  
Ian R. Young ◽  
Leonel Romero ◽  
...  

AbstractThe observation-based source terms available in the third-generation wave model WAVEWATCH III (i.e., the ST6 package for parameterizations of wind input, wave breaking, and swell dissipation terms) are recalibrated and verified against a series of academic and realistic simulations, including the fetch/duration-limited test, a Lake Michigan hindcast, and a 1-yr global hindcast. The updated ST6 not only performs well in predicting commonly used bulk wave parameters (e.g., significant wave height and wave period) but also yields a clearly improved estimation of high-frequency energy level (in terms of saturation spectrum and mean square slope). In the duration-limited test, we investigate the modeled wave spectrum in a detailed way by introducing spectral metrics for the tail and the peak of the omnidirectional wave spectrum and for the directionality of the two-dimensional frequency–direction spectrum. The omnidirectional frequency spectrum E(f) from the recalibrated ST6 shows a clear transition behavior from a power law of approximately f−4 to a power law of about f−5, comparable to previous field studies. Different solvers for nonlinear wave interactions are applied with ST6, including the Discrete Interaction Approximation (DIA), the more expensive Generalized Multiple DIA (GMD), and the very expensive exact solutions [using the Webb–Resio–Tracy method (WRT)]. The GMD-simulated E(f) is in excellent agreement with that from WRT. Nonetheless, we find the peak of E(f) modeled by the GMD and WRT appears too narrow. It is also shown that in the 1-yr global hindcast, the DIA-based model overestimates the low-frequency wave energy (wave period T > 16 s) by 90%. Such model errors are reduced significantly by the GMD to ~20%.


Author(s):  
Sven Näsholm ◽  
Sverre Holm

AbstractThis survey concerns a causal elastic wave equation which implies frequency power-law attenuation. The wave equation can be derived from a fractional Zener stress-strain relation plus linearized conservation of mass and momentum. A connection between this four-parameter fractional wave equation and a physically well established multiple relaxation acoustical wave equation is reviewed. The fractional Zener wave equation implies three distinct attenuation power-law regimes and a continuous distribution of compressibility contributions which also has power-law regimes. Furthermore it is underlined that these wave equation considerations are tightly connected to the representation of the fractional Zener stress-strain relation, which includes the spring-pot viscoelastic element, and by a Maxwell-Wiechert model of conventional springs and dashpots. A purpose of the paper is to make available recently published results on fractional calculus modeling in the field of acoustics and elastography, with special focus on medical applications.


Soft Matter ◽  
2020 ◽  
Vol 16 (33) ◽  
pp. 7797-7807 ◽  
Author(s):  
Bingyu Cui ◽  
Alessio Zaccone

A tensorial replica-field theory is developed to solve the elastic wave scattering problem in amorphous solids, which leads to the logarithmic correction to the Rayleigh scattering law.


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