The calibration of the elastic characteristics of deformed coals is essential for seismic inversion of such units, because the prediction of coal deformation is essential for both mining safety and methane production....The calibration of the elastic characteristics of deformed coals is essential for seismic inversion of such units, because the prediction of coal deformation is essential for both mining safety and methane production. Therefore, many samples of broken and mylonitic deformed coal were tested with ultrasonic waves in the laboratory. These samples came from four mining areas: the Huainan, Pingdingshan, Hebi and Jiaozuo coal mines, which present five different metamorphic ranks shown as cylinders striking across circular limits of steel. Under normal pressures and temperatures, ultrasonic P- and S-wave tests show that the velocities, quality factors, and elastic moduli of the deformed coals were greatly reduced compared with undeformed coals. Also, some correlation was found between the P- and S-wave velocities in the deformed coals. However, there is no evidence of linear correlations between velocity and density, velocity and quality factor, or the quality factors of P- and S-waves. Compared with the elastic characteristics of undeformed coals, such as P- and S-wave velocity ratios or Poisson's ratio, those of deformed coals generally decrease and the P-wave quality factors are less than those of S-waves. Moreover, the analysis of the relationship between pore structure and elastic modulus shows a better correlation between the P- and S-wave velocities and effective porosity, pore volume and specific surface area. Also, there are similar relationships between the pore structure and the Young's and shear moduli. However, there are no such correlations with other moduli. Correlations between these elastic moduli, pore structure, coal rank and density were not found for the various samples of deformed coals, which is consistent with only structural destruction occurring in the deformed coals with other physical properties remaining unchanged. The experimental results show that it is possible to predict the deformation of coals with multi-component seismic elastic inversion.展开更多
In this paper, we study an important class of (α,β)-metrics in the form F = (α + β)m+1/αm on an n-dimensional manifold and get the conditions for such metrics to be weakly-Berwald metrics, where α = aij(x)yiyj i...In this paper, we study an important class of (α,β)-metrics in the form F = (α + β)m+1/αm on an n-dimensional manifold and get the conditions for such metrics to be weakly-Berwald metrics, where α = aij(x)yiyj is a Riemannian metric and β = bi(x)yi is a 1-form and m is a real number with m = 1,0,1/n. Furthermore, we also prove that this kind of (α,β)-metrics is of isotropic mean Berwald curvature if and only if it is of isotropic S-curvature. In this case, S-curvature vanishes and the metric is weakly-Berwald metric.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 41172145, 41372163 and 41104084)National Basic Research Program of China (Grant No. 2014CB440905)+1 种基金National Special Fund of China (Grant Nos. 2011ZX05: 035-001-006HZ and 035-002-003HZ, 008-006-22, 049-01-02 and 019-003)PetroChina Innovation Foundation (Grant No. 2011D-5006-0303)
文摘The calibration of the elastic characteristics of deformed coals is essential for seismic inversion of such units, because the prediction of coal deformation is essential for both mining safety and methane production. Therefore, many samples of broken and mylonitic deformed coal were tested with ultrasonic waves in the laboratory. These samples came from four mining areas: the Huainan, Pingdingshan, Hebi and Jiaozuo coal mines, which present five different metamorphic ranks shown as cylinders striking across circular limits of steel. Under normal pressures and temperatures, ultrasonic P- and S-wave tests show that the velocities, quality factors, and elastic moduli of the deformed coals were greatly reduced compared with undeformed coals. Also, some correlation was found between the P- and S-wave velocities in the deformed coals. However, there is no evidence of linear correlations between velocity and density, velocity and quality factor, or the quality factors of P- and S-waves. Compared with the elastic characteristics of undeformed coals, such as P- and S-wave velocity ratios or Poisson's ratio, those of deformed coals generally decrease and the P-wave quality factors are less than those of S-waves. Moreover, the analysis of the relationship between pore structure and elastic modulus shows a better correlation between the P- and S-wave velocities and effective porosity, pore volume and specific surface area. Also, there are similar relationships between the pore structure and the Young's and shear moduli. However, there are no such correlations with other moduli. Correlations between these elastic moduli, pore structure, coal rank and density were not found for the various samples of deformed coals, which is consistent with only structural destruction occurring in the deformed coals with other physical properties remaining unchanged. The experimental results show that it is possible to predict the deformation of coals with multi-component seismic elastic inversion.
基金the National Natural Science Foundation of China （No. 10671214） the Natural Science Foundation of Chongqing Education Committee （No. KJ080620） the Science Foundation of Chongqing University of Arts and Sciences （No. Z2008SJ14）.
文摘In this paper, we study an important class of (α,β)-metrics in the form F = (α + β)m+1/αm on an n-dimensional manifold and get the conditions for such metrics to be weakly-Berwald metrics, where α = aij(x)yiyj is a Riemannian metric and β = bi(x)yi is a 1-form and m is a real number with m = 1,0,1/n. Furthermore, we also prove that this kind of (α,β)-metrics is of isotropic mean Berwald curvature if and only if it is of isotropic S-curvature. In this case, S-curvature vanishes and the metric is weakly-Berwald metric.
