Estimation of coda wave attenuation in East Central Iran

The attenuation of coda waves, Q _c , has been estimated in Zarand, Jiroft, and Bam regions of east central Iran using a single back-scattering model of S-coda envelopes. For this purpose, the recordings of 97 earthquakes by three seismic networks and a local strong ground motion network have been used. In this research, the frequency-dependent Q _c values are estimated at central frequencies of 1.5, 3, 6, 8, 12, 16, and 24 Hz using different lapse time windows from 20 to 60 s. The frequency-dependent relationships obtained are for Zarand, for Jiroft, and for Bam region. From the strong ground motion data, we obtain the relation . The Q _c frequency-dependent relationship for the entire region of east central Iran from all data (both seismograms and accelerograms) is . The average Q _c values estimated and their frequency dependent relationships correlate well with a highly heterogeneous and highly tectonically active region. Results also show that the attenuation is higher in Bam region compared to Zarand and Jiroft regions.     

The surface roughness and planetary boundary layer

Applications of the entrainment process to layers at the boundary, which meet the self similarity requirements of the logarithmic profile, have been studied. By accepting that turbulence has dominating scales related in scale length to the height above the surface, a layer structure is postulated wherein exchange is rapid enough to keep the layers internally uniform. The diffusion rate is then controlled by entrainment between layers. It has been shown that theoretical relationships derived on the basis of using a single layer of this type give quantitatively correct factors relating the turbulence, wind and shear stress for very rough surface conditions. For less rough surfaces, the surface boundary layer can be divided into several layers interacting by entrainment across each interface. This analysis leads to the following quantitatively correct formula compared to published measurements. 1 $$\begin{gathered} \frac{{\sigma _w }}{{u^* }} = \left( {\frac{2}{{9Aa}}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \left( {1 - 3^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \frac{a}{k}\frac{{d_n }}{z}\frac{{\sigma _w }}{{u^* }}\frac{z}{L}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \hfill \\ = 1.28(1 - 0.945({{\sigma _w } \mathord{\left/ {\vphantom {{\sigma _w } {u^* }}} \right. \kern-\nulldelimiterspace} {u^* }})({z \mathord{\left/ {\vphantom {z L}} \right. \kern-\nulldelimiterspace} L})^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \hfill \\ \end{gathered} $$ where \(u^* = \left( {{\tau \mathord{\left/ {\vphantom {\tau \rho }} \right. \kern-0em} \rho }} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) , σ _w is the standard deviation of the vertical velocity,z is the height andL is the Obukhov scale lenght. The constantsa, A, k andd _n are the entrainment constant, the turbulence decay constant, Von Karman's constant, and the layer depth derived from the theory. Of these,a andA, are universal constants and not empirically determined for the boundary layer. Thus the turbulence needed for the plume model of convection, which resides above these layers and reaches to the inversion, is determined by the shear stress and the heat flux in the surface layers. This model applies to convection in cool air over a warm sea. The whole field is now determined except for the temperature of the air relative to the water, and the wind, which need a further parameter describing sea surface roughness. As a first stop to describing a surface where roughness elements of widely varying sizes are combined this paper shows how the surface roughness parameter,z ₀, can be calculated for an ideal case of a random distribution of vertical cylinders of the same height. To treat a water surface, with various sized waves, such an approach modified to treat the surface by the superposition of various sized roughness elements, is likely to be helpful. Such a theory is particularly desirable when such a surface is changing, as the ocean does when the wind varies. The formula, 2 $$\frac{{0.118}}{{a_s C_D }}< z_0< \frac{{0.463}}{{a_s C_D (u^* )}}$$ is the result derived here. It applies to cylinders of radius,r, and number,m, per unit boundary area, wherea _s =2rm, is the area of the roughness elements, per unit area perpendicular to the wind, per unit distance downwind. The drag coefficient of the cylinders isC _D . The smaller value ofz _o is for large Reynolds numbers where the larger scale turbulence at the surface dominates, and the drag coefficient is about constant. Here the flow between the cylinders is intermittent. When the Reynolds number is small enough then the intermittent nature of the turbulence is reduced and this results in the average velocity at each level determining the drag. In this second case the larger limit forz ₀ is more appropriate.     

Coda wave attenuation in the Parecis Basin,Amazon Craton,Brazil: sensitivity to basement depth

Small local earthquakes from two aftershock sequences in Porto dos Gaúchos, Amazon craton—Brazil, were used to estimate the coda wave attenuation in the frequency band of 1 to 24 Hz. The time-domain coda-decay method of a single backscattering model is employed to estimate frequency dependence of the quality factor (Q _c) of coda waves modeled using Q_c = Q₀ f^hQ_{\rm c} =Q_{\rm 0} f^\eta , where Q ₀ is the coda quality factor at frequency of 1 Hz and η is the frequency parameter. We also used the independent frequency model approach (Morozov, Geophys J Int, 175:239–252, 2008), based in the temporal attenuation coefficient, χ(f) instead of Q(f), given by the equation c(f)=g+\fracpfQ_e \chi (f)\!=\!\gamma \!+\!\frac{\pi f}{Q_{\rm e} }, for the calculation of the geometrical attenuation (γ) and effective attenuation (Q_e^-1 )(Q_{\rm e}^{-1} ). Q _c values have been computed at central frequencies (and band) of 1.5 (1–2), 3.0 (2–4), 6.0 (4–8), 9.0 (6–12), 12 (8–16), and 18 (12–24) Hz for five different datasets selected according to the geotectonic environment as well as the ability to sample shallow or deeper structures, particularly the sediments of the Parecis basin and the crystalline basement of the Amazon craton. For the Parecis basin Q_c = (98±12)f^(1.14±0.08)Q_{\rm c} =(98\pm 12)f^{(1.14\pm 0.08)}, for the surrounding shield Q_c = (167±46)f^(1.03±0.04)Q_{\rm c} =(167\pm 46)f^{(1.03\pm 0.04)}, and for the whole region of Porto dos Gaúchos Q_c = (99±19)f^(1.17±0.02)Q_{\rm c} =(99\pm 19)f^{(1.17\pm 0.02)}. Using the independent frequency model, we found: for the cratonic zone, γ = 0.014 s^− 1, Q_e^-1 = 0.0001Q_{\rm e}^{-1} =0.0001, ν ≈ 1.12; for the basin zone with sediments of ~500 m, γ = 0.031 s^− 1, Q_e^-1 = 0.0003Q_{\rm e}^{-1} =0.0003, ν ≈ 1.27; and for the Parecis basin with sediments of ~1,000 m, γ = 0.047 s^− 1, Q_e^-1 = 0.0005Q_{\rm e}^{-1} =0.0005, ν ≈ 1.42. Analysis of the attenuation factor (Q _c) for different values of the geometrical spreading parameter (ν) indicated that an increase of ν generally causes an increase in Q _c, both in the basin as well as in the craton. But the differences in the attenuation between different geological environments are maintained for different models of geometrical spreading. It was shown that the energy of coda waves is attenuated more strongly in the sediments, Q_c = (78±23)f^(1.17±0.14)Q_{\rm c} =(78\pm 23)f^{(1.17\pm 0.14)} (in the deepest part of the basin), than in the basement, Q_c = (167±46)f^(1.03±0.04)Q_{\rm c} =(167\pm 46)f^{(1.03\pm 0.04)} (in the craton). Thus, the coda wave analysis can contribute to studies of geological structures in the upper crust, as the average coda quality factor is dependent on the thickness of sedimentary layer.     

Edge Detection and Depth Estimation Using a Tilt Angle Map from Gravity Gradient Data of the Kozaklı-Central Anatolia Region,Turkey

In this paper the application of an edge detection technique to gravity data is described. The technique is based on the tilt angle map (TAM) obtained from the first vertical gradient of a gravity anomaly. The zero contours of the tilt angle correspond to the boundaries of geologic discontinuities and are used to detect the linear features in gravity data. I also present that the distance between zero and ±p\mathord

The viscosity of hydrous dacitic liquids: implications for the rheology of evolving silicic magmas

The viscosity of a series of six synthetic dacitic liquids, containing up to 5.04 wt% dissolved water, was measured above the glass transition range by parallel-plate viscometry. The temperature of the 10¹¹ Pa s isokom decreases from 1065 K for the anhydrous liquid, to 864 K and 680 K for water contents of 0.97 and 5.04 wt% H₂O. Including additional measurements at high temperatures by concentric-cylinder and falling-sphere viscometry, the viscosity (η) can be expressed as a function of temperature and water content w according to: where η is in Pa s, T is temperature in K, and w is in weight percent. Within the conditions of measurement, this parameterization reproduces the 76 viscosity data with a root-mean square deviation (RMSD) of 0.16 log units in viscosity, or 7.8 K in temperature. The measurements show that water decreases the viscosity of the dacitic liquids more than for andesitic liquids, but less than for rhyolites. At low temperatures and high water contents, andesitic liquids are more viscous than the dacitic liquids, which are in turn more viscous than rhyolitic liquids, reversing the trend seen for high temperatures and low water contents. This suggests that the relative viscosity of different melts depends on temperature and water content as much as on bulk melt composition and structure. At magmatic temperatures, rhyolites are orders of magnitude more viscous than dacites, which are slightly more viscous than andesites. During degassing, all three liquids undergo a rapid viscosity increase at low water contents, and both dacitic and andesitic liquids will degas more efficiently than rhyolitic liquids. During cooling and differentiation, changing melt chemistry, decreasing temperature and increasing crystal content all lead to increases in the viscosity of magma (melt plus crystals). Under closed system conditions, where melt water content can increase during crystallization, viscosity increases may be small. Conversely, viscosity increases are very abrupt during ascent and degassing-induced crystallization.     

Global upper ocean heat content and climate variability

Observational data from the Global Temperature and Salinity Profile Program were used to calculate the upper ocean heat content (OHC) anomaly. The thickness of the upper layer is taken as 300 m for the Pacific/Atlantic Ocean and 150 m for the Indian Ocean since the Indian Ocean has shallower thermoclines. First, the optimal spectral decomposition scheme was used to build up monthly synoptic temperature and salinity dataset for January 1990 to December 2009 on 1° × 1° grids and the same 33 vertical levels as the World Ocean Atlas. Then, the monthly varying upper layer OHC field (H) was obtained. Second, a composite analysis was conducted to obtain the total-time mean OHC field ([`([`(H)])] \bar{\bar{H}} ) and the monthly mean OHC variability ( [(\textH)\tilde] \widetilde{\text{H}} ), which is found an order of magnitude smaller than [^(\textH)] \widehat{\text{H}} . Third, an empirical orthogonal function (EOF) method is conducted on the residue data ( [^(\textH)] \widehat{\text{H}} ), deviating from [(\textH)\tilde] \widetilde{\text{H}}  +  [(\textH)\tilde] \widetilde{\text{H}} , in order to obtain interannual variations of the OHC fields for the three oceans. In the Pacific Ocean, the first two EOF modes account for 51.46% and 13.71% of the variance, representing canonical El Nino/La Nina (EOF-1) and pseudo-El Nino/La Nina (i.e., El Nino Modoki; EOF-2) events. In the Indian Ocean, the first two EOF modes account for 24.27% and 20.94% of the variance, representing basin-scale cooling/warming (EOF-1) and Indian Ocean Dipole (EOF-2) events. In the Atlantic Ocean, the first EOF mode accounts for 49.26% of the variance, representing a basin-scale cooling/warming (EOF-1) event. The second EOF mode accounts for 8.83% of the variance. Different from the Pacific and Indian Oceans, there is no zonal dipole mode in the tropical Atlantic Ocean. Fourth, evident lag correlation coefficients are found between the first principal component of the Pacific Ocean and the Southern Oscillation Index with a maximum correlation coefficient (0.68) at 1-month lead of the EOF-1 and between the second principal component of the Indian Ocean and the Dipole Mode Index with maximum values (around 0.53) at 1–2-month advance of the EOF-2. It implies that OHC anomaly contains climate variability signals.     

Attenuation of P,S, and coda waves in Koyna region,India

The attenuation properties of the crust in the Koyna region of the Indian shield have been investigated using 164 seismograms from 37 local earthquakes that occurred in the region. The extended coda normalization method has been used to estimate the quality factors for P waves and S waves , and the single back-scattering model has been used to determine the quality factor for coda waves (Q _c). The earthquakes used in the present study have the focal depth in the range of 1–9 km, and the epicentral distance vary from 11 to 55 km. The values of and Q _c show a dependence on frequency in the Koyna region. The average frequency dependent relationships (Q = Q ₀ f ⁿ) estimated for the region are , and . The ratio is found to be greater than one for the frequency range considered here (1.5–18 Hz). This ratio, along with the frequency dependence of quality factors, indicates that scattering is an important factor contributing to the attenuation of body waves in the region. A comparison of Q _c and in the present study shows that for frequencies below 4 Hz and for the frequencies greater than 4 Hz. This may be due to the multiple scattering effect of the medium. The outcome of this study is expected to be useful for the estimation of source parameters and near-source simulation of earthquake ground motion, which in turn are required in the seismic hazard assessment of a region.     

The TKE dissipation rate in the northern South China Sea

The microstructure measurements taken during the summer seasons of 2009 and 2010 in the northern South China Sea (between 18°N and 22.5°N, and from the Luzon Strait to the eastern shelf of China) were used to estimate the averaged dissipation rate in the upper pycnocline 〈ε _p〉 of the deep basin and on the shelf. Linear correlation between 〈ε _p〉 and the estimates of available potential energy of internal waves, which was found for this data set, indicates an impact of energetic internal waves on spatial structure and temporal variability of 〈ε _p〉. On the shelf stations, the bottom boundary layer depth-integrated dissipation \( {\widehat{\varepsilon}}_{\mathrm{BBL}} \) reaches 17–19 mW/m², dominating the dissipation in the water column below the surface layer. In the pycnocline, the integrated dissipation \( {\widehat{\varepsilon}}_{\mathrm{p}} \) was mostly ∼10–30 % of \( {\widehat{\varepsilon}}_{\mathrm{BBL}} \). A weak dependence of bin-averaged dissipation \( \overline{\varepsilon} \) on the Richardson number was noted, according to \( \overline{\varepsilon}={\varepsilon}_0+\frac{\varepsilon_{\mathrm{m}}}{{\left(1+ Ri/R{i}_{\mathrm{cr}}\right)}^{1/2}} \), where ε ₀ + ε _m is the background value of \( \overline{\varepsilon} \) for weak stratification and Ri _cr = 0.25, pointing to the combined effects of shear instability of small-scale motions and the influence of larger-scale low frequency internal waves. The latter broadly agrees with the MacKinnon–Gregg scaling for internal-wave-induced turbulence dissipation.

     

Electromagnetic induction in the earth due to stationary and moving sources

A new approach to the theory of electromagnetic induction is developed that is applicable to moving as well as stationary sources. The source field is considered to be a standing wave generated by two waves travelling in opposite directions along the surface of the earth. For a stationary source the incident waves have velocities of the same magnitude, however for a moving source the velocities of the two incident waves are respectively increased and decreased by the velocity of the source. Electromagnetic induction in the earth is then considered as refraction of these waves and gives, for both stationary and moving sources, the magnetotelluric relation: $$\frac{{ - E_y }}{{H_x }} = \left( {\frac{{i\omega \mu }}{\sigma }} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \left( {1 - i\frac{{v^2 }}{{\omega \mu \sigma }}} \right)^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $$ where ν is the wavenumber of the source, μ is the permeability (4π·10^?7) and σ is the conductivity of the earth. ω is the angular frequency of the variation observed on the earth. For a stationary source the observed frequency is the same as the source frequency, however the effect of moving a time-varying source is to make the observed frequency different from the frequency of the source. Failure to recognise this in previous studies led to some erroneous conclusions. This study shows that a moving source isnot “electromagnetically broader” than a stationary source as had been suggested.     

The boundary value problem of Poisson’s equation with Stokes’ boundary condition

The following Poisson’s equation with the Stokes’ boundary condition is dealt with $$\left\{ \begin{gathered} \nabla ^2 T = - 4\pi Gp outside S, \hfill \\ \left. {\frac{{\partial T}}{{\partial h}} = \frac{1}{\gamma }\frac{{\partial y}}{{\partial h}}T} \right|_s = - \Delta g, \hfill \\ T = O\left( {r^{ - 3} } \right) at infinity, \hfill \\ \end{gathered} \right.$$ whereS is reference ellipsord. Under spherical approximation transformation, the ellipsoidal correction terms about the boundary condition, the equation and the density in the above BVP are respectively given. Therefore, the disturbing potentialT can he obtained if the magnitudes aboveO(ε⁴) are neglected.     

Moment inequality and complete convergence of moving average processes under asymptotically linear negative quadrant dependence assumptions

Let {Y, Y _i , −∞ < i < ∞} be a doubly infinite sequence of identically distributed and asymptotically linear negative quadrant dependence random variables, {a _i , −∞ < i < ∞} an absolutely summable sequence of real numbers. We are inspired by Wang et al. (Econometric Theory 18:119–139, 2002) and Salvadori (Stoch Environ Res Risk Assess 17:116–140, 2003). And Salvadori (Stoch Environ Res Risk Assess 17:116–140, 2003) have obtained Linear combinations of order statistics to estimate the quantiles of generalized pareto and extreme values distributions. In this paper, we prove the complete convergence of under some suitable conditions. The results obtained improve and generalize the results of Li et al. (1992) and Zhang (1996). The results obtained extend those for negative associated sequences and ρ^*-mixing sequences. CIC Number O211, AMS (2000) Subject Classification 60F15, 60G50 Research supported by National Natural Science Foundation of China     

High Frequency PKKP<Subscript>BC</Subscript> Around 2.5 Hz Recorded Globally

Anomalous high frequency PKKP_BC signals (displaying a large amount of energy around 2.5 Hz), recorded globally for deep and intermediate depth earthquakes, are compared to PKKP_AB signals. The attenuation difference t_\textAB^* - t_\textBC^* t_{\text{AB}}^{*} - t_{\text{BC}}^{*} is evaluated from spectral amplitudes in the range 96–111°, being approximately twice the results provided by full-wave theory and PREM (with no low Q_μ zone in the lowermost mantle and a nearly infinite Q_K in the outer core). Most ray paths for such recordings are piercing the D″ region in the proximity of regions where ultra-low velocity zones (ULVZ) have been previously reported beneath the North Atlantic Ocean, the Southwest Pacific and the southwestern part of South America. If BC amplitudes around 2.5 Hz and at low frequencies (0.5–1.5 Hz) are comparable, the observed attenuation difference (in the frequency range 0.2–2.5 Hz) is small (around 0.25 s) and close to the PREM value. The particle motion of the high-frequency PKKP_BC at 2.5 Hz is quite similar to that of the raw recording, suggesting a deep source. An explanation for this might be scattering of the BC branch in some very restricted areas of the lowermost mantle. Alternately, the presence of a thin layer with high attenuation in the D″ region would most likely be associated with either the ultra-low velocity zone (ULVZ) or light sediments on the underside of the core-mantle boundary (CMB). Correlated to other methods to investigate the lowermost mantle, the high-frequency PKKP_BC can be used to map lateral variations of attenuation above the CMB, possibly associated with the boundary of the superplumes, especially when PKKP_AB is observed.     

The TKE dissipation rate in the northern South China Sea

The microstructure measurements taken during the summer seasons of 2009 and 2010 in the northern South China Sea (between 18°N and 22.5°N, and from the Luzon Strait to the eastern shelf of China) were used to estimate the averaged dissipation rate in the upper pycnocline 〈ε _p〉 of the deep basin and on the shelf. Linear correlation between 〈ε _p〉 and the estimates of available potential energy of internal waves, which was found for this data set, indicates an impact of energetic internal waves on spatial structure and temporal variability of 〈ε _p〉. On the shelf stations, the bottom boundary layer depth-integrated dissipation $ {\widehat{\varepsilon}}_{\mathrm{BBL}} $ reaches 17–19 mW/m², dominating the dissipation in the water column below the surface layer. In the pycnocline, the integrated dissipation $ {\widehat{\varepsilon}}_{\mathrm{p}} $ was mostly ～10–30 % of $ {\widehat{\varepsilon}}_{\mathrm{BBL}} $ . A weak dependence of bin-averaged dissipation $ \overline{\varepsilon} $ on the Richardson number was noted, according to $ \overline{\varepsilon}={\varepsilon}_0+\frac{\varepsilon_{\mathrm{m}}}{{\left(1+ Ri/R{i}_{\mathrm{cr}}\right)}^{1/2}} $ , where ε ₀ + ε _m is the background value of $ \overline{\varepsilon} $ for weak stratification and Ri _cr?=?0.25, pointing to the combined effects of shear instability of small-scale motions and the influence of larger-scale low frequency internal waves. The latter broadly agrees with the MacKinnon–Gregg scaling for internal-wave-induced turbulence dissipation.     

A semiempirical mathematical model of the secondary pollution of water bodies by soluble iron and manganese forms

A semiempirical mathematical model of iron and manganese migration from bottom sediments into the water mass of water bodies has been proposed based on some basic regularities in the geochemistry of those elements. The entry of dissolved forms of iron and manganese under aeration conditions is assumed negligible. When dissolved-oxygen concentration is <0.5 mg/L, the elements start releasing from bottom sediments, their release rate reaching its maximum under anoxic conditions. The fluxes of dissolved iron and manganese (Me) from bottom sediments into the water mass (J _Me) are governed by the gradients of their concentrations in diffusion water sublayer adjacent to sediment surface and having an average thickness of h = 0.025 cm: \({J_{Me}} = - {D_{Me}}\frac{{{C_{Me\left( {ss} \right)}} - {C_{Me\left( w \right)}}}}{h}\) (D _Me ≈ 1 × 10^–9 m²/s is molecular diffusion coefficient of component Me in solution; C _Me(ss) and C _Me(w) ≈ 0 are Me concentrations on sediment surface, i.e., on the bottom boundary of the diffusion water sublayer, and in the water mass, i.e., on the upper boundary of the diffusion water sublayer). The value of depends on water saturation with dissolved oxygen (\({\eta _{{O_2}}}\)) in accordance with the empiric relationship \({C_{Me\left( {ss} \right)}} = \frac{{C_{_{Me\left( {ss} \right)}}^{\max }}}{{1 + k{\eta _{{O_2}}}}}\) (k is a constant factor equal to 300 for iron and 100 for manganese; C _Me(ss) ^max is the maximal concentration of Me on the bottom boundary of the diffusion water sublayer with C _Fe(ss) ^max ≈ 200 μM (11 mg/L), and C _Mn(ss) ^max ≈ 100 μM (5.5 mg/L).     

A Crustal Model for the Eastern Alps Region and a New Moho Map in Southeastern Europe

In the last two decades, south-central Europe and the Eastern Alps have been widely explored by many seismic refraction experiments (e.g., CELEBRATION 2000, ALP 2002, SUDETES 2003). Although quite detailed images are available along linear profiles, a comprehensive, three-dimensional crustal model of the region is still missing. This limitation makes this region a weak spot in continental-wide comprehensive representations of crustal structure. To improve on this situation, we select and collect 37 published active-source seismic lines in this region. After geo-referencing each line, we sample them along vertical profiles—every 50?km or less along the line—and derive P-wave velocities in a stack of homogeneous layers (separated by discontinuities: depth of crystalline basement, top of lower crust, and Moho). We finally merge the information using geostatistical methods, and infer S-wave velocity and density using empirical scaling relations. We present here the resulting crustal model for a region encompassing the Eastern Alps, Dinarides, Pannonian basin, Western Carpathians and Bohemian Massif, covering the region within $45^{\circ}\text{--}51^{\circ}\hbox{N}$ and $11^{\circ} \text{--} 22^{\circ}\hbox{E}$ with a resolution of $0.2^{\circ} \times 0.2^{\circ}.$ We are also able to extend and update the map of Moho depth in a wider region within $35^{\circ}\text{--}51^{\circ}\hbox{N}$ and $12^{\circ}\text{--}45^{\circ}\hbox{E},$ gathering Moho values from the collected seismic lines, other published dataset and using the European plate reference EPcrust as a background. All the digitized profiles and the resulting model are available online.     

Estimates of fracture parameters of earthquakes

A new estimate of the fracture parameters of earthquakes is provided in this paper. By theMuskhelishvili method (1953) a number of basic relations among fracture-mechanics parameters are derived. A scheme is proposed to evaluate the slip weakening parameters in terms of fault dimension, average slip, and rise time, and the new results are applied to 49 events compiled in the earthquake catalogue ofPurcaru andBerckhemer (1982). The following empirical relations are found in the paper: $$\begin{gathered} \frac{{\tau _B - \tau _f }}{{\tau _\infty - \tau _f }} = 2.339 \hfill \\ {{\omega _c } \mathord{\left/ {\vphantom {{\omega _c } {W = 0.113}}} \right. \kern-\nulldelimiterspace} {W = 0.113}} \hfill \\ \log G_c \left( {{{dyne} \mathord{\left/ {\vphantom {{dyne} {cm}}} \right. \kern-\nulldelimiterspace} {cm}}} \right) = 2 \log L (km) + 6.167 \hfill \\ \log \delta _c (cm) = 2 \log L (km) - 1.652 \hfill \\ \end{gathered} $$ whereG _c is the specific fracture energy,ω _c the size of the slip weakening zone,δ _c the slip weakening displacement,τ _B ?τ _f the drop in strength in the slip weakening zone,τ _∞?τ _f the stress drop,L the fault length, andW the fault width. The investigation of 49 shocks shows that the range of strength dropτ _B ?τ _f is from several doze to several hundred bars at depthh<400 km, but it can be more than 10³ bars ath>500 km; besides, the range of the sizeω _c of the strength degradation zone is from a few tenths of a kilometer to several dozen kilometers, and the range of the slip weakening displacementδ _c is from several to several hundred centimeters. The specific fracture energyG _c is of the order of 10⁸ to 10¹¹ erg cm^?2 when the momentM ₀ is of the order of 10²³ to 10²⁹ dyne cm.     

A theoretical value for von Karman's constant

This paper extends the theory of the entity and entrainment model of turbulence to obtain a numerical value of von Karman's constant,k=0.37. The formula is, $$k = (2a^3 /A)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \ln \beta $$ where,a=1/12 is the entrainment constant,A=1 is the turbulent decay constant, and β is the ratio in height of the successive self-similar layers of the theory, where β is evaluated as β=e ². These new values fork and β improve the surface roughness length estimates derived from this theory.     

Variation of Seismic Coda Wave Attenuation in the Garhwal Region, Northwestern Himalaya

Seismic coda wave attenuation ( $ Q_{\text{c}}^{ - 1} $ ) characteristics in the Garhwal region, northwestern Himalaya is studied using 113 short-period, vertical component seismic observations from local events with hypocentral distance less than 250?km and magnitude range between 1.0 to 4.0. They are located mainly in the vicinity of the Main Boundary Thrust (MBT) and the Main Central Thrust (MCT), which are well-defined tectonic discontinuities in the Himalayas. Coda wave attenuation ( $ Q_{\text{c}}^{ - 1} $ ) is estimated using the single isotropic scattering method at central frequencies 1.5, 3, 5, 7, 9, 12, 16, 20, 24 and 28?Hz using several starting lapse times and coda window lengths for the analysis. Results show that the ( $ Q_{\text{c}}^{ - 1} $ ) values are frequency dependent in the considered frequency range, and they fit the frequency power law ( $ Q_{\text{c}}^{ - 1} \left( f \right) = Q_{0}^{ - 1} f^{ - n} $ ). The Q ₀ (Q _c at 1?Hz) estimates vary from about 50 for a 10?s lapse time and 10?s window length, to about 350 for a 60?s lapse time and 60?s window length combination. The exponent of the frequency dependence law, n ranges from 1.2 to 0.7; however, it is greater than 0.8, in general, which correlates well with the values obtained in other seismically and tectonically active and highly heterogeneous regions. The attenuation in the Garhwal region is found to be lower than the Q _c ^?1 values obtained for other seismically active regions of the world; however, it is comparable to other regions of India. The spatial variation of coda attenuation indicates that the level of heterogeneity decreases with increasing depth. The variation of coda attenuation has been estimated for different lapse time and window length combinations to observe the effect with depth and it indicates that the upper lithosphere is more active seismically as compared to the lower lithosphere and the heterogeneity decreases with increasing depth.