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.     

Comparative soil CO2 flux measurements and geostatistical estimation methods on Masaya volcano, Nicaragua

We present a comparative study of soil CO₂ flux () measured by five groups (Groups 1–5) at the IAVCEI-CCVG Eighth Workshop on Volcanic Gases on Masaya volcano, Nicaragua. Groups 1–5 measured using the accumulation chamber method at 5-m spacing within a 900 m² grid during a morning (AM) period. These measurements were repeated by Groups 1–3 during an afternoon (PM) period. Measured ranged from 218 to 14,719 g m⁻² day⁻¹. The variability of the five measurements made at each grid point ranged from ±5 to 167%. However, the arithmetic means of fluxes measured over the entire grid and associated total CO₂ emission rate estimates varied between groups by only ±22%. All three groups that made PM measurements reported an 8–19% increase in total emissions over the AM results. Based on a comparison of measurements made during AM and PM times, we argue that this change is due in large part to natural temporal variability of gas flow, rather than to measurement error. In order to estimate the mean and associated CO₂ emission rate of one data set and to map the spatial distribution, we compared six geostatistical methods: arithmetic and minimum variance unbiased estimator means of uninterpolated data, and arithmetic means of data interpolated by the multiquadric radial basis function, ordinary kriging, multi-Gaussian kriging, and sequential Gaussian simulation methods. While the total CO₂ emission rates estimated using the different techniques only varied by ±4.4%, the maps showed important differences. We suggest that the sequential Gaussian simulation method yields the most realistic representation of the spatial distribution of , but a variety of geostatistical methods are appropriate to estimate the total CO₂ emission rate from a study area, which is a primary goal in volcano monitoring research.Editorial responsibility: H Shinohara     

Generous statistical tests

A common statistical problem is deciding which of two possible sources, A and B, of a contaminant is most likely the actual source. The situation considered here, based on an actual problem of polychlorinated biphenyl contamination discussed below, is one in which the data strongly supports the hypothesis that source A is responsible. The problem approach here is twofold: One, accurately estimating this extreme probability. Two, since the statistics involved will be used in a legal setting, estimating the extreme probability in such a way as to be as generous as is possible toward the defendant’s claim that the other site B could be responsible; thereby leaving little room for argument when this assertion is shown to be highly unlikely. The statistical testing for this problem is modeled by random variables {X _i } and the corresponding sample mean the problem considered is providing a bound ɛ for which for a given number a ₀. Under the hypothesis that the random variables {X _i } satisfy E(X _i ) ≤ μ, for some 0  < μ < 1, statistical tests are given, described as “generous”, because ɛ is maximized. The intent is to be able to reject the hypothesis that a ₀ is a value of the sample mean while eliminating any possible objections to the model distributions chosen for the {X _i } by choosing those distributions which maximize the value of ɛ for the test used.     

High-order <Emphasis Type="Italic">h</Emphasis>-adaptive discontinuous Galerkin methods for ocean modelling

In this paper, we present an h-adaptive discontinuous Galerkin formulation of the shallow water equations. For a discontinuous Galerkin scheme using polynomials up to order , the spatial error of discretization of the method can be shown to be of the order of , where is the mesh spacing. It can be shown by rigorous error analysis that the discontinuous Galerkin method discretization error can be related to the amplitude of the inter-element jumps. Therefore, we use the information contained in jumps to build error metrics and size field. Results are presented for ocean modelling problems. A first experiment shows that the theoretical convergence rate is reached with the discontinuous Galerkin high-order h-adaptive method applied to the Stommel wind-driven gyre. A second experiment shows the propagation of an anticyclonic eddy in the Gulf of Mexico. An erratum to this article can be found at     

Steady flows driven by sources of random strength in heterogeneous aquifers with application to partially penetrating wells

Average steady source flow in heterogeneous porous formations is modelled by regarding the hydraulic conductivity K(x) as a stationary random space function (RSF). As a consequence, the flow variables become RSFs as well, and we are interested into calculating their moments. This problem has been intensively studied in the case of a Neumann type boundary condition at the source. However, there are many applications (such as well-type flows) for which the required boundary condition is that of Dirichlet. In order to fulfill such a requirement the strength of the source must be proportional to K(x), and therefore the source itself results a RSF. To solve flows driven by sources whose strength is spatially variable, we have used a perturbation procedure similar to that developed by Indelman and Abramovich (Water Resour Res 30:3385–3393, 1994) to analyze flows generated by sources of deterministic strength. Due to the linearity of the mathematical problem, we have focused on the explicit derivation of the mean head distribution G _d (x) generated by a unit pulse. Such a distribution represents the fundamental solution to the average flow equations, and it is termed as mean Green function. The function G _d (x) is derived here at the second order of approximation in the variance σ² of the fluctuation (where K _A is the mean value of K(x)), for arbitrary correlation function ρ(x), and any dimensionality d of the flow domain. We represent G _d (x) as product between the homogeneous Green function G _d ⁽⁰⁾(x) valid in a domain with constant K _A , and a distortion term Ψ _d (x) = 1 + σ²ψ _d (x) which modifies G _d ⁽⁰⁾(x) to account for the medium heterogeneity. In the case of isotropic formations ψ _d (x) is expressed via one quadrature. This quadrature can be analytically calculated after adopting specific (e.g.. exponential and Gaussian) shape for ρ(x). These general results are subsequently used to investigate flow toward a partially-penetrating well in a semi-infinite domain. Indeed, we construct a σ²-order approximation to the mean as well as variance of the head by replacing the well with a singular segment. It is shown how the well-length combined with the medium heterogeneity affects the head distribution. We have introduced the concept of equivalent conductivity K ^eq(r,z). The main result is the relationship where the characteristic function ψ^(w)(r,z) adjusts the homogeneous conductivity K _A to account for the impact of the heterogeneity. In this way, a procedure can be developed to identify the aquifer hydraulic properties by means of field-scale head measurements. Finally, in the case of a fully penetrating well we have expressed the equivalent conductivity in analytical form, and we have shown that (being the effective conductivity for mean uniform flow), in agreement with the numerical simulations of Firmani et al. (Water Resour Res 42:W03422, 2006).     

Fuzzy process capability indices for quality control of irrigation water

Water covers over 70% of the Earth surface and is a very important resource to people and the environment. Water pollution affects drinking water, rivers, lakes and oceans all over the world. This consequently harms human health and the natural environment. Water pollution can also affect the crops. So, water pollution is an important issue for humanity. Therefore, the control of irrigation water is a necessity. In this paper, a methodology based on process capability indices (PCIs) has been presented to control the levels of pH, dissolved oxygen (DO) and temperature (T) in dam’s water for irrigation. Fuzzy PCIs have been proposed for this aim. The fuzzy estimates of $ \hat C_p Water covers over 70% of the Earth surface and is a very important resource to people and the environment. Water pollution affects drinking water, rivers, lakes and oceans all over the world. This consequently harms human health and the natural environment. Water pollution can also affect the crops. So, water pollution is an important issue for humanity. Therefore, the control of irrigation water is a necessity. In this paper, a methodology based on process capability indices (PCIs) has been presented to control the levels of pH, dissolved oxygen (DO) and temperature (T) in dam’s water for irrigation. Fuzzy PCIs have been proposed for this aim. The fuzzy estimates of and are obtained for pH, DO, and T based on Buckley’s interval estimation approach and based on fuzzy specification limits. An application has been made for Kesikk?prü Dam in Ankara, Turkey. In this paper, Buckley’s approach is re-arranged to obtain a triangular fuzzy membership function because it cannot be obtained from Buckley’s approach in some situation.     

Asymptotic Rayleigh instantaneous unit hydrograph

The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude,N, tends asymptotically, asN grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, , where is a mean link wave travel time.     

Asymptotic Rayleigh instantaneous unit hydrograph

The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude,N, tends asymptotically, asN grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, , where is a mean link wave travel time.     

Characteristics of low-frequency oscillation intensity of air-sea turbulent heat fluxes over the northwest Pacific

Based on the daily turbulent heat fluxes and related meteorological variables datasets (1985–2006) from Objectively Analyzed air-sea Fluxes (OAFlux) Project of Woods Hole Oceanographic Institution (WHOI), characteristics of low-frequency oscillation intensity of air-sea turbulent heat fluxes over the northwest Pacific are analyzed by linear perturbation method and correlation analysis. It can be concluded that: 1) the distribution of low-frequency oscillation intensity of latent heat flux (LHF) over the northwest Pacific is mainly affected by that of low-frequency oscillation intensity of anomalous air-sea humidity gradient (Δq′) as well as mean air-sea humidity gradient (), while the distribution of low-frequency oscillation intensity of sensible heat flux (SHF) is mainly affected by that of low-frequency oscillation intensity of anomalous air-sea temperature gradient (ΔT′). 2) The low-frequency oscillation of turbulent heat fluxes over the northwest Pacific is the strongest in winter and the weakest in summer. And the seasonal transition of low-frequency oscillation intensity of LHF is jointly influenced by those of low-frequency oscillation intensity of Δq′, low-frequency oscillation intensity of anomalous wind speed (U′), and mean wind speed (Ū), while the seasonal transition of low-frequency oscillation intensity of SHF is mainly influenced by those of low-frequency oscillation intensity of ΔT′ and Ū. 3) Over the tropical west Pacific and sea areas north of 20°N, the low-frequency oscillation of LHF (SHF) is mainly influenced by atmospheric variables q _a ′ (T _a ′) and U′, indicating an oceanic response to overlying atmospheric forcing. In contrast, over the tropical eastern and central Pacific south of 20°N, q _s ′ (T _s ′) also greatly influences the low-frequency oscillation of LHF (SHF). Supported by National Natural Science Foundation of China (Grant No. 40675028) and National Basic Research Program of China (Grant No. 2006CB403600)     

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.     

Basaltic thermals and Subplinian plumes: Constraints from acoustic measurements at Shishaldin volcano, Alaska

The 1999 basaltic eruption of Shishaldin volcano (Alaska, USA) included both Strombolian and Subplinian activity, as well as a “pre-Subplinian” phase interpreted as the local coalescence within a long foam in the conduit. Although few visual observations were made of the eruption, a great deal of information regarding gas velocity, gas flux at the vent and plume height may be inferred by using acoustic recordings of the eruption. By relating acoustic power to gas velocity, a time series of gas velocity is calculated for the Subplinian and pre-Subplinian phases. These time series show trends in gas velocity that are interpreted as plumes or, for those signals lasting only a short time, thermals. The Subplinian phase is shown to be composed of a thermal followed by five plumes with a total expelled gas volume of .The initiation of the Subplinian activity is probably related to the arrival of a large overpressurised bubble close to the top of the magma column. A gradual increase in low-frequency (0.01–0.5 Hz) signal prior to this “trigger bubble” may be due to the rise of the bubble in the conduit. This delay corresponds to a reservoir located at ≈3.9 km below the surface, in good agreement with studies on other volcanoes.The presence of two thermal phases is also identified in the middle of the pre-Subplinian phase with a total gas release of and . Gas velocity at the vent is found to be and for the Subplinian plumes and the pre-Subplinian thermals respectively.The agreement is very good between estimates of the gas flux from modelling the plume height and those obtained from acoustic measurements, leading to a new method by which eruption physical parameters may be quantified. Furthermore, direct measurements of gas velocity can be used for better estimates of the flux released during the eruption.     

A multifractal formalism for vector-valued random fields based on wavelet analysis: application to turbulent velocity and vorticity 3D numerical data

Extreme atmospheric events are intimately related to the statistics of atmospheric turbulent velocities. These, in turn, exhibit multifractal scaling, which is determining the nature of the asymptotic behavior of velocities, and whose parameter evaluation is therefore of great interest currently. We combine singular value decomposition techniques and wavelet transform analysis to generalize the multifractal formalism to vector-valued random fields. The so-called Tensorial Wavelet Transform Modulus Maxima (TWTMM) method is calibrated on synthetic self-similar 2D vector-valued multifractal measures and monofractal 3D vector-valued fractional Brownian fields. We report the results of some application of the TWTMM method to turbulent velocity and vorticity fields generated by direct numerical simulations of the incompressible Navier–Stokes equations. This study reveals the existence of an intimate relationship between the singularity spectra of these two vector fields which are found significantly more intermittent than previously estimated from longitudinal and transverse velocity increment statistics.

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An algorithm for the optimum distribution of a regional seismic network — II. An analysis of the accuracy of location of local earthquakes depending on the number of seismic stations

Summary Seven optimal networks consisting of 4 to 10 stations are compared for a given region, where velocity-depth profiles and the distribution of seismic intensity are known. Assuming that the standard error of arrival time is _t =0.05 s and the standard errors of the parameters of velocity-depth profiles are equal to 5% of their values, the average standard errors of the origin time and focus coordinates are estimated. The application of optimum methods to the planning of seismic networks in the Lublin Coal Basin is presented, and maps of standard errors of origin time , depth and epicenter ( _xy ) for the case of an optimum network of 6 seismic stations are given.     

On some problems of seismic crustal phase

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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     

New Approach to the Characterization of M max and of the Tail of the Distribution of Earthquake Magnitudes

We develop a new method for the statistical estimation of the tail of the distribution of earthquake sizes recorded in the Harvard catalog of seismic moments converted to m _W -magnitudes (1977–2004 and 1977–2006). For this, we suggest a new parametric model for the distribution of main-shock magnitudes, which is composed of two branches, the pure Gutenberg-Richter distribution up to an upper magnitude threshold m ₁, followed by another branch with a maximum upper magnitude bound M _max, which we refer to as the two-branch model. We find that the number of main events in the catalog (N = 3975 for 1977–2004 and N = 4193 for 1977–2006) is insufficient for a direct estimation of the parameters of this model, due to the inherent instability of the estimation problem. This problem is likely to be the same for any other two-branch model. This inherent limitation can be explained by the fact that only a small fraction of the empirical data populates the second branch. We then show that using the set of maximum magnitudes (the set of T-maxima) in windows of duration T days provides a significant improvement, in particular (i) by minimizing the negative impact of time-clustering of foreshock/main shock/aftershock sequences in the estimation of the tail of magnitude distribution, and (ii) by providing via a simulation method reliable estimates of the biases in the Moment estimation procedure (which turns out to be more efficient than the Maximum Likelihood estimation). We propose a method for the determination of the optimal choice of the T value minimizing the mean-squares-error of the estimation of the form parameter of the GEV distribution approximating the sample distribution of T-maxima, which yields T _optimal = 500 days. We have estimated the following quantiles of the distribution of T-maxima for the whole period 1977–2006: Q _16%(M _max) = 9.3, Q _50%(M _max) = 9.7 and Q _84%(M _max) = 10.3. Finally, we suggest two more stable statistical characteristics of the tail of the distribution of earthquake magnitudes: The quantile Q _T (q) of a high probability level q for the T-maxima, and the probability of exceedance of a high threshold magnitude ρ _T (m*)  = P{m _k  ≥ m*}. We obtained the following sample estimates for the global Harvard catalog and The comparison between our estimates for the two periods 1977–2004 and 1977–2006, where the latter period included the great Sumatra earthquake 24.12.2004, m _W  = 9.0 confirms the instability of the estimation of the parameter M _max and the stability of Q _T (q) and ρ _T (m*) = P{m _k  ≥ m*}.     

Fermat's Variational Principle for Anisotropic Inhomogeneous Media

Fermat's variational principle states that the signal propagates from point S to R along a curve which renders Fermat's functional (l) stationary. Fermat's functional (l) depends on curves l which connect points S and R, and represents the travel times from S to R along l. In seismology, it is mostly expressed by the integral (l) = (x ^k,x ^k ')du, taken along curve l, where (x ^k,x ^k ') is the relevant Lagrangian, x ^k are coordinates, u is a parameter used to specify the position of points along l, and x ^k ' = dx ^k÷du. If Lagrangian (x ^k,x ^k ') is a homogeneous function of the first degree in x ^k ', Fermat's principle is valid for arbitrary monotonic parameter u. We than speak of the first-degree Lagrangian ⁽¹⁾(x ^k,x ^k '). It is shown that the conventional Legendre transform cannot be applied to the first-degree Lagrangian ⁽¹⁾(x ^k,x ^k ') to derive the relevant Hamiltonian ⁽¹⁾(x ^k,p _k), and Hamiltonian ray equations. The reason is that the Hessian determinant of the transform vanishes identically for first-degree Lagrangians ⁽¹⁾(x ^k,x ^k '). The Lagrangians must be modified so that the Hessian determinant is different from zero. A modification to overcome this difficulty is proposed in this article, and is based on second-degree Lagrangians ⁽²⁾. Parameter u along the curves is taken to correspond to travel time , and the second-degree Lagrangian ⁽²⁾(x ^k, ^k ) is then introduced by the relation ⁽²⁾(x ^k, ^k ) = [⁽¹⁾(x ^k, ^k )]², with ^k = dx ^k÷d. The second-degree Lagrangian ⁽²⁾(x ^k, ^k ) yields the same Euler/Lagrange equations for rays as the first-degree Lagrangian ⁽¹⁾(x ^k, ^k ). The relevant Hessian determinant, however, does not vanish identically. Consequently, the Legendre transform can then be used to compute Hamiltonian ⁽²⁾(x ^k,p _k) from Lagrangian ⁽²⁾(x ^k, ^k ), and vice versa, and the Hamiltonian canonical equations can be derived from the Euler-Lagrange equations. Both ⁽²⁾(x ^k, ^k ) and ⁽²⁾(x ^k,p _k) can be expressed in terms of the wave propagation metric tensor g _ij(x ^k, ^k ), which depends not only on position x ^k, but also on the direction of vector ^k . It is defined in a Finsler space, in which the distance is measured by the travel time. It is shown that the standard form of the Hamiltonian, derived from the elastodynamic equation and representing the eikonal equation, which has been broadly used in the seismic ray method, corresponds to the second-degree Lagrangian ⁽²⁾(x ^k, ^k ), not to the first-degree Lagrangian ⁽¹⁾(x ^k, ^k ). It is also shown that relations ⁽²⁾(x ^k, ^k ) = ; and ⁽²⁾(x ^k,p _k) = are valid at any point of the ray and that they represent the group velocity surface and the slowness surface, respectively. All procedures and derived equations are valid for general anisotropic inhomogeneous media, and for general curvilinear coordinates x ⁱ. To make certain procedures and equations more transparent and objective, the simpler cases of isotropic and ellipsoidally anisotropic media are briefly discussed as special cases.     

Zur Interpretation von seismischen Refraktionsmessungen

Zusammenfassung Unter der Voraussetzung, dass die Frontgeschwindigkeitc eine stetige und monoton wachsende Funktion von der Tiefez ist, wird dargelegt, wie man aus einer gemessenen Laufzeitkurve () die zuc inverse Funktionz=z (c) auf einfache Weise berechnen kann. Weiter wird die Eindringtiefez _m in Funktion von ermittelt und abschliessend ein Beispiel gegeben.

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Summary Based on a recorded travel-time curve (), a simple direct method is developed for calculating the functionz=z (c), under the asumption that the wave velocityc is a regularly monotone increasing function of the depthz. Finally a rumerical example is given.