Higher and lowest order mixed finite element approximation of subsurface flow problems with solutions of low regularity

In this work we study mixed finite element approximations of Richards’ equation for simulating variably saturated subsurface flow and simultaneous reactive solute transport. Whereas higher order schemes have proved their ability to approximate reliably reactive solute transport (cf., e.g. [Bause M, Knabner P. Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping. Comput Visual Sci 7;2004:61–78]), the Raviart–Thomas mixed finite element method (RT₀) with a first order accurate flux approximation is popular for computing the underlying water flow field (cf. [Bause M, Knabner P. Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods. Adv Water Resour 27;2004:565–581, Farthing MW, Kees CE, Miller CT. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv Water Resour 26;2003:373–394, Starke G. Least-squares mixed finite element solution of variably saturated subsurface flow problems. SIAM J Sci Comput 21;2000:1869–1885, Younes A, Mosé R, Ackerer P, Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J Comp Phys 149;1999:148–167, Woodward CS, Dawson CN. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media. SIAM J Numer Anal 37;2000:701–724]). This combination might be non-optimal. Higher order techniques could increase the accuracy of the flow field calculation and thereby improve the prediction of the solute transport. Here, we analyse the application of the Brezzi-Douglas-Marini element (BDM₁) with a second order accurate flux approximation to elliptic, parabolic and degenerate problems whose solutions lack the regularity that is assumed in optimal order error analyses. For the flow field calculation a superiority of the BDM₁ approach to the RT₀ one is observed, which however is less significant for the accompanying solute transport.     

Peak ground accelerations from large (<Emphasis Type="Bold">M</Emphasis> ≥ 7.2) shallow crustal earthquakes: a comparison with predictions from eight recent ground-motion models

Strong-motion data from large (M ≥ 7.2) shallow crustal earthquakes invariably make up a small proportion of the records used to develop empirical ground motion prediction equations (GMPEs). Consequently GMPEs are more poorly constrained for large earthquakes than for small events. In this article peak ground accelerations (PGAs) observed in 38 earthquakes worldwide with M ≥ 7.2 are compared with those predicted by eight recent GMPEs. Well over half of the 38 earthquakes were not considered when deriving these GMPEs but the data were identified by a thorough literature review of strong-motion reports from the past 60 years. These data are provided in an electronic supplement for future investigations on ground motions from large earthquakes. The addition of these data provides better constraint of the between-event ground-motion variability in large earthquakes. It is found that the eight models generally provide good predictions for PGAs from these earthquakes, although there is evidence for slight under- or over-prediction of motions by some models (particularly for M > 7.6). The between-event variabilities predicted by most models match the observed variability, if data from two events (2001 Bhuj and 2005 Crescent City) that are likely atypical of earthquakes in active regions are excluded. For some GMPEs there is evidence that they are over-predicting PGAs in the near-source region of large earthquakes as well as over-predicting motions on hard rock. Overall, however, all the considered models, despite having been derived using limited data, provide reliable predictions of PGAs in the largest crustal earthquakes.     

Historical intermediate-depth earthquakes in the southern Aegean Sea Benioff zone: modeling their anomalous macroseismic patterns with stochastic ground-motion simulations

We model the macroseismic damage distribution of four important intermediate-depth earthquakes of the southern Aegean Sea subduction zone, namely the destructive 1926 M?=?7.7 Rhodes and 1935 M?=?6.9 Crete earthquakes, the unique 1956 M?=?6.9 Amorgos aftershock (recently proposed to be triggered by a shallow event), and the more recent 2002 M?=?5.9 Milos earthquake, which all exhibit spatially anomalous macroseismic patterns. Macroseismic data for these events are collected from published macroseismic databases and compared with the spatial distribution of seismic motions obtained from stochastic simulation, converted to macroseismic intensity (Modified Mercalli scale, I_MM). For this conversion, we present an updated correlation between macroseismic intensities and peak measures of seismic motions (PGA and PGV) for the intermediate-depth earthquakes of the southern Aegean Sea. Input model parameters for the simulations, such as fault dimensions, stress parameters, and attenuation parameters (e.g. back-arc/along anelastic attenuation) are adopted from previous work performed in the area. Site-effects on the observed seismic motions are approximated using generic transfer functions proposed for the broader Aegean Sea area on the basis of V_S30 values from topographic slope proxies. The results are in very good agreement with the observed anomalous damage patterns, for which the largest intensities are often observed at distances >?100 km from the earthquake epicenters. We also consider two additional “prediction” but realistic intermediate-depth earthquake scenarios, and model their macroseismic distributions, to assess their expected damage impact in the broader southern Aegean area. The results suggest that intermediate-depth events, especially north of central Crete, have a prominent effect on a wide area of the outer Hellenic arc, with a very important impact on modern urban centers along northern Crete coasts (e.g. city of Heraklion), in excellent agreement with the available historical information.     

Ground-motion prediction equations for interface earthquakes of M7 to M9 based on empirical data from Japan

Ground motion prediction equations (GMPEs) have a major impact on seismic hazard estimates, because they control the predicted amplitudes of ground shaking. The prediction of ground-motion amplitudes due to mega-thrust earthquakes in subduction zones has been hampered by a paucity of empirical ground-motion data for the very large magnitudes (moment magnitude (M) $>$ 7) of most interest to hazard analysis. Recent data from Tohoku M9.0 2011 earthquake are important in this regard, as this is the largest well-recorded subduction event, and the only such event with sufficient data to enable a clear separation of the overall source, path and site effects. In this study, we use strong-ground-motion records from the M9 Tohoku event to derive an event-specific GMPE. We then extend this M9 GMPE to represent the shaking from other M $>$ 7 interface events in Japan by adjusting the source term. We focus on events in Japan to reduce ambiguity that results when combining data in different regions having different source, path and site effect attributes. Source levels (adjustment factors) for other Japanese events are determined as the average residuals of ground-motions with respect to the Tohoku GMPE, keeping all other coefficients fixed. The mean residuals (source terms) scale most steeply with magnitude at the lower frequencies; this is in accord with expectations based on overall source-scaling concepts. Interpolating source terms over the magnitude range of 7.0–9.0, we produce a GMPE for large interface events of M7–M9, for NEHRP B/C boundary site conditions (time-averaged shear-wave velocity of 760 m/s over the top 30 m) in both fore-arc and back-arc regions of Japan. We show how these equations may be adjusted to account for the deeper soil profiles (for the same value of $\hbox {V}_\mathrm{S30})$ in western North America. The proposed GMPE predicts lower motions at very long periods, higher motions at short periods, and similar motions at intermediate periods, relative to the simulation-based GMPE model of Atkinson and Macias (2009) for the Cascadia subduction zone.     

Bias and uncertainty in regression-calibrated models of groundwater flow in heterogeneous media

Groundwater models need to account for detailed but generally unknown spatial variability (heterogeneity) of the hydrogeologic model inputs. To address this problem we replace the large, m-dimensional stochastic vector β that reflects both small and large scales of heterogeneity in the inputs by a lumped or smoothed m-dimensional approximation γθ_∗, where γ is an interpolation matrix and θ_∗ is a stochastic vector of parameters. Vector θ_∗ has small enough dimension to allow its estimation with the available data. The consequence of the replacement is that model function f(γθ_∗) written in terms of the approximate inputs is in error with respect to the same model function written in terms of β, f(β), which is assumed to be nearly exact. The difference f(β) − f(γθ_∗), termed model error, is spatially correlated, generates prediction biases, and causes standard confidence and prediction intervals to be too small. Model error is accounted for in the weighted nonlinear regression methodology developed to estimate θ_∗ and assess model uncertainties by incorporating the second-moment matrix of the model errors into the weight matrix. Techniques developed by statisticians to analyze classical nonlinear regression methods are extended to analyze the revised method. The analysis develops analytical expressions for bias terms reflecting the interaction of model nonlinearity and model error, for correction factors needed to adjust the sizes of confidence and prediction intervals for this interaction, and for correction factors needed to adjust the sizes of confidence and prediction intervals for possible use of a diagonal weight matrix in place of the correct one. If terms expressing the degree of intrinsic nonlinearity for f(β) and f(γθ_∗) are small, then most of the biases are small and the correction factors are reduced in magnitude. Biases, correction factors, and confidence and prediction intervals were obtained for a test problem for which model error is large to test robustness of the methodology. Numerical results conform with the theoretical analysis.     

Multi-resolution adaptive modeling of groundwater flow and transport problems

Many groundwater flow and transport problems, especially those with sharp fronts, narrow transition zones, layers and fingers, require extensive computational resources. In this paper, we present a novel multi-resolution adaptive Fup approach to solve the above mentioned problems. Our numerical procedure is the Adaptive Fup Collocation Method (AFCM), based on Fup basis functions and designed through a method of lines (MOL). Fup basis functions are localized and infinitely differentiable functions with compact support and are related to more standard choices such as splines or wavelets. This method enables the adaptive multi-resolution approach to solve problems with different spatial and temporal scales with a desired level of accuracy using the entire family of Fup basis functions. In addition, the utilized collocation algorithm enables the mesh free approach with consistent velocity approximation and flux continuity due to properties of the Fup basis functions. The introduced numerical procedure was tested and verified by a few characteristic groundwater flow and transport problems, the Buckley–Leverett multiphase flow problem, the 1-D vertical density driven problem and the standard 2-D seawater intrusion benchmark–Henry problem. The results demonstrate that the method is robust and efficient particularly when describing sharp fronts and narrow transition zones changing in space and time.     

Upscaling unsaturated hydraulic parameters for flow through heterogeneous anisotropic sediments

We compare two methods for determining the upscaled water characteristics and saturation-dependent anisotropy in unsaturated hydraulic conductivity from a field-scale injection test. In both approaches an effective medium approximation is used to reduce a porous medium of M textures to an equivalent homogenous medium. The first approach is a phenomenological approach based on homogenization and assumes that moisture-based Richards’ equation can be treated like the convective–dispersive equation (CDE). The gravity term, dK_z(θ)/d(θ), analogous to the vertical convective velocity in the CDE, is determined from the temporal evolution of the plume centroid along the vertical coordinate allowing calculation of an upscaled K_z(θ). As with the dispersion tensor in the CDE, the rate of change of the second spatial moment in 3D space is used to calculate the water diffusivity tensor, D(θ), from which an upscaled K(θ) is calculated. The second approach uses the combined parameter scale inverse technique (CPSIT). Parameter scaling is used first to reduce the number of parameters to be estimated by a factor M. Upscaled parameters are then optimized by inverse modeling to produce an upscaled K(θ) characterized by a pore tortuosity–connectivity tensor, L. Parameters for individual textures are finally determined from the optimized parameters by inverse scaling using scale factors determined a priori. Both methods produced upscaled K(θ) that showed evidence of saturation dependent anisotropy. Flow predictions with the STOMP simulator, parameterized with upscaled parameters, were compared with field observations. Predictions based on the homogenization method were able to capture the mean plume behavior but could not reproduce the asymmetry caused by heterogeneity and lateral spreading. The CPSIT method captured the effects of heterogeneity and anisotropy and reduced the mean squared residual by nearly 90% compared to local-scale and upscaled parameters from the homogenization method. The Pacific Northwest National Laboratory is operated for the US Department of Energy by Battelle under Contract DE-AC05-76RL01830.     

Spatial relation between the tidal component of seismic noise and development zones of strong earthquakes (from long-term regular observations on the Kamchatka Peninsula)

The results of long-term studies of seismic noise before strong regional earthquakes on the Kamchatka Peninsula in 1992–2006 are presented. These results show that parameters of seismic noise variations caused by the tidal effect depend on the source position of the forthcoming earthquake. The reproducibility of the observed effects is demonstrated by the example of two strong deep (～200 km) subduction earthquakes with similar parameters that occurred on June 16, 2003 (M = 6.9), and on June 10, 2004 (M = 6.8). The physical mechanism of the synchronization of the tidal component extracted from high-frequency seismic noise with the wave of the gravitational tidal potential can be related to the possible development of near-surface dilatancy zones.     

Magnitude estimation of Koyna-Warna earthquakes, India

The paper presents the current state of magnitude estimation for Koyna earthquakes exceeding magnitude 3.0. We estimate coda duration magnitude from analogue seismograms recorded on the short period vertical (SPZ) seismometer at Hyderabad seismic observatory HYB and determine moment magnitude using very broad-band (VBB) data from the Geoscope station (HYB)and short period digital data from the local seismic network of NationalGeophysical Research Institute (NGRI) around the Koyna and Warna reservoirs.Firstly, the seismograms of 97 Koyna earthquakes exceeding magnitude 4.0 havebeen used to establish a new empirical coda duration magnitude scale which includes the higher order terms of log₁₀, where is the coda length in seconds. Four background noise levels (1, 2, 6 and 10 mm) areconsidered to estimate the coda duration. We found that the duration magnitudes for 1 mm background level are more stable than those for 2, 6 and 10 mm. The new coda duration magnitude (M_dnew) scale, for 1 mmlevel, is:M_dnew = –0.594 + 2.04 log₁₀ – 0.0435 (log₁₀)²The estimated M_dnew are compatible with the reported M_S values of the NGRI observatory and the m_b values of the United States Geological Survey (USGS). These magnitudes can be obtained within the standard deviation of ± 0.26 units of M_S (NGRI). A new relatively homogeneous catalog for Koyna earthquakes of M_dnew 4.0 is obtained. The momentmagnitudes for 34 Koyna-Warna events of M_dnew ranging from 3.0 to 5.4 have been estimated using two techniques. The first utilizes amplitudes of band-pass filtered (between 15 and 30 sec) velocity traces of moderate Koyna-Warna earthquakes of M_W} 4.4 to 5.4, we abbreviate the magnitude using M_A. The second is based on the S-wave spectrum of short period seismograms of local earthquakes (M_W < 3.8). Moment magnitudes estimated by spectral analysis mainly depend on the estimation of event's long-period spectral level and appears to saturate for moderate Koyna-Warnaearthquakes (M_W > 3.8). We recommend the use of both techniques whenever possible. The estimated moment magnitudes and M_dnew show an almost linear relationship with a standard deviation of ± 0.05.     

Activation of seismicity in Central and South Asia after the Makran earthquakes: Possible acceleration of preparation of large seismic events in the Tien Shan region

Two zones of seismicity (ten events with M _w = 7.0–7.7) stretching from Makran and the Eastern Himalaya to the Central and EasternTien Shan, respectively, formed over 11 years after the great Makran earthquake of 1945 (M _w = 8.1). Two large earthquakes (M _w = 7.7) hit theMakran area in 2013. In addition, two zones of seismicity (M ≥ 5.0) occurred 1–2 years after theMakran earthquake in September 24, 2013, stretching in the north-northeastern and north-northwestern directions. Two large Nepal earthquakes struck the southern extremity of the “eastern” zone (April 25, 2015, M _w = 7.8 and May 12, 2015, M _w = 7.3), and the Pamir earthquake (December 7, 2015, M _w = 7.2) occurred near Sarez Lake eastw of the “western” zone. The available data indicate an increase in subhorizontal stresses in the region under study, which should accelerate the possible preparation of a series of large earthquakes, primarily in the area of the Central Tien Shan, between 70° and 79° E, where no large earthquakes (M _w ≥ 7.0) have occurred since 1992.     

Determination of source parameters of strong earthquakes of Kamchatka,the Kurile Islands,and Japan from aftershock sequences

Aftershock sequences of some strong earthquakes of Kamchatka, the Kurile Islands, and Japan are examined. Such source parameters as the length L, along-dip width W, motion on fault D, and stress drop Δσ are determined from the aftershock sequences considered. The values of these parameters were obtained by the formal estimation of linear source parameters (lower bound estimates) and visually (upper bound estimates). The correlation dependences of the obtained parameters on the surface wave (M _S ) and seismic moment (M _W ) magnitudes are calculated.     

Scaling relations of moment magnitude,local magnitude,and duration magnitude for earthquakes originated in northeast India

In this study, we aim to improve the scaling between the moment magnitude (M _W), local magnitude (M _L), and the duration magnitude (M _D) for 162 earthquakes in Shillong-Mikir plateau and its adjoining region of northeast India by extending the M _W estimates to lower magnitude earthquakes using spectral analysis of P-waves from vertical component seismograms. The M _W-M _L and M _W-M _D relationships are determined by linear regression analysis. It is found that, M _W values can be considered consistent with M _L and M _D, within 0.1 and 0.2 magnitude units respectively, in 90 % of the cases. The scaling relationships investigated comply well with similar relationships in other regions in the world and in other seismogenic areas in the northeast India region.     

Re-visiting large historical earthquakes in the Colombian Eastern Cordillera

A re-assessment of the historic seismicity of the central sector of the Colombian Eastern Cordillera (EC) is made by revision of bibliographic sources, by calibration with modern instrumental earthquakes, and by interpretations in terms of current knowledge of the tectonics and seismicity of the region. Throughout the process we have derived an equation to estimate M_w for shallow crustal earthquakes in Colombia using the length of isoseismal VIII, L_VIII:

Triggering of repeated earthquakes

Based on the analysis of the world’s earthquakes with magnitudes M ≥ 6.5 for 1960–2013, it is shown that they cause global-scale coherent seismic oscillations which most distinctly manifest themselves in the period interval of 4–6 min during 1–3 days after the event. After these earthquakes, a repeated shock has an increased probability to occur in different seismically active regions located as far away as a few thousand km from the previous event, i.e., a remote interaction of seismic events takes place. The number of the repeated shocks N(t) decreases with time, which characterizes the memory of the lithosphere about the impact that has occurred. The time decay N(t) can be approximated by the linear, exponential, and powerlaw dependences. No distinct correlation between the spatial locations of the initial and repeated earthquakes is revealed. The probable triggering mechanisms of the remote interaction between the earthquakes are discussed. Surface seismic waves traveling several times around the Earth’s, coherent oscillations, and global source are the most preferable candidates. This may lead to the accumulation and coalescence of ruptures in the highly stressed or weakened domains of a seismically active region, which increases the probability of a repeated earthquake.     

Experience in registration of variations caused by strong earthquakes in the level and physicochemical parameters of ground waters in the piezometric wells: the case of Kamchatka

The hardware complex that was produced by OOO Polynom, Khabarovsk, for registration of the level, temperature, and electrical conductivity of ground water in wells and meteorological parameters (atmospheric pressure, air temperature) at a measurement frequency from 5 min to 1 h is described. The equipment is installed in the wells of Kamchatka and has been used for several years to register variations caused by earthquakes in the parameters of ground waters. Different variations in measured parameters of ground waters due to strong earthquakes of February 28, 2013, M _W = 6.8 and May 24, 2013, M _W = 8.3 are registered with this equipment in wells YuZ-5 and E-1. The registered variations and their systematization are described taking into account the mechanisms of a seismic impact on the state of the well–water-saturated rock system.     

Seismic performance of buildings during 2011 Van earthquakes and rebuilding efforts

The October 23, 2011 M7.2 Tabanli- Van and November 9, 2011 M5.2 Edremit – Van earthquakes caused damage in a widespread area across the Van province in Turkey. The ground motions, the damage caused by these earthquakes and the recent progress related to recovery efforts are presented herein. First, the key properties of the recorded strong ground motions like spectral amplitudes and directionality are evaluated. The observed damage in the affected reinforced concrete and masonry structures are discussed. The set of common structural damage mechanisms(i.e., soft story failure, torsional response due to plan irregularity, short column failure, pull out failure, pounding) observed in the damaged buildings were identified. The relationship between the key structural properties and the extent of damage is investigated. The primary loss drivers across the region were identified to be the poor quality of workmanship and improper use of building materials. The results from the investigation suggest that a large portion of the loss could have been prevented if sufficient attention and care were given to the implementation of the design regulations and in particular to the construction practice. Lastly, the recent progress in the ongoing rebuilding activities is presented.     

Laboratory Generated M -6 Earthquakes

We consider whether mm-scale earthquake-like seismic events generated in laboratory experiments are consistent with our understanding of the physics of larger earthquakes. This work focuses on a population of 48 very small shocks that are foreshocks and aftershocks of stick–slip events occurring on a 2.0 m by 0.4 m simulated strike-slip fault cut through a large granite sample. Unlike the larger stick–slip events that rupture the entirety of the simulated fault, the small foreshocks and aftershocks are contained events whose properties are controlled by the rigidity of the surrounding granite blocks rather than characteristics of the experimental apparatus. The large size of the experimental apparatus, high fidelity sensors, rigorous treatment of wave propagation effects, and in situ system calibration separates this study from traditional acoustic emission analyses and allows these sources to be studied with as much rigor as larger natural earthquakes. The tiny events have short (3–6 μs) rise times and are well modeled by simple double couple focal mechanisms that are consistent with left-lateral slip occurring on a mm-scale patch of the precut fault surface. The repeatability of the experiments indicates that they are the result of frictional processes on the simulated fault surface rather than grain crushing or fracture of fresh rock. Our waveform analysis shows no significant differences (other than size) between the M -7 to M -5.5 earthquakes reported here and larger natural earthquakes. Their source characteristics such as stress drop (1–10 MPa) appear to be entirely consistent with earthquake scaling laws derived for larger earthquakes.     

FCaZm intelligent recognition system for locating areas prone to strong earthquakes in the Andean and Caucasian mountain belts

The fuzzy clustering and zoning method (FCAZm) of systems analysis is suggested for recognizing the areas of the probable generation of the epicenters of significant, strong, and the strongest earthquakes. FCAZm is a modified version of the previous FCAZ algorithmic system, which is advanced by the creation of the blocks of artificial intelligence that develop the system-forming algorithms. FCAZm has been applied for recognizing areas where the epicenters of the strongest (M ≥ 7³/4) earthquakes within the Andes mountain belt in the South America and significant earthquakes (M ≥ 5) in the Caucasus can emerge. The reliability of the obtained results was assessed by the seismic-history type control experiments. The recognized highly seismic zones were compared with the ones previously recognized by the EPA method and by the initial version of the FCAZ system. The modified FCAZm system enabled us to pass from simple pattern recognition in the problem of recognizing the locations of the probable emergence of strong earthquakes to systems analysis. In particular, using FCAZm we managed to uniquely recognize a subsystem of highly seismically active zones from the nonempty complement using the exact boundary.