Green’s function of the linearized Saint-Venant equations in laminar and turbulent flows

In the present paper, an analytical expression of the Green’s function of linearized Saint-Venant equations (LSVEs) for shallow water waves is provided and applied to analyse the propagation of a perturbation superposed to a uniform flow. Independently of the kinematic character of the base flow, i.e., subcritical or supercritical uniform flow, the effects of a non-uniform vertical velocity profile and a non-constant resistance coefficient are accounted for. The use of the Darcy-Weisbach friction law allows a unified treatment of both laminar and turbulent conditions. The influence on the wave evolution of the wall roughness and the fluid viscosity are finally discussed, showing that in turbulent regime the assumption of constant friction coefficient may lead to an underestimation of both amplification and damping factors on the wave fronts, especially at low Reynolds numbers. This conclusion has to be accounted for, particularly in describing hyper-concentrated suspensions or other kinds of Newtonian mixtures, for which the high values of the kinematic viscosity may lead to relatively low Reynolds numbers.     

The algorithms for calculating synthetic seismograms from a dipole source using the derivatives of Green’s function

The problem of calculating complete synthetic seismograms from a point dipole with an arbitrary seismic moment tensor in a plane parallel medium composed of homogeneous elastic isotropic layers is considered. It is established that the solutions of the system of ordinary differential equations for the motion–stress vector have a reciprocity property, which allows obtaining a compact formula for the derivative of the motion vector with respect to the source depth. The reciprocity theorem for Green’s functions with respect to the interchange of the source and receiver is obtained for a medium with cylindrical boundary. The differentiation of Green’s functions with respect to the coordinates of the source leads to the same calculation formulas as the algorithm developed in the previous work (Pavlov, 2013). A new algorithm appears when the derivatives with respect to the horizontal coordinates of the source is replaced by the derivatives with respect to the horizontal coordinates of the receiver (with the minus sign). This algorithm is more transparent, compact, and economic than the previous one. It requires calculating the wavenumbers associated with Bessel function’s roots of order 0 and order 1, whereas the previous algorithm additionally requires the second order roots.     

The 2014 Mihoub earthquake (Mw4.3), northern Algeria: empirical Green’s function analysis of the mainshock and the largest aftershock

On November 15, 2014, an Mw4.3 earthquake occurred 2 km west of Mihoub village, 60 km SE of Algiers. In this study, we retrieve the relative source-time functions of the mainshock and largest aftershock (Mw3.9) for rupture analysis using the empirical Green’s function method. The two events are nearly colocated with a smaller aftershock (Mw3.5), which is treated as the empirical Green’s function. Moreover, these three events have similar focal mechanisms, suggesting that deconvolution is well posed in this case. The three events were recorded by nine stations of the Algerian permanent network. We use mainly P-wave data. The focal mechanism solution shows dominant reverse faulting with a strong strike-slip component. The two nodal planes align almost E-W, dipping to the south, and NNE-SSW, dipping to the NW, respectively; the fault and auxiliary planes cannot be resolved from hypocenter locations alone because too few aftershocks were recorded by the permanent network. The results show unilateral rupture propagation to the ENE and complex rupture with multiple episodes for the mainshock. The largest aftershock shows similar behavior with slightly less pronounced directivity at some sites. The rupture directivity for the mainshock is estimated at about N66° E, and the rupture velocity is Vr = 0.66β. The E-W nodal plane of the best-fit focal mechanism is the preferred fault plane because it best agrees with the directivity direction and is consistent with the E-W faulting that dominates in the region.     

High-resolution optical dating of Late Holocene storm surge deposits – a showcase from Schokland (Noordoostpolder,the Netherlands)

Storm surges have a major impact on land use and human habitation in coastal regions. Our knowledge of this impact can be improved by correlating long-term historical storm records with sedimentary evidence of storm surges, but so far few studies have applied such an approach. Here we apply, for the first time, state-of-the-art optically stimulating luminescence (OSL) methods to obtain high-resolution age information on a sequence of Late Holocene storm surge deposits. By combining this chronological framework of storm surges with other reconstruction methods, we investigate the storm surge impact on the former island Schokland, located in a former inlet of the North Sea (central Netherlands).During the Late Holocene, Schokland transformed from a peat area that gradually inundated (~800 CE) via an island in a marginal marine environment (~1600 CE) to a land-locked island in the reclaimed Province of Flevoland (1942 CE). These transitions are recorded in the sediment archive of the island, consisting of silty clay with sandy intervals deposited during storm surges. A series of ten quartz OSL ages, obtained using best-practice methods to deal with incomplete resetting of the OSL signal and dose rate heterogeneity, reveal two periods of storm surge deposition, around 1600 CE and between 1742 and 1822 CE. Historical sources indicate that major storm surges hit Schokland during these periods. Laboratory analyses (thermogravimetry, grain-size, foraminifera, bivalves and ostracods) corroborates the existence of the two sets of storm surge deposits within the clay sequence. Our study sets a benchmark for obtaining robust depositional age constraints from storm surge sediments, and demonstrates the great potential of modern OSL methods to contribute to improved assessment of storm surge risk. © 2018 John Wiley & Sons, Ltd.     

Numerical modeling of the impact of hurricanes on ocean dynamics: sensitivity of the Gulf Stream response to storm’s track

Ocean Dynamics - The study is focused on the disruption that a storm can cause to ocean stratification and ocean currents in a region dominated by a western boundary current and meso-scale...     

Strong ground motion simulation of the 2003 Bam, Iran, earthquake using the empirical Green’s function method

The 2003 Bam, Iran, earthquake caused catastrophic damage to the city of Bam and neighboring villages. Given its magnitude (M _w ) of 6.5, the damage was remarkably large. Large-amplitude ground motions were recorded at the Bam accelerograph station in the center of Bam city by the Building and Housing Research Center (BHRC) of Iran. We simulated the Bam earthquake acceleration records at three BHRC strong-motion stations—Bam, Abaraq, and Mohammad-Abad—by the empirical Green’s function method. Three aftershocks were used as empirical Green’s functions. The frequency range of the empirical Green’s function simulations was 0.5–10 Hz. The size of the strong motion generation area of the mainshock was estimated to be 11 km in length by 7 km in width. To estimate the parameters of the strong motion generation area, we used 1D and 2D velocity structures across the fault and a combined source model. The empirical Green’s function method using a combination of aftershocks produced a source model that reproduced ground motions with the best fit to the observed waveforms. This may be attributed to the existence of two distinct rupture mechanisms in the strong motion generation area. We found that the rupture starting point for which the simulated waveforms best fit the observed ones was near the center of the strong motion generation area, which reproduced near-source ground motions in a broadband frequency range. The estimated strong motion generation area could explain the observed damaging ground motion at the Bam station. This suggests that estimating the source characteristics of the Bam earthquake is very important in understanding the causes of the earthquake damage.     

Numerical Green’s function method:Application to quantifying ground motion variations of M7 earthquakes

The concept of "numerical Green’s functions" (NGF or Green’s function database) is developed. The basic idea is: a large seismic fault is divided into subfaults of appropriate size, for which synthetic Green’s functions at the surface (NGF) are calculated and stored. Consequently, ground motions from arbitrary kinematic sources can be simulated, rapidly, for the whole fault or parts of it by superposition. The target fault is a simplified, vertical model of the Newport-Inglewood fault in the Los Angeles basin. This approach and its functionality are illustrated by investigating the variations of ground motions (e.g. peak ground velocity and synthetic seismograms) due to the source complexity. The source complexities are considered with two respects: hypocenter location and slip history. The results show a complex behavior, with dependence of absolute peak ground velocity and their variation on source process directionality, hypocenter location, local structure, and static slip asperity location. We concluded that combining effect due to 3-D structure and finite-source is necessary to quan- tify ground motion characteristics and their variations. Our results will facilitate the earthquake hazard assessment projects.     

The 11-year solar cycle,the sun’s rotation,and the middle stratosphere in winter: Part I: Response of zonal means

The effect of the 11-year solar cycle on the response of the stratospheric geopotential height and temperature fields at 10 and 30 hPa in winter to solar activity oscillations with periods related to the period of the Sun’s rotation (27.2 days) is discussed, applying methods of statistical spectral analysis to daily data for the period from 1965 to 1996. Atmospheric responses for three periodicities — 27.2 days (period of the Sun’s rotation), 25.3 days (periodicity caused by the modulation of the 27.2 days oscillation by annual atmospheric variation), and 54.4 days (doubled period of the solar rotation) — are studied. A significant effect of the 11-year solar cycle on the atmospheric response to the 27.2 days solar periodicity has not been found. We explain it by a frequency shift of the response from the 27.2 days to the 25.3 days periodicity via amplitude modulation. For the 25.3 days oscillation, prominent differences between the maximum and minimum of the 11-year solar cycle have been found in the coherence between the 10.7 cm solar radio flux and the height/temperature fields: the relationships are stronger at solar maximum than at the minimum of the 11-year cycle. The same differences, but to a greater extent, are revealed for the oscillation with a period of 54.4 days. Coherence and amplitude estimates for this doubled solar rotation periodicity exhibit strong differences between extrema of the 11-year solar cycle. Phase estimates also demonstrate a clear difference between high and low solar activity: on the average, the delay of the atmospheric response after the solar signal is smaller at solar maximum than at solar minimum. Thus, we conclude that the mechanism of the influence of the 11-year solar cycle on the winter middle stratosphere can include both a direct effect of the frequency corresponding to the doubled solar rotation periodicity and an indirect effect of modulation of the intensity of the interaction between the solar 27.2 days oscillation and seasonal atmospheric variations.     

Joy’s law and its features according to the data of three sunspot catalogs

This paper investigates the trend towards an increase in the tilt of sunspot groups with increasing latitude (Joy??s law) and the relationship between the features of this law and solar activity parameters. In addition to the known data of the Mount Wilson and Kodaikanal observatories, the analysis uses the Pulkovo database of solar activity, which allows for the estimation of the reliability of the conclusions obtained by other authors from the first two catalogs. It is shown that Joy??s law is manifested in all three data series and has many features in common. In particular at latitudes above 25?C30°, the tilt of sunspot groups is not linearly dependent on latitude and displays a slight decrease. However, some features of this law found previously in the data of the first two observatories (e.g., a decrease in its strength with an increase in the strength of the solar cycle) are not confirmed by our analysis.     

Fault-block structure and the stress state of the upper crust of lake Baikal’s eastern coast (field observations and modeling)

The fault-block structure and stress state of the upper crust at one of the sites of the Baikal rift (Ust-Barguzin fault node) is studied on the basis of a complex of geomorphological, geological-structural, and tectonophysical methods. A map reflecting specific features of the fault-block structure of the upper crust in the region under investigation is compiled. In situ data are collected, and the stress state is reconstructed from residual deformations in local rock volumes. Systematization of the reconstructed stress fields with respect to ruptures of various ranks made it possible to reveal specific features of the stress state of the upper crust of the region associated with its fault-block structure. Optical modeling of the stress state was performed both for the area of the Ust-Barguzin fault node as a whole (regional structure) and for the vicinity of conjugation zones of lower-rank ruptures (local structures) composing zones of regional faults. It is shown that stress changes in the areas of fault conjugation nodes, both in value and in the strike of the principal axes, can be caused by the cooperative behavior of ruptures during the activation in the zone of influence of a larger fault or a fault node.     

Correctives to the scheme of the Earth’s structure inferred from new data on nutation,tides, and free oscillations

When analyzing the new high-accuracy observations of the forced nutation and tidal variations in the acceleration of gravity, it was found that they are in sharp contradiction to the present-day models of the Earth’s interior based on seismic data and the data on the periods and damping constants of the free oscillations of the Earth. The elimination of these contradictions requires analyzing the uniqueness of the interpretation of the free oscillations of the Earth, taking into account the new data.     

The 2010–2012 eruption of Kizimen Volcano: The greatest output (from the data of remote-sensing observations) for eruptions in Kamchatka in the early 21st century part I. The November 11, 2010 to December 11, 2011 phase

This paper presents the results from the detailed analysis of aerial photographs and space images for the Kizimen area, which characterize the geologic and geomorphologic effects of the ongoing eruption over the 2010–2011 period. It is shown that the total volume (>0.5 km³) and total mass (>10⁹ t) of the discharged (resurgent plus juvenile) material makes this eruption the most productive in Kamchatka for the first 12 years of the 21st century. The dominant component (>90%) is juvenile material with andesitic composition. The pyroclastics (tephra, deposits of the juvenile pyroclastic avalanches and incandescent debris avalanches) comprise >0.3 km³and >0.45× 10⁹ t, the lava (a very thick block lava flow 3.052 km long and 2.163 km² in area) occupies about 0.195 km³ and 0.45 × 10⁹ t. With the exception of the tephra, which fell over an area of about 100000 km², the rest of the material was accumulated on the Kizimen cone and at its base. The mean discharge rate of juvenile ejecta was about 15 m³/s (29 t/s) for 13 months (November 11, 2010 to December 11, 2011). Appreciable changes also occurred at the near-summit part of the volcano’s cone.     

Modeling the strong ground motion and rupture characteristics of the March 31, 2006, Darb-e-Astane earthquake,Iran, using a hybrid of near-field SH-wave and empirical Green’s function method

We analyze the strong motion accelerograms of the moderate (M _w = 6.1), March 31, 2006, Darb-e-Astane earthquake of western Iran and also those of one of its prominently recorded, large (M _w = 5.1) foreshock and (M _w = 4.9) aftershock. (1) Using derived SH-wave spectral data, we first objectively estimate the parameters W _o\mathit{\Omega} _{\rm o} (long period spectral level), f _c (corner frequency) and Q(f) (frequency dependent, average shear wave quality factor), appropriate for the best-fit Brune ω ^− 2 spectrum of each of these three events. We then perform a non-linear least square analysis of the SH-wave spectral data to provide approximate near-field estimates of the strike, dip, and rake of the causative faults and also the seismic moment, moment magnitude, source size, and average stress drop of these three events. (2) In the next step, we use these approximate values and an empirical Green’s function approach, in an iterative manner, to optimally model the strong ground motion and rupture characteristics of the main event in terms of peak ground acceleration/velocity/displacement and duration of ground shaking and thereby provide improved, more reliable estimates of the causative fault parameters of the main event and its asperities. Our near-field estimates for both the main moderate event and the two smaller events are in good conformity with the corresponding far-field estimates reported by other studies.     

Ground motion prediction in Beirut: a multi-step procedure coupling empirical Green’s functions,ground motion prediction equations and instrumental transfer functions

The strike slip Yammouneh fault is the longest fault in Lebanon, crossing the territory from South to North. It was responsible for major historical earthquakes like the 1202 A.D. earthquake, estimated to M_s7.6. This paper presents a site-specific estimation of the ground motion caused by a potential M_w7.5 earthquake on the Yammouneh fault, similar to the 1202 event, for various sites within the Beirut area. The empirical Green’s function technique EGF is used to estimate the median and the standard deviations of the seismic ground motion at the reference station BHL, taking into account epistemic and aleatory uncertainties related to source parameters. These uncertainties were quantified through a sensitivity analysis of the position of the rupture nucleation X_nuc, the slip roughness parameter K, the corner frequency f_c and the magnitude M_c of the EGF. The rock ground motion is then transferred to various other sites within the Beirut area, using instrumental Fourier transfer functions. Site amplification factors are next deduced by computing the ratio between response spectra at sediment sites and at a reference rock station. Considering the limits of the EGF method in the near field of extended sources, the EGF approach is considered only up to a magnitude M_w of 6.5. Selected Ground Motion Predictive Equations are then used to simulate a M_w7.5 event at a reference station. By applying the amplification factors, the response spectra at the different sites of Beirut are also calculated and compared with the actual response spectra used in the Lebanese regulations.     

Palaeo- and rock-magnetic investigations across Jurassic-Cretaceous boundary at St Bertrand’s Spring,Drôme,France: applications to magnetostratigraphy

Palaeo- and rock-magnetic investigations of the St Bertrand’s Spring (Le Ravin de Font de St Bertrand) locality in France were carried out in order to contribute to, and improve, the stratigraphy of the Jurassic-Cretaceous boundary interval. Magnetic susceptibility shows slightly diamagnetic behaviour in the lowermost part of the profile and an increase (paramagnetic) towards its middle and upper parts. Rock-magnetic measurements throughout the section show magnetite as the main magnetic fraction, together with traces of hematite. Additionally, thermal demagnetization indicates the presence of goethite. Our magnetostratigraphy indicates three normal/reversed polarity sequences; possibly encompassing the magnetozones M19r to the M17n. This suggests that the St Bertrand section straddles the Tithonian/Berriasian boundary and reaches the middle Berriasian sensu lato.