Stability and Grid Dispersion of the P-SV 4th-Order Staggered-Grid Finite-Difference Schemes

Stability and grid dispersion in the P-SV 4th-order in space, 2nd-order in time, displacement-stress staggered-grid finite-difference scheme is investigated in the case of a homogeneous unbounded medium. All results, however, also apply to the velocity-stress and displacement- velocity-stress finite-difference schemes. Independent stability conditions for the P and S waves are obtained by exact separation of equations for the two types of waves. Since the S-wave group velocity can differ from the actual velocity as much as 5% for the sampling ratio 1/5, commonly used in numerical modelling, the sampling of the minimum S wavelength by 6 grid spacings (with the velocity difference not larger than 2.5%) is recommended. Grid dispersion is strongest for a wave propagating in a direction of a coordinate axis and weakest for a wave propagating along a plane diagonal. Grid dispersion in the 4 ^th -order scheme for the sampling ratios s = 1/5 and s = 1/6 is smaller than grid dispersion in the 2 ^nd -order scheme for s = 1/10 and s = 1/12, respectively.     

3D Hybrid Ray-FD and DWN-FD Seismic Modeling for Simple Models Containing Complex Local Structures

Hybrid approaches find broad applications wherever all-in-one modelling of source, path, and site effects is too expensive. Our new 3D hybrid approach allows to compute the seismic wavefield in elastic isotropic models containing a complex local structure embedded in a large, but considerably simpler, regional structure. The hybrid modelling is realized in two successive steps.In the 1^st step, the ray or discrete wave number (DWN) method is used to compute the seismic wavefield due to the source and simple regional structure. The complex local structure is not present. Thus, the excitation contains the source and regional path effects. The time history of this wavefield (excitation), recorded at the points of so called excitation box, is stored on a disk. The excitation box envelopes a small portion of a computational domain.The 2^nd step of the hybrid method, now containing the complex local structure, is computed by finite differences (FD) inside the excitation box and its close vicinity. The excitation from the 1^st step is now used to inject the 1^st step wavefield into the 2^nd step computation. After that, the hybrid combination of the 1^st and 2^nd steps contains the source, regional path, and local structure effects at reasonably lower computational costs than in case of all-in-one modelling.The 3D ray-FD method is tested on models in which the locally complex structure is the well-known Volvi lake basin, embedded in various 1D structures. The wavefield is excited by the point source situated outside the basin. Although the structure outside the excitation box may be less dimensional (2D, 1D, homogeneous), the whole problem is actually 3D due to the 3D features of the structure inside the excitation box, 3D shape of the excitation box, and arbitrary source — excitation-box configuration. Simple (1D) structures outside the excitation box allow for comparison with the alternative hybrid DWN-FD results. However the ray method is suitable for computation of 3D regional structures outside the excitation box. The results from both approaches show a very good agreement for realistic crustal and local structural models.     

Efficient Methods to Simulate Planar Free Surface in the 3D 4th-Order Staggered-Grid Finite-Difference Schemes

We numerically tested accuracy of two formulations of Levander's (1988) stress-imaging technique for simulating a planar free surface in the 4^th-order staggered-grid finite-difference schemes. We have found that both formulations (one with normal stress-tensor components at the surface, the other with shear stress-tensor components at the surface) require at least 10 grid spacings per minimum wavelength ( _min÷h = 10) if Rayleigh waves are to be propagated without significant grid dispersion in the range of epicentral distances up to 15 _dom ^S.Because interior 4^th-order staggered-grid schemes usually do not require more than 6 grid spacings per minimum wavelength, in the considered range of epicentral distances, it was desirable to find alternative techniques to simulate a planar free surface, which would not require denser spatial sampling than _min÷h = 6. Therefore, we have developed and tested new techniques: 1. Combination of the stress imaging (with the shear stress-tensor components at the surface) with Rodrigues' (1993) vertically refined grid near the free surface. 2. Application of the adjusted finite-difference approximations to the z-derivatives at the grid points at and below the surface that uses no virtual values above the surface and no stress imaging. The normal stress-tensor components are at the surface in one formulation, while the shear stress-tensor components are at the surface in the other formulation.The three developed formulations give for the spatial sampling _min÷h = 6 results very close to those obtained by the discrete-wavenumber method. Because, however, the technique with the vertically refined grid near the free surface requires 3 times smaller time step (due to the refined grid), the technique with adjusted finite-difference approximations is the most accurate and efficient technique from the examined formulations in the homogeneous halfspace.     

从溧阳六级地震的前兆特征讨论中强震的预报问题

扬州～铜陵地震带位于大华北强震活动区和华南地震相对平静区的交接部位,中强震比较活跃。由于中强震震源应力场作用范围有限,时间不长,每个中强震的前兆有其相对的独立性——很少受大华北强震与本区其他中强震的影响。这就为检验前兆的准确性提供了较好的环境。1979年7月9日溧阳六级地震后经历了一年多时间的检验,我们将其较可靠的前兆     

Foreshock sequence of September 26th, 1997 Umbria-Marche earthquakes

On September 3^rd (22:07 UTC), 1997 a small earthquake with Mw=4.54 started the foreshocks sequence (1500 events with M_L <3.1) of the September 26^th seismic sequence. Two days after, three seismic stations of the University of Camerino were installed around the macroseismic epicenter of the foreshock. We present in this paper the location of foreshocks (with 2.1L<3.3) which occurred between September 3^rd and 26^th. Foreshocks location, with horizontal (ERH) and vertical (ERZ) error less than 1.5 km, define an area 4 km large. Foreshocks have been localized between the epicenters of the two major events of September 26^th, which occurred at 00:33 UTC with Mw=5.6 and at 09:40 UTC with Mw=6.0 (Amato et al., 1998; Ekström et al., 1998). In a vertical cross-section, hypocenters show a low angle (30^°) structure with SW dip-direction. Focal mechanisms for three of the major events show dip-slip fault solutions with strike direction of about N130, in agreement with the CMT solutions of September 3^rd and September 26^th earthquakes (Ekström et al., 1998). Data recorded at two stations Popola (POP) e Capodacqua (CPQ) located on the rupture area of the September 26^th faults, allowed us to calculate a mean Vp/Vs ratio of 1.84±0.03 for the foreshock. This value is lower than the Vp/Vs ratio of 1.89±0.02 calculated for the aftershock sequence occurred in the same area. Besides, the Vp/Vs ratio during the foreshocks sequence is not stable in time but it seems to increase approaching September 26^th. After September 26^th mainshocks, this value tends to stabilize around a higher value of 1.89. Following the dilatancy model, we suggest that the relative low Vp/Vs ratio before the main shocks could indicate the presence of fluid in the focal volume. The presence of fluids could have increased the effective stress on the fault plane and could be responsible for the long foreshock activity before the two main earthquakes of September 26^th. Therefore, we suggest that this foreshock activity could have also contributed to reduce the friction along the September 26^th fault plane, breaking the active structure in two smaller segments. In this hypothesis, foreshock activity could have drastically contributed to mitigate the seismic potential of the Colfiorito's active structure.     

L'assorbimento della radiazione solare da parte di uno strato di polveri vulcaniche

Riassunto Servendosi dei risultati ottenuti in precedenti lavori, si perviene alle equazioni che regolano la propagazione dei raggi solari attraverso ad uno strato di polveri vulcaniche le quali, applicate ai dati forniti dalle osservazioni effettuate nell'estate e nell'autunno 1912, dopo il violento parossismo del Katmai, hanno permesso di pervenire alle conclusioni seguenti: 1^o) lo strato di polveri dovette essere tale da contenere circa 15×10⁶ granuli in un cilindro ad asse verticale, di altezza uguale allo spessore dello strato e di sezione 1 cm², numero circa 44 volte più grande di quello determinato dall'Humphreys con altro metodo assai più semplificato applicato alle medesime osservazioni del 1912; 2^o) ammettendo come probabile uno spessore equivalente di 1 Km per lo strato, il numero di granuli per cm³ risulta di circa 150.

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Summary Using the results obtained in preceding investigations we arrived to the equations of propagation of the solar beams through a layer of volcanic dusts. These equations applied to the data furnished by the observations made in the summer and autumn of 1912 after the violent Katmai paroxysm, brought to the following conclusions: 1 ^st ) the layer of dusts had to be such to contain approximately 15×10⁶ granules in a vertical cylinder of a height equal to the thickness and with a section of 1 cm², number about 44 times higher than the one obtained byHumphreys with a much more simplified method applied to the same observations of 1912; 2 ^nd ) assuming as likely an equivalent thickness of 1 Km for the layer, the number of granules for each cm³ results to be about 150.

     

Effects of substorms on the stormtime ring current index Dst

There has been some discussion in recent times regarding whether or not substorm expansive phase activity plays any role of importance in the formation of the stormtime ring current. I explore this question using the K_p index as a proxy for substorm expansive phase activity and the D_st index as a proxy for symmetric ring current strength. I find that increases in D_st are mildly related to the strength of substorm expansive phase activity during the development of the storm main phase. More surprisingly, I find that the strength of D_st during the storm recovery phase is positively correlated with the strength of substorm expansive phase activity. This result has an important bearing on the question of how much the Dst index reflects activity other than that of the stormtime symmetric ring current strength for which it is supposed to be a proxy.     

重力剖面和激电测深联合勘测在涡河断裂研究中的应用

为查明涡河断裂的位置、性质等参数,选择重力剖面和激电测深联合勘测方法,对指定区域进行物探勘测工作。结果表明:由密度差异引起的重力异常位置和岩石电阻率、极化率异常位置基本吻合,说明以重力剖面和激电测深为手段的联合勘测是查找断裂的有效方法。     

RECURSIVE MIGRATION IN THREE DIMENSIONS*

A simple theory is presented to derive explicit recursive migration schemes in three dimensions which are suitable for situations with lateral velocity variations. The proposed schemes can be realized by one-dimensional convolutions along the x-axis and y-axis. An investigation is made on the errors of each scheme. For each frequency component the amplitude error and the phase error are computed as a function of the immergence angle (dip). Based on the error analysis a critical discussion is given on the stability of explicit schemes.     

Predicting geomagnetic storms from solar-wind data using time-delay neural networks

We have used time-delay feed-forward neural networks to compute the geomagnetic-activity index D_st one hour ahead from a temporal sequence of solar-wind data. The input data include solar-wind density n, velocity V and the southward component B_z of the interplanetary magnetic field. D_st is not included in the input data. The networks implement an explicit functional relationship between the solar wind and the geomagnetic disturbance, including both direct and time-delayed non-linear relations. In this study we especially consider the influence of varying the temporal size of the input-data sequence. The networks are trained on data covering 6600 h, and tested on data covering 2100 h. It is found that the initial and main phases of geomagnetic storms are well predicted, almost independent of the length of the input-data sequence. However, to predict the recovery phase, we have to use up to 20 h of solar-wind input data. The recovery phase is mainly governed by the ring-current loss processes, and is very much dependent on the ring-current history, and thus also the solar-wind history. With due consideration of the time history when optimizing the networks, we can reproduce 84% of the D_st variance.     

Prediction of variations from Polar Cap indices using time-delay neural network

The hourly averaged Polar Cap (PC) index was used as the input parameter for the ring current index D_st variation forecasting. The PC index is known to describe well the principal features of the interplanetary magnetic field as well as the total energy input to the magnetosphere. This allowed us to design a neural network that was able to forecast the D_st variations 1 h ahead. 1995 PC and D_st data sets were used for training and testing and 1997 data sets were used for validation. From 15 moderate and strong geomagnetic storms observed during 1997, 10 were successfully forecasted. In 3 cases the observed minimum D_st value was less than the predicted value, and only in 3 cases the neural network was not able to reproduce the features of the geomagnetic storm.     

Effects of site geology on seismic ground motion: early history

This is the 6^th contribution in the series of Historical Notes on seminal concepts in earthquake engineering and structural dynamics. It documents the origins and early developments (from the 1880s through 1992) of the effects of site geology on seismic ground motion. Copyright © 2014 John Wiley & Sons, Ltd.     

Geochemistry of the Submarine Gaseous Emissions of Panarea (Aeolian Islands, Southern Italy): Magmatic vs. Hydrothermal Origin and Implications for Volcanic Surveillance

The marine sector surrounding Panarea Island (Aeolian Islands, South Italy) is affected by widespread submarine emissions of CO₂ -rich gases and thermal water discharges which have been known since the Roman Age. On November 3^rd, 2002 an anomalous degassing event affected the area, probably in response to a submarine explosion. The concentrations of minor reactive gases (CO, CH₄ and H₂) of samples collected in November and December, 2002 show drastic compositional changes when compared to previous samples collected from the same area in the 1980s. In particular the samples collected after the November 3^rd phenomenon display relative increases in H₂ and CO and a strong decrease in the CH₄ contents, while other gas species show no significant change. The interaction of the original gas with seawater explains the variable contents of CO₂, H₂S, N₂, Ar and He which characterize the different samples, but cannot explain the large variations of CO, CH₄ and H₂ which are instead compatible with changes in the redox, temperature and pressure conditions of the system. Two models, both implying an increasing input of magmatic fluids are compatible with the observed variations of minor reactive species. In the first one, the input of magmatic fluids drives the hydrothermal system towards atypical (more oxidizing) redox conditions, slowly pressurizing the system up to a critical state. In the second one, the hydrothermal system is flashed by the rising high-T volcanic fluid, suddenly released by a magmatic body at depth. The two models have different implications for volcanic surveillance and risk assessment: In the first case, the November 3^rd event may represent both the culmination of a relatively slow process which caused the overpressurization of the hydrothermal system and the beginning of a new phase of quiescence. The possible evolution of the second model is unforeseeable because it is mainly related to the thermal, baric and compositional state of the deep magmatic system that is poorly known.     

Prediction of geomagnetic storms from solar wind data with the use of a neural network

An artificial feed-forward neural network with one hidden layer and error back-propagation learning is used to predict the geomagnetic activity index (D_st) one hour in advance. The B_z-component and _Bz, the density, and the velocity of the solar wind are used as input to the network. The network is trained on data covering a total of 8700 h, extracted from the 25-year period from 1963 to 1987, taken from the NSSDC data base. The performance of the network is examined with test data, not included in the training set, which covers 386 h and includes four different storms. Whilst the network predicts the initial and main phase well, the recovery phase is not modelled correctly, implying that a single hidden layer error back-propagation network is not enough, if the measured D_st is not available instantaneously. The performance of the network is independent of whether the raw parameters are used, or the electric field and square root of the dynamical pressure.     

Edge‐, bottom‐, and Rossby waves in a rotating stratified fluid

Abstract

It is found that in a rotating stratified fluid bounded by a single rigid wall, edge waves may occur at all frequencies less than or equal to N sin a (a is the angle of the wall from the horizontal and N the Brunt‐Vaisala frequency). These decay exponentially away from the boundary, in a distance of O(S) wavelengths, for α = O(1), or O(S ^‐1) wavelengths, for αS ≤ O(1), where S is the ratio of N to the Coriolis parameter f, taken for illustration to be large. The phase and energy both move with a component to the left, facing shallow water. The waves could, for example, appear as an internal tide at the continental rise or as baroclinic meandering of currents over a slope.

The low‐frequency limit, αS ? 1, is studied in detail. To allow for large scales of motion other rigid boundaries and variations in f are included. The edge (actually “bottom") waves then merge with topographic‐planetary waves as the wavelengths increase; the familiar depth‐independent mode is found to be possible in the sea for wavelengths exceeding about 450 km. The ß‐effect introduces modes complementary to that trapped at the bottom, which instead are isolated from it.     

Nonlinear internal waves in ideal rotating basins

Abstract

Starting from Euler's equations of motion a nonlinear model for internal waves in fluids is developed by an appropriate scaling and a vertical integration over two layers of different but constant density. The model allows the barotropic and the first baroclinic mode to be calculated. In addition to the nonlinear advective terms dispersion and Coriolis force due to the Earth's rotation are taken into account. The model equations are solved numerically by an implicit finite difference scheme. In this paper we discuss the results for ideal basins: the effects of nonlinear terms, dispersion and Coriolis force, the mechanism of wind forcing, the evolution of Kelvin waves and the corresponding transport of particles and, finally, wave propagation over variable topography. First applications to Lake Constance are shown, but a detailed analysis is deferred to a second paper [Bauer et al. (1994)].     

An analytical study of general hyper-diffusivity and barotropic eddies

An exact solution to the barotropic potential vorticity equation is used to examine the properties of barotropic vortices under arbitrary nth-order hyper-diffusivity. Analytical expressions are derived for an eddy's lifetime, meridional drift, decay in size, and energy, as functions of the Coriolis parameter, order and magnitude of diffusivity, and the eddy's size, shape and strength. These expressions provide a simple explanation for many observed features of oceanic and atmospheric vortices. For example, the competition between the Coriolis effect and eddy strength in giving permitted eddy geometries; the bias towards a zonal anisotropy for large vortices but not for small ones; energetic preference for axisymmetry; poleward meridional drift of cyclonic vortices; and meridional speed variation depending on eddy geometry and strength.     

Sensitivity of Typhoon Vamei (2001) Simulation to Planetary Boundary Layer Parameterization Using PSU/NCAR MM5

This paper investigates the sensitivity of the numerical simulations of a near equatorial Typhoon Vamei (2001) to various planetary boundary layer (PBL) parameterization schemes in the Pennsylvania State University (PSU)/National Centre for Atmospheric Research (NCAR) non-hydrostatic mesoscale model (MM5). The numerical simulations are conducted on two domains at 45 and 15 km grids nested in a one-way fashion. Four different PBL parameterization schemes including the Blackadar (BLK) scheme, the Burk–Thompson (BURKT) scheme, the NCEP Eta model scheme and the NCEP medium range forecast (MRF) model scheme are investigated. Results indicate that the intensity and propagation track of the simulated near equatorial typhoon system is not very sensitive to the different PBL treatments. The simulated minimum central pressures and the maximum surface wind speeds differ by only 5–6 hPa and 6–8 ms⁻¹, respectively. Larger variations between the simulations occur during the weakening phase of the typhoon system. While all schemes simulated the typhoon with reasonable accuracy, the ETA scheme produces the strongest storm intensity with the largest heat exchanges over the marine environment and the highest warm moisture air content in the PBL around the core of the storm.     

Response of secondary systems in structures subjected to transient excitation

An analytical method, based on matrix perturbation theory, is developed whereby a simple estimate can be obtained of the maximum dynamic response of lightly damped, light equipment (modelled as a n(²)-degree-of-freedom system) attached to a structure (modelled as a n(¹)-degree-of-freedom system) subjected to ground motion or impact. A natural frequency of the equipment is considered close or equal to a natural frequency of the structure. It is assumed that the information available to the designer is a time history of the ground motion or impact, or an associated design spectrum; the fixed base modal properties of the structure; and the fixed base modal properties of the equipment. The method employed avoids the direct conventional analysis of a n(²) + n(¹)-degree-of-freedom system either by modal or by matrix time-marching methods; as well as errors in estimates of peak response due to the possible unreliability of numerical schemes because of the lightness of the equipment, or due to uncertainty as to the appropriate procedure for summing the contributions of the two closely spaced modes which occur in the system. The proposed procedure is demonstrated for an example equipment-structure system. Computed results based on the method are in close agreement with results obtained through a Newmark time-integration scheme.