Comparison of Seismic Dispersion and Attenuation Models

The frequency-dependent attenuation of seismic waves causes decreased resolution of seismic images with depth, and the difference in transmission losses induces amplitude variations with offset. Transmission losses may occur due to friction or fluid movement, or may result from scattering in thin-layer. Whatever the physical mechanism, they can often be conveniently described using an empirical formulation wherein the elastic moduli and propagation velocity are complex functions of frequency.We have compiled and compared algebraically and numerically eight different models involving complex velocity: the Kolsky-Futterman model, the power-law model, Kjartansson's model, Müller's model, Azimi's second and third model, the Cole-Cole model, and the standard linear-solid model.For two different parameter sets, the attenuation and phase velocity are computed in the seismic frequency band, and the plane-wave propagation of a Ricker wavelet for the other models is compared with that for the Kolsky-Futterman model. The first parameter set consists of parameters for each of the models calculated from expressions given in the appendix. These expressions make the different models behave similarly to the KF model. The second parameter set consists of model parameters that are numerically adapted to the KF model.By selecting proper parameters, all models, except the standard linear-solid model, show behavior similar to that of the Kolsky-Futterman model. The SLS model behaves differently from the other models as the frequency goes to zero or infinity. Broadband measurement data is needed to select a specific model for a given seismic experiment.     

Erratum: Comparison of Seismic Dispersion and Attenuation Models: Stud. Geophys. Geod., 46(2002), 293-320

Studia Geophysica et Geodaetica -     

On the circulation in the East Frisian Wadden Sea: numerical modeling and data analysis

 In this paper we use a combination of numerical modeling and data analysis to gain a better understanding of the major characteristics of the circulation in the East Frisian Wadden Sea. In particular, we concentrate on the asymmetry of the tidal wave and its modulation in the coastal area, which results in a complex pattern of responses to the sea-level forcing from the North Sea. The numerical simulations are based on the 3-D primitive equation General Estuarine Transport Model (GETM) with a horizontal resolution of 200 m and terrain-following vertical coordinates. The model is forced at its open boundaries with sea-level data from an operational model for the German Bight (German Hydrographic Office). The validation data for our model simulations include time series of tidal gauge data and surface currents measured at a pile in the back-barrier basin of the Island Langeoog, as well as several ADCP transects in the Accumer Ee tidal inlet. Circulation and turbulence characteristics are investigated for typical situations driven by spring and neap tides, and the analysis is focused on dominating temporal and spatial patterns. By investigating the response of five back-barrier basins with rather different morphologies to external forcing, an attempt is made to elucidate the dominating physical balances controlling the circulation in the individual sub-basins. It is demonstrated that the friction at the seabed tends to slow down the tidal signal in the shallow water. This leads to the establishment of flood dominance in the shallow sea north of the barrier islands. South of the islands, where the water volume of the channels at low tide is smaller than the tidal prism, the asymmetry of the tidal signal is shifted towards ebb dominance, a feature which is particularly pronounced at spring tide. At the northern open boundary, the tidal wave propagating from west to east generates a sea-level difference of ∼1 m along the boundary, and thereby triggers vigorous alongshore currents. The frictional control in the model is located in the inlets, as well as along the northern boundary. The correlation between velocity and turbulent kinetic energy tends to the establishment of a net southward transport, giving theoretical support to the observed accumulation of sediments on the intertidal flats. Weak turbulence along the northern shores of the barrier islands and the small magnitude of the residual currents there promote accumulation of suspended matter in these areas, although wave action will generally counteract this effect. Received: 29 May 2002 / Accepted: 26 September 2002 Responsible Editor: Jean-Marie Beckers Acknowledgements We are indebted to S. Dick for providing the data from the operational model of BSH and to B. Flemming for the useful discussions. The topography data and Fig. 1 have been prepared in cooperation with F. Meyer. Figure 2 has been prepared by G. Brink-Spalink. We also thank for the comments from an anonymous reviewer which helped to improve our paper.     

First-Order Chemistry in the Surface-Flux Layer

We have discussed the behavior of a non-conserved scalar in the stationary, horizontally homogeneous, neutral surface-flux layer and, on the basis of conventional second-order closure, derived analytic expressions for flux and for mean concentration of a gas, subjected to a first-order removal process. The analytic flux solution showed a clear deviation from the constant flux, characterizing a conserved scalar in the surface-flux layer. It decreases with height and is reduced by an order of magnitude of the surface flux at a height equal to about the typical mean distance a molecule can travel before destruction. The predicted mean concentration profile, however, shows only a small deviation from the logarithmic behavior of a conserved scalar. The solution is consistent with assuming a flux-gradient relationship with a turbulent diffusivity corrected by the Damköhler ratio, the ratio of a characteristic turbulent time scale and the scalar mean lifetime. We show that if we use only first-order closure and neglect the effect of the Damköhler ratio on the turbulent diffusivity we obtain another analytic solution for the profiles of the flux and the mean concentration which, from an experimental point of view, is indistinguishable from the first analytic solution. We have discussed two cases where the model should apply, namely NO which, by night, is irreversibly destroyed by interaction with mainly O₃ and the radioactive ²²⁰Rn. Only in the last case was it possible to find data to shed light on the validity of our predictions. The agreement seemed such that a falsification of our model was impossible. It is shown how the model can be used to predict the surface flux of ²²⁰Rn from measured concentration profiles.     

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

On the variability of the flow along the Meso-American Barrier Reef system: a numerical model study of the influence of the Caribbean current and eddies

A high resolution (3–8 km grid), 3D numerical ocean model of the West Caribbean Sea (WCS) is used to investigate the variability and the forcing of flows near the Meso-American Barrier Reef System (MBRS) which runs along the coasts of Mexico, Belize, Guatemala and Honduras. Mesoscale variations in velocity and temperature along the reef were found in seasonal model simulations and in observations; these variations are associated with meandering of the Caribbean current (CC) and the propagation of Caribbean eddies. Diagnostic calculations and a simple assimilation technique are combined to infer the dynamically adjusted flow associated with particular eddies. The results demonstrate that when a cyclonic eddy (negative sea surface height anomaly (SSHA)) is found near the MBRS the CC shifts offshore, the cyclonic circulation in the Gulf of Honduras (GOH) intensifies, and a strong southward flow results along the reef. However, when an anticyclonic eddy (positive SSHA) is found near the reef, the CC moves onshore and the flow is predominantly westward across the reef. The model results help to explain how drifters are able to propagate in a direction opposite to the mean circulation when eddies cause a reversal of the coastal circulation. The effect of including the Meso-American Lagoon west of the Belize Reef in the model topography was also investigated, to show the importance of having accurate coastal topography in determining the variations of transports across the MBRS. The variations found in transports across the MBRS (on seasonal and mesoscale time scales) may have important consequences for biological activities along the reef such as spawning aggregations; better understanding the nature of these variations will help ongoing efforts in coral reef conservation and maintaining the health of the ecosystem in the region.     

A critical evaluation of multi‐proxy dendroclimatology in northern Finland

Twentieth‐century summer (July–August) temperatures in northern Finland are reconstructed using ring widths, maximum density and stable carbon isotope ratios (δ¹³C) of Scots pine tree rings, and using combinations of these proxies. Verification is based on the coefficient of determination (r²), reduction of error (RE) and coefficient of efficiency (CE) statistics. Of the individual proxies, δ¹³C performs best, followed by maximum density. Combining δ¹³C and maximum density strengthens the climate signal but adding ring widths leads to little improvement. Blue intensity, an inexpensive alternative to X‐ray densitometry, is shown to perform similarly. Multi‐proxy reconstruction of summer temperatures from a single site produces strong correlations with gridded climate data over most of northern Fennoscandia. Since relatively few trees are required (<15) the approach could be applied to long sub‐fossil chronologies where replication may be episodically low. Copyright © 2010 John Wiley & Sons, Ltd.     

New major element analyses of proximal tephras from the Azores and suggested correlations with cryptotephras in North-West Europe

The Azores Archipelago is one of the most active volcanic areas in the North Atlantic region. Approximately 30 eruptions have been reported over the last 600 years with some major VEI 5 (Volcanic Explosivity Index) eruptions further back in time. The geochemical composition of associated tephra-derived glass, however, is not well characterized. An Azorean origin of cryptotephras found in distal areas such as North Africa, the British Isles and Greenland has been suggested, but proximal data from the Azores are scarce and the correlations have only been tentative. These tephras have a traychtic composition, which excludes an Icelandic origin. In a previous study, we presented major element analyses of proximal tephra-derived glass from five Holocene eruptions on the Azores Islands. There is a striking geochemical similarity between tephras from volcanoes on São Miguel and Irish cryptotephras, and especially with eruptives from the Furnas volcano. Here we present new analyses of proximal tephras that confirm and strengthen a link between Furnas and cryptotephras found in south-west Ireland. We also suggest a correlation between a previously unsourced tephra found in a Swedish bog with an eruption of the Sete Cidades volcano c. 3880 a cal BP.