2D equivalent linear site effect simulation: example applications to two deep valleys

In the framework of the Sismovalp European project, an equivalent linear 2D code was developed to compute the response of a valley to SH waves, using the discrete wave-number method proposed by Aki and Larner (Aki K, Larner KL (1970) J Geophys Res 75:5). To overcome the frequency upper bound limitation, the Aki and Larner’s method is combined with a one-dimensional computation using a classical multi-layer method (Aki K, Richards PG (1980) Quantitative Seismology: Theory and Methods, vols. 1 & 2. W.H. Freeman & Co, San Francisco). The so-called “Aki–Larner extended method” is associated to an iterative algorithm, as proposed by Seed and Idriss (Seed HB, Idriss IM (1969) Report No. EERC 70–10, Earthquake Research Center, University of California, Berkeley, California) which accounts for the modulus and damping degradation using a linear visco-elastic model. A comparison of the results in the linear and the equivalent linear cases, for a magnitude 6.0 earthquake, shows that the account for the equivalent linear behaviour of the soil significantly reduces the amplification level, especially at frequencies higher than the fundamental resonance frequency of the site. In the case of site effects or microzonation studies devoted to produce design spectra for engineering structures, this can have a major impact on the associated results and costs, depending on the frequency of interest for the considered structure. As a first application of the developed technique, 2D equivalent linear Aki–Larner computations are used to perform the seismic microzonation study of the upper Rhone valley, in the Visp area (Switzerland), a typical 2D alpine valley. These investigations made it possible to determine site specific spectra, associated with different zones, to be used instead of the code spectra that do not take into account the local 2D amplification.     

About the Efficiency of Numerical 1-D and 2-D Modelling of Site Effects in Basin Structures

—In the present study we compare results obtained from experimental estimates of local site amplification effects with those from numerical modelling using four different techniques. We benefit from an extremely precise knowledge of the near-surface structure and experimental estimates of the local amplification factors which are determined from seismic weak-motion data recorded by a dense array across a sedimentary basin at a European test-site in Northern Greece. The possibilities and limitations of the different modelling techniques (a 1-D technique, and three 2-D techniques) to model the effects of local amplification effects are tested. Amplifications calculated by the numerical techniques are only qualitatively compared with observed data from experimental studies in the time domain and directly in the frequency domain.¶As a result we conclude that, in the case of a complex subsurface geometry, 1-D modelling underestimates the amplification patterns in terms of absolute amplification level, and cannot correctly account for resonant frequencies, at least for modes higher than the fundamental mode. If a more realistic incident wave field than just a plane wave is taken into account, 2-D modelling reveals the fundamental frequency and shows adequate amplifications not only at the fundamental frequency but also at higher frequencies. The general trend of the amplifications at the lowest frequencies is well determined by the 2-D numerical modelling, and can therefore supply information for seismic risk analysis.     

GGR Biennial Critical Review: Analytical Developments Since 2014

This GGR biennial critical review covers developments and innovations in key analytical methods published since January 2014, relevant to the chemical, isotopic and crystallographic characterisation of geological and environmental materials. In nine selected analytical fields, publications considered to be of wide significance are summarised, background information is provided and their importance evaluated. In addition to instrumental technologies, this review also presents a summary of new developments in the preparation and characterisation of rock, microanalytical and isotopic reference materials, including a précis of recent changes and revisions to ISO guidelines for reference material characterisation and reporting. Selected reports are provided of isotope ratio determinations by both solution nebulisation MC‐ICP‐MS and laser ablation‐ICP‐MS, as well as of radioactive isotope geochronology by LA‐ICP‐MS. Most of the analytical techniques elaborated continue to provide new applications for geochemical analysis; however, it is noted that instrumental neutron activation analysis has become less popular in recent years, mostly due to the reduced availability of nuclear reactors to act as a neutron source. Many of the newer applications reported here provide analysis at increasingly finer resolution. Examples include atom probe tomography, a very sensitive method providing atomic scale information, nanoscale SIMS, for isotopic imaging of geological and biological samples, and micro‐XRF, which has a spatial resolution many orders of magnitude smaller than conventional XRF.     

Three-dimensional hydromechanical modeling of internal erosion in dike-on-foundation

Currently, numerical studies at the real scale of an entire engineering structure considering internal erosion are still rare. This paper presents a three-dimensional (3D) numerical simulation of the effects of internal erosion within a linear dike located on a foundation. A two-dimensional (2D) finite element code has been extended to 3D in order to analyze the impact of internal erosion under more realistic hydromechanical conditions. The saturated soil has been considered as a mixture of four interacting constituents: soil skeleton, erodible fines, fluidized fine particles, and fluid. The detachment and transport of the fine particles have been modeled with a mass exchange model between the solid and the fluid phases. An elastoplastic constitutive model for sand-silt mixtures has been developed to monitor the effect of the evolution of both the porosity and the fines content induced by internal erosion upon the behavior of the soil skeleton. An unsaturated flow condition has been implemented into this coupled hydromechanical model to describe more accurately the seepage within the dike and the foundation. A stabilized finite element method was used to eliminate spurious numerical oscillations in solving the convection-dominated transport of fluidized particles. This numerical tool was then applied to a specific dike-on-foundation case subjected to internal erosion induced by a leakage located at the bottom of the foundation. Different failure modes were observed and analyzed for different boundary conditions, including the significant influence of the leakage cavity size and the elevation of the water level at the upstream and downstream sides of the dike.     

Glacial/interglacial sea surface temperature changes in the Southwest Pacific ocean over the past 360 ka

The phase relationship between climate parameters during terminations gives insight into deglaciation mechanisms. By combining foraminiferal Mg/Ca and alkenone thermometers with planktonic and benthic foraminiferal δ¹⁸O, we determined the phase relationship between local sea surface temperature (SST) and global seawater δ¹⁸O changes in the Coral Sea in the Southwestern Pacific over the last 360 ka. The onset of the SST warming preceded the seawater δ¹⁸O change by several ka for Termination I, II and III. During Termination I, the SST warming started at 20 ka BP, earlier than atmospheric CO₂ rise suggesting that the greenhouse effect was not the main trigger of this early warming. Compilation of ¹⁴C-dated SST records from the whole Pacific during Termination I reveals that the onset of the warming is generally earlier in the Southern and the tropical Pacific than in the North Pacific. This spatio-temporal warming pattern suggests linkage between the southern ocean and tropical Pacific. The early tropical warming could provide heat and moisture to the northern high latitudes, modifying radiative balance and precipitation over ice sheets at the onset of deglaciation.     

A procedure to analyze nonlinear density waves in Saturn's rings using several occultation profiles

Cassini radio science experiments have provided multiple occultation optical depth profiles of Saturn's rings that can be used in combination to analyze density waves. This paper establishes an accurate procedure of inversion of the wave profiles to reconstruct the wave kinematic parameters as a function of semi-major axis, in the nonlinear regime. This procedure is established using simulated data in the presence of realistic noise perturbations, to control the reconstruction error. It is then applied to the Mimas 5:3 density wave. There are two important concepts at the basis of this procedure. The first one is that it uses the nonlinear representation of density waves, and the second one is that it relies on a combination of optical depth profiles instead of just one profile. A related method to analyze density waves was devised by Longaretti and Borderies [Longaretti, P.-Y., Borderies, N., 1986. Icarus 67, 211-223] to study the nonlinear density wave associated with the Mimas 5:3 resonance, but the single photopolarimetric profile provided limited constraints. Other studies of density waves analyzing Cassini data [Colwell, J.E., Esposito, L.W., 2007. Bull. Am. Astron. Soc. 39, 461; Tiscareno, M.S., Burns, J.A., Nicholson, P.D., Hedman, M.M., Porco, C.C., 2007. Icarus 189, 14-34] are based on the linear theory and find inconsistent results from profile to profile. Multiple cuts of the rings are helpful in a fundamental way to ensure the accuracy of the procedure by forcing consistency among the various optical depth profiles. By way of illustration we have applied our procedure to the Mimas 5:3 density wave. We were able to recover precisely the kinematic parameters from the radio experiment occultation data in most of the propagation region; a preliminary analysis of the pressure-corrected dispersion allowed us to determine new but still uncertain values for the opacity (K?0.02 cm²/g) and velocity dispersion of (c₀?0.6 cm/s) in the wave region. Our procedure constitutes the first step in our planned analysis of the density waves of Saturn's rings. It is very accurate and efficient in the far-wave region. However, improvements are required within the first wavelength. The ways in which this method can be used to establish diagnostics of ring physics are outlined.     

Site Effect Study in Urban Area: Experimental Results in Grenoble (France)

—?Three methods are used to determine the site effect in the town of Grenoble, located in the Western Alps. First we use the classical spectral ratio method in 14 sites to calculate the transfer function of the basin. We find an amplification of 10 in the frequency range of 0.25 to 10?Hz. Second, we compare these results with the H over V spectral ratio method, and propose a map of resonance frequency of the basin. We find a lower resonance frequency in the center of the basin than on the edge, that is consistent with the structure deduced from a gravity Bouguer anomaly map. Finally we use the empirical Green's function method to simulate a M _w 5.5 earthquake at a distance of 20?km from the town. The simulated acceleration reaches the level of 2?m/s² in the center of the basin compared to 0.2?m/s² on the edges. The simulated ground motion we compute is smaller than the French seismic codes on the edge of the valley but significantly larger in the center.     

Site effects in Mexico City eight years after the September 1985 Michoacan earthquakes

The purpose of this paper is to take a comprehensive look at site effects in Mexico City for the 1985 Michoacan earthquake. We examine, successively, 1D and 2D models. For the latter, we consider in detail both large scale and small scale heterogeneities, using extensively the Aki-Larner wave propagation method, in the version given by Bard and Gariel. In particular, we make a critical review of the different explanations proposed for the large duration of strong ground motion in the lake zone. Our purpose is two-sided. We first outline the difference between what is well established and what remains still unexplained regarding the seismic response of Mexico City basin. On the other hand, we wish to make explicit the conditions that the proposed models require to explain strong motion duration. Our results allow us to qualify the models proposed to date and to point out what could be the experiments and the new data required to find a truly satisfactory explanation of strong ground motion at Mexico City.     

Theory of metamorphic segregation and related processes

Metamorphic segregation is defined here as the formation and growth of bands or domains of different bulk compositions within an originally unbanded rock. It can result from an instability arising in some deforming rocks when diffusion transfer is significant. The nature of this instability is demonstrated separately for a differentiation associated with a crenulation (Type C) and for one without crenulation (Type L). However, the continuous gradation between the two types observed in nature is also expected from the models.A requirement for both types is that one chemical component of the rock, typically silica, diffuse more rapidly than others, e.g. phyllosilicate components, in response to stress-induced pressure gradients. In addition, Type L requires that, at least at an early stage, portions of the rock rich in this mobile component, e.g. rich in quartz, be more competent than those portions which are poor in quartz. By a process akin to the development of pressure shadows, silica diffuses toward domains which are already the richest in quartz. Alternatively, if the rock is chemically open to loss of silica, this silica preferentially originates from dissolution of quartz in the more mica-rich domains. In either case the compositional contrast between domains is increased and metamorphic segregation results. Type C differentiation is best explained if we accept the suggestion made by many petrographers that layer silicates catalyse the pressure-induced transfer of silica. This suggestion can in fact account for other features of metamorphic segregation bands.Metamorphic segregation should also proceed during the development of quartz segregations, quartz rods, slaty cleavage and mylonite banding. The stress distribution argued for Type L bands may also occur in many banded migmatites. In migmatites. however, the assemblage crystallizing in the leucosome may be derived from a circulating hydrothermal fluid as well as from diffusion transfer.