A non-periodic two scale asymptotic method to take account of rough topographies for 2D elastic wave propagation

International audienceWe propose a two scale asymptotic method to compute the effective effect of a free surface topography varying much faster than the minimum wavelength for 2-D P-SV elastic wave propagation. The topography variation is assumed to be non-periodic but with a deterministic description and, in this paper, the elastic body below the topography is assumed to be ho- mogeneous. Two asymptotic expansions are used, one in the boundary layer close to the free surface and one in the volume. Both expansions are matched appropriately up to the order 1 to provide an effective topography and an effective boundary condition. We show that the effective topography is not the averaged topography but it is a smooth free surface lying below the fast variations of the real topography. Moreover, the free boundary condition has to be modified to take account of the inertial effects of the fast variations of the topography above the effective topography. In other words, the wave is not propagating in the fast topography but below it and is slowed down by the weight of the fast topography. We present an iterative scheme allowing to find this effective topography for a given minimum wavelength. We do not attempt any mathematical proof of the proposed scheme, nevertheless, numerical tests show good results

1-D non periodic homogenization for the seismic wave equation

International audienceWhen considering numerical acoustic or elastic wave propagation in media containing small heterogeneities with respect to the minimum wavelength of the wavefield, being able to upscale physical properties (or homogenize them) is valuable mainly for two reasons. First, replacing the original discontinuous and very heterogeneous medium by a smooth and more simple one, is a judicious alternative to the necessary fine and difficult meshing of the original medium required by many wave equation solvers. Second, it helps to understand what properties of a medium are really ‘seen' by the wavefield propagating through, which is an important aspect in an inverse problem approach. This paper is an attempt of a pedagogical introduction to non- periodic homogenization in 1-D, allowing to find the effective wave equation and effective physical properties, of the elastodynamics equation in a highly heterogeneous medium. It can be extrapolated from 1-D to a higher space dimensions. This development can be seen as an extension of the classical two-scale homogenization theory applied to the elastic wave equation in periodic media, with this limitation that it does not hold beyond order 1 in the asymptotic expansion involved in the classical theory

2-D non-periodic homogenization of the elastic wave equation: SH case

International audienceIn the Earth, seismic waves propagate through 3-D heterogeneities characterized by a large variety of scales, some of them much smaller than their minimum wavelength. The costs of computing the wavefield in such media using purely numerical methods, are very high. To lower them, and also to obtain a better geodynamical interpretation of tomographic images, we aim at calculating appropriate effective properties of heterogeneous and discontinuous media, by deriving convenient upscaling rules for the material properties and for the wave equation. To progress towards this goal we extend our successful work from 1-D to 2-D. We first apply the so-called homogenization method (based on a two-scale asymptotic expansion of the field variables) to model antiplane wave propagation in 2-D periodic media. These latter are characterized by short-scale variations of elastic properties, compared to the smallest wavelength of the wavefield. Seismograms are obtained using the 0th-order term of this asymptotic expansion, plus a partial first-order correction. Away from boundaries, they are in excellent agreement with solutions calculated at a much higher computational cost, using spectral elements simulations in the reference media. We then extend the homogenization of the wave equation, to 2-D non-periodic, deterministic media

Reproductive Cycle and Plasma Levels of Sex Steroids in Female Eurasian Perch Perca Fluviatilis

From April 1995 to April 1996, the annual reproductive cycle of the Eurasian perch Perca fluviatilis was studied at the Fishfarming Lindre Center (Moselle, France). At monthly intervals (at intervals of 10 days during the periovulatory period), 5 females were caught and dissected. From sampled organs, the gonado-, hepato- and viscerosomatic indexes (GSI, HSI, VSI) were calculated, oocyte diameters (OD) and the plasma levels of testosterone (T), 17P-estradiol (E2), 17,20P-dihydroxy-4-pregnen-3-one (17,2Op-P) and protein-phosphorus (PPP) were measured. After the sexual resting period observed from May to August (GSI \u3c 1 %, OD \u3c 200 urn, VSI = 4-6 %), oogenesis began in September when the water temperature decreased from 26.4 to 14.1 “C. The GSI increased progressively until mid March (15 %), then rapidly until spawning (25 %, OD = 850 urn) which occurred in April (14- 15 “C). The plasma levels of T, E,, 17,2Op-P and PPP were low during the sexual resting period. E, and PPP levels increased significantly at the onset of the oogenesis in September, then the E, level raised abruptly in November (3-4 ng mL-‘). In December, the T level increased rapidly to 15-20 ng . mL-’ The testosterone, E, and PPP levels remained very high until spawning, indicating the existence of active vitellogenesis. The highest HSI (2.1-2.2 %) recorded in winter confirmed this. During the periovulatory period, a peak of E, (4 ng . mL-‘) appeared, whereas T level diminished. In this study, 17,2Op-P levels remained low (0.2-0.6 ng mL-‘) and relatively constant. No 17,2Op-P peak was observed during the periovulatory period. Sampling at 10 day intervals was probably inadequate to specify the hormonal variations related to the final oocyte maturation and the ovulation. 0 Ifremer-Elsevier, Paris

2-D non-periodic homogenization to upscale elastic media for P-SV waves

International audienceThe pur pose of this paper is to give an upscaling tool valid for the wave equation in general elastic media. This paper is focused on P–SV wave propagation in 2-D, but the methodology can be extended without any theoretical difficulty to the general 3-D case. No assumption on the heterogeneity spectrum is made and the medium can show rapid variations of its elastic properties in all spatial directions. The method used is based on the two-scale homogenization expansion, but extended to the non-periodic case. The scale separation is made using a spatial low-pass filter. The ratio of the filter wavelength cut-off and the minimum wavelength of the propagating wavefield defines a parameter ε0 with which the wavefield propagating in the homogenized medium converges to the reference wavefield. In the general case, this non- periodic extension of the homogenization technique is only valid up to the leading order and for the so-called first-order cor rector. We apply this non-periodic homogenization procedure to two kinds of heterogeneous media: a randomly generated, highly heterogeneous medium and the Marmousi2 geological model. The method is tested with the Spectral Element Method as a solver to the wave equation. Comparing computations in the homogenized media with those obtained in the original ones shows that convergence with ε0 is even better than expected. The effects of the leading order cor rection to the source and first cor rection at the receivers' location are shown

Reproductive Cycle and Plasma Sex Steroid Profiles in Male Eurasian Perch Perca Fluviatilis

From April 1995 to April 1996, the annual reproductive cycle of male Eurasian perch Perca fluviatilis was studied at the Lindre Center (Moselle, France). At monthly intervals, five males (mean body weight of 133 ± 43 g and total length of 175 ± 9 mm) were caught. From sampled organs, the gonadosomatic (GSI), hepatosomatic (HSI) and viscerosomatic indexes (VSI) were calculated and plasma testosterone (T) and 11-ketotestosterone (11KT) levels were measured. After the spawning period in mid-April, GSI and HSI dropped and VSI increased to 3.8 ± 0.1 %. In September, GSI reached its maximum (8.5 ± 1.8 %). At this time, spermatocytes, spermatids and spermatozoa were abundant, whereas in June only spermatogonia were observed. During winter, GSI was stable at approximately 5 %, HSI reached its maximum (1.9 ± 0.3 %) and VSI was low (2.6 ± 0.2 %). From April to November 1995, plasma T and 11KT concentrations were low (\u3c 0.5 ng·mL–1). Plasma T levels increased significantly in December and reached peak levels (12.3 ± 2.1 ng·mL–1) in January, then decreased in February and increased again until spawning in April (6.8 ± 2.1 ng·mL–1). This second elevation could be related to the beginning of a new spermatogenic cycle. Plasma levels of 11KT increased significantly from October to February 1996 (4.9 ± 1.1 ng·mL–1). From February to the spawning period (April 1996), plasma 11KT decreased significantly, but values were significantly higher than those measured in fall. Males were spermiating from January to spawning in April. © 2000 Ifremer/Cnrs/Inra/Ird/Cemagref/Éditions scientifiques et médicales Elsevier SA

Altimetry for the future: Building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the ‘‘Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

Altimetry for the future: building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the “Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

Multicriteria evaluation of animal welfare at farm level: an application of MCDA methodologies

International audienceConsumers are more and more concerned about the living conditions of farm animals. As a consequence, numerous trade groups (producers, distributors, retailers, chain restaurants) have created certification schemes which include animal welfare. These initiatives aim at allowing consumers to choose ‘high welfare standard’ products, but the assessment of welfare varies from one scheme to another. There is no European standard to assess animal welfare and to bring that information to consumers. The EU project Welfare Quality R seeks to fill this gap for cattle, pigs and poultry, by proposing an overall assessment system based on multicriteria analysis and widely accepted by stakeholders. In this paper we present a possible contribution of MCDA to this problem. This application has been run for cattle and will be extended later to other animal species. Animal welfare is a multidimensional concept, including several aspects like good health, comfort, expression of behaviour, and so on. Thus, the overall assessment of animal welfare on farms is a multicriteria evaluation problem that needs a constructive strategy to compound information produced by multiple animal-based measures. We propose a methodology based on the construction of 12 subcriteria, grouped to form four criteria (good feeding, good housing, good health, and appropriate behaviour ) essentially to facilitate communication toward consumers, as defined in Welfare Quality R [1]. Each subcriterion is expressed on the same utility scale [0, 100] where 50 represents a neutral element. The aggregation process includes several steps. First, using several data-sets of farms graded by experts on each criterion, we derive the mathematical model linking criterion values to subcriteria values. This step is performed using the Choquet integral, the capacity being obtained by minimization of the overall quadratic error over examples provided by different experts. The second step of the aggregation process consists in producing an overall evaluation of farms in terms of welfare, from criterion values. We propose to define 4 ordered categories (with a system of stars, from zero to three) to characterize how bad or good is the level of welfare on the farm considered. These categories are characterized by limit profiles in the space of criteria. Then a sorting procedure of type ELECTRE TRI is used in order to perform the assignment of farms to predefined categories while limiting compensations in the final aggregation process. Scientific evidence, observations on a large set of farms, and expert opinion are used to determine the parameters and, if necessary, refine the model. Stakeholders’ approval of general principles is sought in order to provide a system that will receive the agreement of all the persons concerned with the construction of such a certification scheme on animal welfare. This approach illustrates the use of MCDA methodologies in a context of a multidimensional concept where numerous agents are involved, from the scientists who developed the measures of welfare to all stakeholders involved in the decision process