Improved forward wave propagation and adjoint-based sensitivity kernel calculations using a numerically stable finite-element PML

International audienceIn recent years, the application of time-domain adjoint methods to improve large, complex underground tomographic models at the regional scale has led to new challenges for the numerical simulation of forward or adjoint elastic wave propagation problems. An important challenge is to design an efficient infinite-domain truncation method suitable for accurately truncating an infinite domain governed by the second-order elastic wave equation written in displacement and computed based on a finite-element (FE) method. In this paper, we make several steps towards this goal. First, we make the 2-D convolution formulation of the complex-frequency-shifted unsplit-field perfectly matched layer (CFS-UPML) derived in previous work more flexible by providing a new treatment to analytically remove singular parameters in the formulation. We also extend this new formulation to 3-D. Furthermore, we derive the auxiliary differential equation (ADE) form of CFS-UPML, which allows for extension to higher order time schemes and is easier to implement. Secondly, we rigorously derive the CFS-UPML formulation for time-domain adjoint elastic wave problems, which to our knowledge has never been done before. Thirdly, in the case of classical low-order FE methods, we show numerically that we achieve long-time stability for both forward and adjoint problems both for the convolution and the ADE formulations. In the case of higher order Legendre spectral-element methods, we show that weak numerical instabilities can appear in both formulations, in particular if very small mesh elements are present inside the absorbing layer, but we explain how these instabilities can be delayed as much as needed by using a stretching factor to reach numerical stability in practice for applications. Fourthly, in the case of adjoint problems with perfectly matched absorbing layers we introduce a computationally efficient boundary storage strategy by saving information along the interface between the CFS-UPML and the main domain only, thus avoiding the need to solve a backward wave propagation problem inside the CFS-UPML, which is known to be highly ill-posed. Finally, by providing several examples we show numerically that our formulation is efficient at absorbing acoustic waves for normal to near-grazing incident body waves as well as surface waves

Revisiting the 1/L problem in rheological models for time-domain seismic wave propagation

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Optimized PML for 3D time-domain full-wave spectral-elements simulations with solid ocean bottoms

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A perfectly matched layer for fluid-solid problems: Application to ocean-acoustics simulations with solid ocean bottoms

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Erythropoietin reduces necrosis in critically ischemic myocutaneous tissue by protecting nutritive perfusion in a dose-dependent manner

BACKGROUND: Erythropoietin (Epo), the primary regulator of erythropoiesis, has recently been shown to exert antiinflammatory and antiapoptotic properties in neuronal and myocardial tissue. We herein studied whether Epo pretreatment can reduce cell death and ischemic necrosis in a chronic in vivo model. METHODS: C57BL/6 mice were treated daily for 3 consecutive days with either 500 IU EPO/kg body weight (bw) (group Epo 500, n = 8) or 5000 IU EPO/kg bw (group Epo 5000, n = 8) administered intraperitoneally 24 hours before surgery. Thereafter, a random pattern myocutaneous flap subjected to acute persistent ischemia was elevated and fixed into a dorsal skinfold chamber. Flap elevation in animals receiving the water-soluble vitamin E analog Trolox (6-hydroxy-2, 5, 7, 8-tetramethylchroman-2-carboxylic acid) served as a nonspecific antiinflammatory agent control group (Tro); untreated control animals (Con) received saline only. Capillary perfusion, leukocyte-endothelial cell interaction, apoptotic cell death, and tissue necrosis were determined over a 10-day observation period using intravital multifluorescence microscopy. RESULTS: Epo 5000 (44 +/- 26 cm/cm(2)) but, more noticeably, Epo 500 (116 +/- 32 cm/cm(2)) improved capillary perfusion compared with the two control groups, particularly the Con group (9 +/- 7 cm/cm(2); P < .05). The ischemia-associated leukocytic inflammation was found drastically attenuated in both Epo-pretreatment groups. Epo 500 further decreased apoptotic cell death and was effective in significantly reducing tissue necrosis (16% +/- 4% vs Tro: 48% +/- 7% and Con: 52% +/- 4%; P < .001). No angiogenic blood vessel formation could be observed in either of the Epo groups. Of interest, Epo 5000-but not Epo 500-increased systemic hematocrit. CONCLUSION: Despite the lack of neovascularization, Epo pretreatment was capable of reducing ischemic tissue necrosis by protecting capillary perfusion, ie, nutrition of the tissue. Low-dose pretreatment was more effective, a result that was most likely due to the better perfusion conditions without an increase of the hematocrit values. Thus, low-dose Epo pretreatment might represent a promising strategy to protect critically perfused ischemic tissue