111 research outputs found

    Non-Linear Constraints with Application to Self-Potential Source Inversion

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    We investigate the use of non-linear constraints for geophysical inverse problems, with specific examples applied to source inversion of self-potential data. Typical regularization methods often produce smooth solutions by introducing a quadratic term in the objective function that minimizes the L2 norm of a low-order differential operator applied to the model. In some cases, however, the properties of interest may not vary smoothly. Two alternative constraints are examined that provide inversion stability while allowing for solutions with non-smooth properties. One method, often referred to as ‘compactness’ or ‘minimum support’, seeks to minimize the area (in 2D) or volume (in 3D) occupied by non-zero model parameters. The second method, ‘total variation’, minimizes an approximation of the L1 norm of the gradient of the model. Both approaches involve a non-linear regularization functional, and must therefore be solved iteratively. We discuss the practical aspects of implementing these regularization methods and compare several examples using self-potential source inversion on a synthetic model. We also apply the compactness constraint for self-potential source inversion using a field data example.Kuwait-MIT Center for Natural Resources and the EnvironmentMassachusetts Institute of Technology. Earth Resources Laborator

    Applying Compactness Constraints to Differential Traveltime Tomography

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    Tomographic imaging problems are typically ill-posed and often require the use of regularization techniques to guarantee a stable solution. Minimization of a weighted norm of model length is one commonly used secondary constraint. Tikhonov methods exploit low-order differential operators to select for solutions that are small, flat, or smooth in one or more dimensions. This class of regularizing functionals may not always be appropriate, particularly in cases where the anomaly being imaged is generated by a non-smooth spatial process. Timelapse imaging of flow-induced velocity anomalies is one such case; flow features are often characterized by spatial compactness or connectivity. By performing inversions on differenced arrival time data, the properties of the timelapse feature can be directly constrained. We develop a differential traveltime tomography algorithm which selects for compact solutions i.e. models with a minimum area of support, through application of model-space iteratively reweighted least squares. Our technique is an adaptation of minimum support regularization methods previously explored within the potential theory community. We compare our inversion algorithm to the results obtained by traditional Tikhonov regularization for two simple synthetic models; one including several sharp localized anomalies and a second with smoother features. We use a more complicated synthetic test case based on multiphase flow results to illustrate the efficacy of compactness constraints for contaminant infiltration imaging. We conclude by applying the algorithm to a CO[subscript 2] sequestration monitoring dataset acquired at the Frio pilot site. We observe that in cases where the assumption of a localized anomaly is correct, the addition of compactness constraints improves image quality by reducing tomographic artifacts and spatial smearing of target features.Massachusetts Institute of Technology. Earth Resources Laborator

    Applying Compactness Constraints to Seismic Traveltime Tomography

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    Tomographic imaging problems are typically ill-posed and often require the use of regularization techniques to guarantee a stable solution. Minimization of a weighted norm of model length is one commonly used secondary constraint. Tikhonov methods exploit low-order differential operators to select for solutions that are small, flat, or smooth in one or more dimensions. This class of regularizing functionals may not always be appropriate, particularly in cases where the anomaly being imaged is generated by a non-smooth spatial process. Timelapse imaging of flow-induced seismic velocity anomalies is one such case; flow features are often characterized by spatial compactness or connectivity. We develop a traveltime tomography algorithm which selects for compact solutions through application of model-space iteratively reweighted least squares. Our technique is an adaptation of minimum support regularization methods previously developed within the potential theory community. We emphasize the application of compactness constraints to timelapse datasets differenced in the data domain, a process which allows recovery of compact perturbations in model properties. We test our inversion algorithm on a simple synthetic dataset generated using a velocity model with several localized velocity anomalies. We then demonstrate the efficacy of the algorithm on a CO2 sequestration monitoring dataset acquired at the Frio pilot site. In both cases, the addition of compactness constraints improves image quality by reducing spatial smearing due to limited angular aperture in the acquisition geometry.Toksoz, M. NafiMassachusetts Institute of Technology. Earth Resources Laborator

    The potential of distributed acoustic sensing (DAS) in teleseismic studies: insights from the Goldstone experiment

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    Distributed acoustic sensing (DAS) is a recently developed technique that has demonstrated its utility in the oil and gas industry. Here we demonstrate the potential of DAS in teleseismic studies using the Goldstone OpticaL Fiber Seismic experiment in Goldstone, California. By analyzing teleseismic waveforms from the 10 January 2018 M7.5 Honduras earthquake recorded on ~5,000 DAS channels and the nearby broadband station GSC, we first compute receiver functions for DAS channels using the vertical‐component GSC velocity as an approximation for the incident source wavelet. The Moho P‐to‐s conversions are clearly visible on DAS receiver functions. We then derive meter‐scale arrival time measurements along the entire 20‐km‐long array. We are also able to measure path‐averaged Rayleigh wave group velocity and local Rayleigh wave phase velocity. The latter, however, has large uncertainties. Our study suggests that DAS will likely play an important role in many fields of passive seismology in the near future

    How liquid is biological signalling?

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    This paper proposes an investigation of the global statistics of synthetic protein networks-a step towards a systemic understanding of their design space. We derive a liquidity index which describes the onset of the phase transition where an ensemble of agents aggregates into a giant cluster. This index captures the influence of both the domain distribution of agents and the binding strengths of their various domains in the limit of infinite populations. In simple cases it is possible to derive an explicit analytical expression of this index, which allows to compare with simulations, and get a sense of how it transfers to the concrete finite case

    Genetically encoded sender-receiver system in 3D mammalian cell culture

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    Engineering spatial patterning in mammalian cells, employing entirely genetically encoded components, requires solving several problems. These include how to code secreted activator or inhibitor molecules and how to send concentration-dependent signals to neighboring cells, to control gene expression. The Madin-Darby Canine Kidney (MDCK) cell line is a potential engineering scaffold as it forms hollow spheres (cysts) in 3D culture and tubulates in response to extracellular hepatocyte growth factor (HGF). We first aimed to graft a synthetic patterning system onto single developing MDCK cysts. We therefore developed a new localized transfection method to engineer distinct sender and receiver regions. A stable reporter line enabled reversible EGFP activation by HGF and modulation by a secreted repressor (a truncated HGF variant, NK4). By expanding the scale to wide fields of cysts, we generated morphogen diffusion gradients, controlling reporter gene expression. Together, these components provide a toolkit for engineering cell-cell communication networks in 3D cell culture.Facultad de Ciencias Exacta
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