3,239 research outputs found
Inversion of multiconfiguration complex EMI data with minimum gradient support regularization: A case study
Frequency-domain electromagnetic instruments allow the collection of data in
different configurations, that is, varying the intercoil spacing, the
frequency, and the height above the ground. Their handy size makes these tools
very practical for near-surface characterization in many fields of
applications, for example, precision agriculture, pollution assessments, and
shallow geological investigations. To this end, the inversion of either the
real (in-phase) or the imaginary (quadrature) component of the signal has
already been studied. Furthermore, in many situations, a regularization scheme
retrieving smooth solutions is blindly applied, without taking into account the
prior available knowledge. The present work discusses an algorithm for the
inversion of the complex signal in its entirety, as well as a regularization
method that promotes the sparsity of the reconstructed electrical conductivity
distribution. This regularization strategy incorporates a minimum gradient
support stabilizer into a truncated generalized singular value decomposition
scheme. The results of the implementation of this sparsity-enhancing
regularization at each step of a damped Gauss-Newton inversion algorithm (based
on a nonlinear forward model) are compared with the solutions obtained via a
standard smooth stabilizer. An approach for estimating the depth of
investigation, that is, the maximum depth that can be investigated by a chosen
instrument configuration in a particular experimental setting is also
discussed. The effectiveness and limitations of the whole inversion algorithm
are demonstrated on synthetic and real data sets
Variational Downscaling, Fusion and Assimilation of Hydrometeorological States via Regularized Estimation
Improved estimation of hydrometeorological states from down-sampled
observations and background model forecasts in a noisy environment, has been a
subject of growing research in the past decades. Here, we introduce a unified
framework that ties together the problems of downscaling, data fusion and data
assimilation as ill-posed inverse problems. This framework seeks solutions
beyond the classic least squares estimation paradigms by imposing proper
regularization, which are constraints consistent with the degree of smoothness
and probabilistic structure of the underlying state. We review relevant
regularization methods in derivative space and extend classic formulations of
the aforementioned problems with particular emphasis on hydrologic and
atmospheric applications. Informed by the statistical characteristics of the
state variable of interest, the central results of the paper suggest that
proper regularization can lead to a more accurate and stable recovery of the
true state and hence more skillful forecasts. In particular, using the Tikhonov
and Huber regularization in the derivative space, the promise of the proposed
framework is demonstrated in static downscaling and fusion of synthetic
multi-sensor precipitation data, while a data assimilation numerical experiment
is presented using the heat equation in a variational setting
Identification of linear response functions from arbitrary perturbation experiments in the presence of noise - Part I. Method development and toy model demonstration
Existent methods to identify linear response functions from data require tailored perturbation experiments, e.g., impulse or step experiments, and if the system is noisy, these experiments need to be repeated several times to obtain good statistics. In contrast, for the method developed here, data from only a single perturbation experiment at arbitrary perturbation are sufficient if in addition data from an unperturbed (control) experiment are available. To identify the linear response function for this ill-posed problem, we invoke regularization theory. The main novelty of our method lies in the determination of the level of background noise needed for a proper estimation of the regularization parameter: this is achieved by comparing the frequency spectrum of the perturbation experiment with that of the additional control experiment. The resulting noise-level estimate can be further improved for linear response functions known to be monotonic. The robustness of our method and its advantages are investigated by means of a toy model. We discuss in detail the dependence of the identified response function on the quality of the data (signal-to-noise ratio) and on possible nonlinear contributions to the response. The method development presented here prepares in particular for the identification of carbon cycle response functions in Part 2 of this study (Torres Mendonça et al., 2021a). However, the core of our method, namely our new approach to obtaining the noise level for a proper estimation of the regularization parameter, may find applications in also solving other types of linear ill-posed problems
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