Reservoir-scale transdimensional fracture network inversion

The Waiwera aquifer hosts a structurally complex geothermal groundwater system, where a localized thermal anomaly feeds the thermal reservoir. The temperature anomaly is formed by the mixing of waters from three different sources: fresh cold groundwater, cold seawater and warm geothermal water. The stratified reservoir rock has been tilted, folded, faulted, and fractured by tectonic movement, providing the pathways for the groundwater. Characterization of such systems is challenging, due to the resulting complex hydraulic and thermal conditions which cannot be represented by a continuous porous matrix. By using discrete fracture network models (DFNs) the discrete aquifer features can be modelled, and the main geological structures can be identified. A major limitation of this modelling approach is that the results are strongly dependent on the parametrization of the chosen initial solution. Classic inversion techniques require to define the number of fractures before any interpretation is done. In this research we apply the transdimensional DFN inversion methodology that overcome this limitation by keeping fracture numbers flexible and gives a good estimation on fracture locations. This stochastic inversion method uses the reversible-jump Markov chain Monte Carlo algorithm and was originally developed for tomographic experiments. In contrast to such applications, this study is limited to the use of steady-state borehole temperature profiles – with significantly less data. This is mitigated by using a strongly simplified DFN model of the reservoir, constructed according to available geological information. We present a synthetic example to prove the viability of the concept, then use the algorithm on field observations for the first time. The fit of the reconstructed temperature fields cannot compete yet with complex three-dimensional continuum models, but indicate areas of the aquifer where fracturing plays a big role. This could not be resolved before with continuum modelling. It is for the first time that the transdimensional DFN inversion was used on field data and on borehole temperature logs as input.DFG, 318763901, SFB 1294, Data Assimilation - The seamless integration of data and models, Assimilating data with different degrees of uncertainty into statistical models for earthquake occurrence (B04)TU Berlin, Open-Access-Mittel - 201

Controlling overestimation of error covariance in ensemble Kalman filters with sparse observations: A variance limiting Kalman filter

We consider the problem of an ensemble Kalman filter when only partial observations are available. In particular we consider the situation where the observational space consists of variables which are directly observable with known observational error, and of variables of which only their climatic variance and mean are given. To limit the variance of the latter poorly resolved variables we derive a variance limiting Kalman filter (VLKF) in a variational setting. We analyze the variance limiting Kalman filter for a simple linear toy model and determine its range of optimal performance. We explore the variance limiting Kalman filter in an ensemble transform setting for the Lorenz-96 system, and show that incorporating the information of the variance of some un-observable variables can improve the skill and also increase the stability of the data assimilation procedure.Comment: 32 pages, 11 figure

Data assimilation: the Schrödinger perspective

Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based algorithms. In addition to surveying recent developments for discrete- and continuous-time data assimilation, both in terms of mathematical foundations and algorithmic implementations, we also provide a unifying framework from the perspective of coupling of measures, and Schrödinger’s boundary value problem for stochastic processes in particular

Particle-based algorithm for stochastic optimal control

The solution to a stochastic optimal control problem can be determined by computing the value function from a discretization of the associated Hamilton-Jacobi-Bellman equation. Alternatively, the problem can be reformulated in terms of a pair of forward-backward SDEs, which makes Monte-Carlo techniques applicable. More recently, the problem has also been viewed from the perspective of forward and reverse time SDEs and their associated Fokker-Planck equations. This approach is closely related to techniques used in diffusion-based generative models. Forward and reverse time formulations express the value function as the ratio of two probability density functions; one stemming from a forward McKean-Vlasov SDE and another one from a reverse McKean-Vlasov SDE. In this paper, we extend this approach to a more general class of stochastic optimal control problems and combine it with ensemble Kalman filter type and diffusion map approximation techniques in order to obtain efficient and robust particle-based algorithms

Can GNSS reflectometry detect precipitation over oceans?

For the first time, a rain signature in Global Navigation Satellite System Reflectometry (GNSS‐R) observations is demonstrated. Based on the argument that the forward quasi‐specular scattering relies upon surface gravity waves with lengths larger than several wavelengths of the reflected signal, a commonly made conclusion is that the scatterometric GNSS‐R measurements are not sensitive to the surface small‐scale roughness generated by raindrops impinging on the ocean surface. On the contrary, this study presents an evidence that the bistatic radar cross section σ0 derived from TechDemoSat‐1 data is reduced due to rain at weak winds, lower than ≈ 6 m/s. The decrease is as large as ≈ 0.7 dB at the wind speed of 3 m/s due to a precipitation of 0–2 mm/hr. The simulations based on the recently published scattering theory provide a plausible explanation for this phenomenon which potentially enables the GNSS‐R technique to detect precipitation over oceans at low winds