New equipment and processing for magnetotelluric remote reference observations

Robust estimates of magnetotelluric and geomagnetic response functions are determined using the coherency and expected uniformity of the magnetic source field as quality criteria. The method is applied on data sets of three simultaneously recording sites. For the data acquisition we used a new generation of geophysical equipment (S.P.A.M. MkIII), which comprises novel concepts of parallel computing and networked, digital data transmission. The data-processing results show that the amount of noise on the horizontal components of the magnetic field varies considerably in time, between sites and over the frequency range. The removal of such contaminated data beforehand is essential for most data-processing schemes, as the magnetic channels are usually assumed to be free of noise. The standard remote reference method is aimed at reducing bias in response function estimates. However, this does not necessarily improve their precision as our results clearly show. With our method, on the other hand, we can filter out source field irregularities, thereby providing suitable working conditions for the robust algorithm, and eventually obtain considerably improved results. Contrary to previous concepts, we suggest rejecting as much data as feasible in order to concentrate on the remaining parts of high-quality observations.     

Methodology and use of tensor invariants for satellite gravity gradiometry

Although its use is widespread in several other scientific disciplines, the theory of tensor invariants is only marginally adopted in gravity field modeling. We aim to close this gap by developing and applying the invariants approach for geopotential recovery. Gravitational tensor invariants are deduced from products of second-order derivatives of the gravitational potential. The benefit of the method presented arises from its independence of the gradiometer instrument’s orientation in space. Thus, we refrain from the classical methods for satellite gravity gradiometry analysis, i.e., in terms of individual gravity gradients, in favor of the alternative invariants approach. The invariants approach requires a tailored processing strategy. Firstly, the non-linear functionals with regard to the potential series expansion in spherical harmonics necessitates the linearization and iterative solution of the resulting least-squares problem. From the computational point of view, efficient linearization by means of perturbation theory has been adopted. It only requires the computation of reference gravity gradients. Secondly, the deduced pseudo-observations are composed of all the gravitational tensor elements, all of which require a comparable level of accuracy. Additionally, implementation of the invariants method for large data sets is a challenging task. We show the fundamentals of tensor invariants theory adapted to satellite gradiometry. With regard to the GOCE (Gravity field and steady-state Ocean Circulation Explorer) satellite gradiometry mission, we demonstrate that the iterative parameter estimation process converges within only two iterations. Additionally, for the GOCE configuration, we show the invariants approach to be insensitive to the synthesis of unobserved gravity gradients.     

Evaluation of the Weather Research and Forecasting Mesoscale Model for GABLS3: Impact of Boundary-Layer Schemes,Boundary Conditions and Spin-Up

We evaluated the performance of the three-dimensional Weather Research and Forecasting (WRF) mesoscale model, specifically the performance of the planetary boundary-layer (PBL) parametrizations. For this purpose, Cabauw tower observations were used, with the study extending beyond the third GEWEX Atmospheric Boundary-Layer Study (GABLS3) one-dimensional model intercomparison. The WRF model (version 3.4.1) contains 12 different PBL parametrizations, most of which have been only partially evaluated. The GABLS3 case offers a clear opportunity to evaluate model performance, focusing on time series of near-surface weather variables, radiation and surface flux budgets, vertical structure and the nighttime inertial oscillation. The model results revealed substantial differences between the PBL schemes. Generally, non-local schemes tend to produce higher temperatures and higher wind speeds than local schemes, in particular, for nighttime. The WRF model underestimates the 2-m temperature during daytime (about \(2\) K) and substantially underestimates it at night (about \(4\) K), in contrast to the previous studies where modelled 2-m temperature was overestimated. Considering the 10-m wind speed, during the night turbulent kinetic energy based schemes tend to produce lower wind speeds than other schemes. In all simulations the sensible and latent heat fluxes were well reproduced. For the net radiation and the soil heat flux we found good agreement with daytime observations but underestimations at night. Concerning the vertical profiles, the selected non-local PBL schemes underestimate the PBL depth and the low-level jet altitude at night by about 50 m, although with the correct wind speed. The latter contradicts most previous studies and can be attributed to the revised stability function in the Yonsei University PBL scheme. The local, turbulent kinetic energy based PBL schemes estimated the low-level jet altitude and strength more accurately. Compared to the observations, all model simulations show a similar structure for the potential temperature, with a consistent cold bias ( \(\approx \) 2 K) in the upper PBL. In addition to the sensitivity to the PBL schemes, we studied the sensitivity to technical features such as horizontal resolution and domain size. We found a substantial difference in the model performance for a range of 12, 18 and 24 h spin-up times, longer spin-up time decreased the modelled wind speed bias, but it strengthened the negative temperature bias. The sensitivity of the model to the vertical resolution of the input and boundary conditions on the model performance is confirmed, and its influence appeared most significant for the non-local PBL parametrizations.     

Efficient GOCE satellite gravity field recovery based on least-squares using QR decomposition

We develop and apply an efficient strategy for Earth gravity field recovery from satellite gravity gradiometry data. Our approach is based upon the Paige-Saunders iterative least-squares method using QR decomposition (LSQR). We modify the original algorithm for space-geodetic applications: firstly, we investigate how convergence can be accelerated by means of both subspace and block-diagonal preconditioning. The efficiency of the latter dominates if the design matrix exhibits block-dominant structure. Secondly, we address Tikhonov-Phillips regularization in general. Thirdly, we demonstrate an effective implementation of the algorithm in a high-performance computing environment. In this context, an important issue is to avoid the twofold computation of the design matrix in each iteration. The computational platform is a 64-processor shared-memory supercomputer. The runtime results prove the successful parallelization of the LSQR solver. The numerical examples are chosen in view of the forthcoming satellite mission GOCE (Gravity field and steady-state Ocean Circulation Explorer). The closed-loop scenario covers 1 month of simulated data with 5 s sampling. We focus exclusively on the analysis of radial components of satellite accelerations and gravity gradients. Our extensions to the basic algorithm enable the method to be competitive with well-established inversion strategies in satellite geodesy, such as conjugate gradient methods or the brute-force approach. In its current development stage, the LSQR method appears ready to deal with real-data applications.     

Ensemble filter methods with perturbed observations applied to nonlinear problems

The ensemble Kalman filter (EnKF) has been shown repeatedly to be an effective method for data assimilation in large-scale problems, including those in petroleum engineering. Data assimilation for multiphase flow in porous media is particularly difficult, however, because the relationships between model variables (e.g., permeability and porosity) and observations (e.g., water cut and gas–oil ratio) are highly nonlinear. Because of the linear approximation in the update step and the use of a limited number of realizations in an ensemble, the EnKF has a tendency to systematically underestimate the variance of the model variables. Various approaches have been suggested to reduce the magnitude of this problem, including the application of ensemble filter methods that do not require perturbations to the observed data. On the other hand, iterative least-squares data assimilation methods with perturbations of the observations have been shown to be fairly robust to nonlinearity in the data relationship. In this paper, we present EnKF with perturbed observations as a square root filter in an enlarged state space. By imposing second-order-exact sampling of the observation errors and independence constraints to eliminate the cross-covariance with predicted observation perturbations, we show that it is possible in linear problems to obtain results from EnKF with observation perturbations that are equivalent to ensemble square-root filter results. Results from a standard EnKF, EnKF with second-order-exact sampling of measurement errors that satisfy independence constraints (EnKF (SIC)), and an ensemble square-root filter (ETKF) are compared on various test problems with varying degrees of nonlinearity and dimensions. The first test problem is a simple one-variable quadratic model in which the nonlinearity of the observation operator is varied over a wide range by adjusting the magnitude of the coefficient of the quadratic term. The second problem has increased observation and model dimensions to test the EnKF (SIC) algorithm. The third test problem is a two-dimensional, two-phase reservoir flow problem in which permeability and porosity of every grid cell (5,000 model parameters) are unknown. The EnKF (SIC) and the mean-preserving ETKF (SRF) give similar results when applied to linear problems, and both are better than the standard EnKF. Although the ensemble methods are expected to handle the forecast step well in nonlinear problems, the estimates of the mean and the variance from the analysis step for all variants of ensemble filters are also surprisingly good, with little difference between ensemble methods when applied to nonlinear problems.     

Evaluation of the Reduction in Uncertainty Obtained by Conditioning a 3D Stochastic Channel to Multiwell Pressure Data

A stochastic channel embedded in a background facies is conditioned to data observed at wells. The background facies is a fixed rectangular box. The model parameters consist of geometric parameters that describe the shape, size, and location of the channel, and permeability and porosity in the channel and nonchannel facies. We extend methodology previously developed to condition a stochastic channel to well-test pressure data, and well observations of the channel thickness and the depth of the top of the channel. The main objective of this work is to characterize the reduction in uncertainty in channel model parameters and predicted reservoir performance that can be achieved by conditioning to well-test pressure data at one or more wells. Multiple conditional realizations of the geometric parameters and rock properties are generated to evaluate the uncertainty in model parameters. The ensemble of predictions of reservoir performance generated from the suite of realizations provides a Monte Carlo estimate of the uncertainty in future performance predictions. In addition, we provide some insight on how prior variances, data measurement errors, and sensitivity coefficients interact to determine the reduction in model parameters obtained by conditioning to pressure data and examine the value of active and observation well data in resolving model parameters.     

Controls of δS and δO in dissolved sulphate: Learning from a detailed survey in the Llobregat River (Spain)

The S and O isotopic composition of dissolved SO₄, used as a tracer for SO₄ sources, was applied to the water of the Llobregat River system (NE Spain). The survey was carried out at 30 sites where surface water was sampled on a monthly basis over a period of 2a. The concentration of dissolved SO₄ varied from 20 to 1575 mg L⁻¹. Sulphur isotopic compositions clustered in two populations: one – 93% of the samples – had positive values with a mode of +9‰; the other had negative values and a mode of −5‰. Data for δ¹⁸O_SO4 showed a mean value of +11‰, with no bi-modal distribution, though lower values of δ¹⁸O corresponded to samples with negative δ³⁴S. These values can not be explained solely by the contribution of bedrock SO₄ sources: that is, sulphide oxidation and the weathering of outcrops of sulphates, though numerous chemical sediments exist in the basin. Even in a river with a high concentration of natural sources of dissolved SO₄, such as the Llobregat River, the δ³⁴S values suggest that dissolved SO₄ is controlled by a complex mix of both natural and anthropogenic sources. The main anthropogenic sources in this basin are fertilizers, sewage, potash mine effluent and power plant emissions. Detailed river water sampling, together with the chemical and isotopic characterisation of the main anthropogenic inputs, allowed determination of the influence of redox processes, as well as identification of the contribution of natural and anthropogenic SO₄ sources and detection of spatial variations and seasonal changes among these sources. For instance, in the Llobregat River the input of fertilisers is well marked seasonally. Minimum values of δ³⁴S are reported during fertilization periods – from January to March – indicating a higher contribution of this source. The dual isotope approach, δ³⁴S and δ¹⁸O, is useful to better constrain the sources of SO₄. Moreover, in small-scale studies, where the inputs are well known and limited, the mixing models can be enhanced and the contribution of the different sources can be quantified to some extent.