Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations

Model calibration and history matching are important techniques to adapt simulation tools to real-world systems. When prediction uncertainty needs to be quantified, one has to use the respective statistical counterparts, e.g., Bayesian updating of model parameters and data assimilation. For complex and large-scale systems, however, even single forward deterministic simulations may require parallel high-performance computing. This often makes accurate brute-force and nonlinear statistical approaches infeasible. We propose an advanced framework for parameter inference or history matching based on the arbitrary polynomial chaos expansion (aPC) and strict Bayesian principles. Our framework consists of two main steps. In step 1, the original model is projected onto a mathematically optimal response surface via the aPC technique. The resulting response surface can be viewed as a reduced (surrogate) model. It captures the model’s dependence on all parameters relevant for history matching at high-order accuracy. Step 2 consists of matching the reduced model from step 1 to observation data via bootstrap filtering. Bootstrap filtering is a fully nonlinear and Bayesian statistical approach to the inverse problem in history matching. It allows to quantify post-calibration parameter and prediction uncertainty and is more accurate than ensemble Kalman filtering or linearized methods. Through this combination, we obtain a statistical method for history matching that is accurate, yet has a computational speed that is more than sufficient to be developed towards real-time application. We motivate and demonstrate our method on the problem of CO₂ storage in geological formations, using a low-parametric homogeneous 3D benchmark problem. In a synthetic case study, we update the parameters of a CO₂/brine multiphase model on monitored pressure data during CO₂ injection.     

Carboniferous–Permian volcanic evolution in Central Europe—U/Pb ages of volcanic rocks in Saxony (Germany) and northern Bohemia (Czech Republic)

Nine SHRIMP U/Pb ages on zircon and two Pb/Pb single zircon ages have been determined from Late Paleozoic volcanic rocks from Saxony and northern Bohemia. Samples came from the Teplice-Altenberg Volcanic Complex, the Meissen Volcanic Complex, the Chemnitz Basin, the Döhlen Basin, the Brandov-Olbernhau Basin, and the North Saxon Volcanic Complex. The Teplice-Altenberg Volcanic Complex is subdivided into an early Namurian phase (Mikulov Ignimbrite, 326.8 ± 4.3 Ma), thus older than assumed by previous studies, and a late caldera-forming phase (Teplice Ignimbrite, 308.8 ± 4.9 Ma). The age of the latter, however, is not well constrained due to a large population of inherited zircon and possible hydrothermal overprint. The Leutewitz Ignimbrite, product of an early explosive volcanic episode of the Meissen Volcanic Complex yielded an age of 302.9 ± 2.5 Ma (Stephanian A). Volcanic rocks intercalated in the Brandov-Olbernhau Basin (BOB, 302 ± 2.8 Ma), Chemnitz Basin (CB, 296.6 ± 3.0 Ma), Döhlen Basin (DB, 296 ± 3.0 Ma), and the North Saxon Volcanic Complex (NSVC, c. 300–290 Ma) yielded well-constrained Stephanian to Sakmarian ages. The largest Late Paleozoic ignimbrite-forming eruption in Central Europe, the Rochlitz Ignimbrite, has a well-defined middle Asselian age of 294.4 ± 1.8 Ma. Ages of palingenic zircon revealed that the Namurian-Westphalian magmatism assimilated larger amounts of crystalline basement that formed during previous Paleozoic geodynamic phases. The Precambrian inherited ages support the chronostratigraphic structure assumed for the Saxo-Thuringian Zone of the Variscan Orogen. The present results help to improve the chronostratigraphic allocation of the Late Paleozoic volcanic zones in Central Europe. At the same time, the radiometric ages have implications for the interbasinal correlation and for the geodynamic evolution of the Variscan Orogeny.     

Effects of placer mining on suspended sediment budget: case study of north of Russia’s Kamchatka Peninsula

Abstract

Placer mines are located in river valleys, along river benches, or along the pathways of ancient channels. Open-pit mining alters the stream hydrology and enhances sediment transport. The present study focuses on sediment transport in the area of the platinum placer mining located at the north of Russia’s Kamchatka Peninsula (Seynav-Galmoenan placer deposits). Based on hydrological field investigations, a conceptual model was derived to assess anthropogenic effects on the total sediment budget of rivers. The model illustrates key processes controlling sediment dynamics in the Vyvenka River basin. Field work included water-discharge and sediment-load measurements, assessment of annual channel change in rivers in mining site areas, and evaluation of the relative importance of sediment sources and transport processes. In this study, we estimated total sediment delivery from opencast placer mining of 60 t year^-1; the annual mass wasting rate ranges from 2 to 5.5 kg m^-2 year^-1, which is three orders of magnitude higher than from non-mined streams. Mass wasting dominates surface erosion on the hillslopes and produces significant wastewater effluents; however, erosion of the artificially stratified channel reaches is the primary contributor to the annual sediment yield of the mined rivers (21.4%).

Editor D. Koutsoyiannis

Citation Chalov, S.R., 2014. Effects of placer mining on suspended sediment budget: case study of north of Russia’s Kamchatka Peninsula. Hydrological Sciences Journal, 59 (5), 1081–1094.     

Non‐hyperbolic common reflection surface

The method of common reflection surface (CRS) extends conventional stacking of seismic traces over offset to multidimensional stacking over offset‐midpoint surfaces. We propose a new form of the stacking surface, derived from the analytical solution for reflection traveltime from a hyperbolic reflector. Both analytical comparisons and numerical tests show that the new approximation can be significantly more accurate than the conventional CRS approximation at large offsets or at large midpoint separations while using essentially the same parameters.     

Seismic data analysis using local time‐frequency decomposition

Many natural phenomena, including geologic events and geophysical data, are fundamentally nonstationary ‐ exhibiting statistical variation that changes in space and time. Time‐frequency characterization is useful for analysing such data, seismic traces in particular. We present a novel time‐frequency decomposition, which aims at depicting the nonstationary character of seismic data. The proposed decomposition uses a Fourier basis to match the target signal using regularized least‐squares inversion. The decomposition is invertible, which makes it suitable for analysing nonstationary data. The proposed method can provide more flexible time‐frequency representation than the classical S transform. Results of applying the method to both synthetic and field data examples demonstrate that the local time‐frequency decomposition can characterize nonstationary variation of seismic data and be used in practical applications, such as seismic ground‐roll noise attenuation and multicomponent data registration.     

Vertical structure of the Venus cloud top from the VeRa and VIRTIS observations onboard Venus Express

We investigate the Venus cloud top structure by joint analysis of the data from Visual and Thermal Infrared Imaging Spectrometer (VIRTIS) and the atmospheric temperature sounding by the Radio Science experiment (VeRa) onboard Venus Express. The cloud top altitude and aerosol scale height are derived by fitting VIRTIS spectra at 4–5 μm with temperature profiles taken from the VeRa radio occultation. Our study shows gradual descent of the cloud top from 67.2 ± 1.9 km in low latitudes to 62.8 ± 4.1 km at the pole and decrease of the aerosol scale height from 3.8 ± 1.6 km to 1.7 ± 2.4 km. These changes correlate with the mesospheric temperature field. In the cold collar and high latitudes the cloud top position remarkably coincides with the sharp minima in temperature inversions suggesting importance of radiative cooling in their maintenance. This behaviour is consistent with the earlier observations. Spectral trend of the cloud top altitude derived from a comparison with the earlier observations in 1.6–27 μm wavelength range is qualitatively consistent with sulphuric acid composition of the upper cloud and suggests that particle size increases from equator to pole.     

The spectrum of comet C/2009 R1 (McNaught) in 4140–5240 Å wavelength region

The spectroscopic observations of comet C/2009 R1 (McNaught) were carried out with the 2 m Zeiss-RCC Telescope of Pik Terskol Observatory operated by the International Center for Astronomical and Medico-Ecological Research (Ukraine, Russia). The Multi Mode Cassegrain spectrometer was used to obtain spectra of moderate spectral resolving power with a wavelength coverage from 4140 to 5240 Å. The spectrum is characterized by the extremely low continuum level and strong molecular features. 192 emission lines of C₂, CN, CH, NH₂, CO⁺, and CH⁺ have been identified by the comparison of the observed and theoretical spectra of the molecules. The ratios of the gas production rates of Q(C₂)/Q(CN)=1.32, Q(CH)/Q(CN)=0.49, and Q(NH₂)/Q(CN)=0.81 were derived using a Haser model.     

Seismic characterization of the fall 2007 eruptive sequence at Bezymianny Volcano,Russia

We examine an eruptive sequence in late 2007 at Bezymianny Volcano to characterize the magmatic plumbing system and eruption-related seismicity. Earthquake locations reveal seismicity below and offset to the north of the volcano along a tectonic fault. Based on historical seismicity, the magma chamber is postulated to have a top at about 6 km depth. Minor dome explosions, large sub-plinian eruptions and dome collapses are analyzed using an automated event classification scheme. Low-frequency tremor, interpreted as gas escape, and low-frequency earthquakes are a dominant proportion of the energy released. We also examine multiplet earthquakes whose behavior during the study period changed significantly and systematically before the largest eruption, demonstrating the potential of tracking multiplets to assess changing conditions with the conduit.     

An Elliptical Model for Deformation Due to Groundwater Fluctuations

Historically, surface subsidence as a result of subsurface groundwater fluctuations have produced important and, at times, catastrophic effects, whether natural or anthropogenic. Over the past 30?years, numerical and analytical techniques for the modeling of this surface deformation, based upon elastic and poroelastic theory, have been remarkably successful in predicting the magnitude of that deformation (Le Mouélic and Adragna in Geophys Res Lett 29:1853, 2002). In this work we have extended the formula for a circular-shaped aquifer (Geertsma in J Petroleum Tech 25:734–744, 1973) to a more realistic elliptical shape. We have improved the accuracy of the approximation by making use of the cross terms of the expansion for the elliptic coordinates in terms of the eccentricity, e, and the mean anomaly angle, M, widely used in astronomy. Results of a number of simulations, in terms of e and M developed from the transcendental Kepler equation, are encouraging, giving realistic values for the elliptical approximation of the vertical deformation due to groundwater change. Finally, we have applied the algorithm to modeling of groundwater in southern California.