Towards non-linear inversion for characterization of time-lapse phenomena through numerical modelling

We compare two geophysical survey measurements of the same type made at different times in order to characterize the change in the geological medium during the elapsed time. The aim of this study is to develop a strategy using a full non-linear inversion algorithm as the interpretation tool. In this way, not only the location and the form of the changes are recovered, but also the changes in the material parameters of the geological medium can be estimated. In order to solve this fully non-linear problem, the so-called ‘multiplicative regularized contrast source inversion’ (MR-CSI) method is employed. The unique property of this iterative method is that it does not solve the forward problem at each iterative step. This makes it possible to use the non-linear inversion algorithm for large-scale computation problems. The numerical results show that by taking into account the non-linear nature of the problem, interpretation of the time-lapse data can be significantly improved, compared with that obtained using linear inversion.     

A record of phosphorus dynamics in oligotrophic lake sediment

Historical phosphorus (P) dynamics were studied using sediment cores from three oligotrophic, acidic lakes in Maine, USA. Long-term oligotrophy of these lakes is consistent with high sediment aluminum (as Al(OH)₃) concentrations, as Al inhibits internal P loading, even under reducing conditions. The role of microbially-mediated reactions in controlling redox conditions was evaluated by estimating microbial biomass and relative abundance of specific functional groups. Sediments were fractionated using a sequential chemical extraction technique and all lakes met criteria for P retention based on threshold sediment concentrations of Al, Fe, and P fractions as determined by (Kopáček et al. (2005) Limnol Oceanogr 52: 1147–1155). Sediment NaOH-extractable molybdate-reactive P (rP) and non-reactive P (nrP) represent P associated with non-reducible phases, and organic matter-related P, respectively. Total P (TP) does not decrease with sediment depth, as is typical of eutrophic lake sediments; however, nrP/TP decreases and rP/TP increases for all three lakes, indicating nrP mineralization without any significant upward diffusion and release into the hypolimnion; i.e. diagenesis of P is conservative within the sediment. Two diagenetic models were developed based on nrP and rP concentrations as a function of sediment age. The first model assumes a first-order decay of nrP, the rate coefficient being a function of time, and represents irreversible nrP mineralization, where the produced PO₄ is permanently sequestered by the sediment. The second model assumes a first-order reversible transformation between nrP and rP, representing biotic mineralization of organic P followed by incorporation of inorganic P into microbial biomass. Both models reflect preservation of TP with no loss to overlying water. The rate coefficients give us insight into qualities of the sediment that have affected mineralization and sequestration of phosphorus throughout the ²¹⁰Pb-dateable history of each lake. Similar models could be constructed for other lakes to help reconstruct their trophic histories. Paleolimnological reconstruction of the sediment P record in oligotrophic lakes shows mineralization of nrP to rP, but unlike the case in eutrophic lake sediments, sediment TP is preserved in these sediments.     

Multi-proxy paleolimnological assessment of biogeochemical versus food web controls on the trophic states of two shallow,mesotrophic lakes

The frequency of nuisance algal blooms has been increasing during the last two decades in the shallow, headwater East Pond (Smithfield, Maine, USA). Meanwhile, the hydrologically linked North Pond has not experienced an increase in algal blooms, despite similar morphometry and higher external nutrient loads. Possible explanations for this difference include stronger trophic cascade effects from planktivorous white perch (Morone americana) in East Pond as well as differences in phosphorus (P) release from the sediments of these two lakes. We conducted a paleolimnological investigation of these two lakes to assess whether sedimentary evidence supported trophic cascade effects based on cladoceran ephippia size, diatom fossils, and fossil pigments or biogeochemical controls based on potential sedimentary P release as the primary driver of these increased algal blooms in East Pond. At the time of white perch introduction (~1930–1950), ephippia size increases in East Pond, although no changes are observed in either diatom abundance or trends in the algal pigments. Instead, algal pigments increase in recent decades (~1980 to present) along with an increase in diatom taxa with higher TP optima These results suggest that predation by white perch is not resulting in top-down effects on algal abundance in East Pond, as predicted by the trophic cascade hypothesis. While the P content of sediments from both lakes is relatively equal, the releasable P in the top 10 cm of sediment in East Pond constitutes a greater percentage of the P extracted. Also, North Pond sediments exhibit a greater capacity to permanently bury P via the mechanisms of sorption to Al(OH)_3(s) and a slower mineralization of organic P compounds. The results of this investigation suggest that the ultimate driver of the recent algal blooms in East Pond is internal P release from the sediments instead of trophic cascade effects.     

Kinetics of sorption and abiotic oxidation of arsenic(III) by aquifer materials

The fate of arsenic in groundwater depends largely on its interaction with mineral surfaces. We investigated the kinetics of As(III) oxidation by aquifer materials collected from the USGS research site at Cape Cod, MA, USA, by conducting laboratory experiments. Five different solid samples with similar specific surface areas (0.6-0.9 m² g⁻¹) and reductively extractable iron contents (18-26 μmol m⁻²), but with varying total manganese contents (0.5-3.5 μmol m⁻²) were used. Both dissolved and adsorbed As(III) and As(V) concentrations were measured with time up to 250 h. The As(III) removal rate from solution increased with increasing solid manganese content, suggesting that manganese oxide is responsible for the oxidation of As(III). Under all conditions, dissolved As(V) concentrations were very low. A quantitative model was developed to simulate the extent and kinetics of arsenic transformation by aquifer materials. The model included: (1) reversible rate-limited adsorption of As(III) onto both oxidative and non-oxidative (adsorptive) sites, (2) irreversible rate-limited oxidation of As(III), and (3) equilibrium adsorption of As(V) onto adsorptive sites. Rate constants for these processes, as well as the total oxidative site densities were used as the fitting parameters. The total adsorptive site densities were estimated based on the measured specific surface area of each material. The best fit was provided by considering one fast and one slow site for each adsorptive and oxidative site. The fitting parameters were obtained using the kinetic data for the most reactive aquifer material at different initial As(III) concentrations. Using the same parameters to simulate As(III) and As(V) surface reactions, the model predictions were compared to observations for aquifer materials with different manganese contents. The model simulated the experimental data very well for all materials at all initial As(III) concentrations. The As(V) production rate was related to the concentrations of the free oxidative surface sites and dissolved As(III), as with apparent second-order rate constants of and for the fast and the slow oxidative sites, respectively. The As(III) removal rate decreased approximately by half for a pH increase from 4 to 7. The pH dependence was explained using the acid-base behavior of the surface oxidative sites by considering a surface pK_a = 6.2 (I = 0). In the presence of excess surface adsorptive and oxidative sites, phosphate diminished the rate of As(III) removal and As(V) production only slightly due to its interaction with the oxidative sites. The observed As(III) oxidation rate here is consistent with previous observations of As(III) oxidation over short transport distances during field-scale transport experiments. The model developed here may be incorporated into groundwater transport models to predict arsenic speciation and transport in chemically heterogeneous systems.     

Magneto-elasticSH-type of motion

Summary TheSH-type of motion in an isotropic elastic halfspace with infinite electrical conductivity subjected to an uniform magnetic field and disturbed by a buried source is investigated. Expressions for the surface displacements for various type of sources are obtained by an application of Cagniard technique. Numerical calculation has been performed for the case of a diapole source moving parallel to the surface of the halfspace with an uniform velocity.     

Comparative studies of various missing data treatment methods - Malaysian experience

In practice, there are problems of data reliability and ability of the data to represent the phenomena being considered. Often, the presence of gaps will shorten the records and will render spurious results or misleading conclusions. The aim of this study is to compare various treatment methods to make up the missing records. Temporal and spatial characteristics are studied before any record is being treated. Reference will be made to rainfall records for the Klang River basin, Malaysia. Studies indicate that the most appropriate approach is the modified normal ratio method.     

Preconditioned non‐linear conjugate gradient method for frequency domain full‐waveform seismic inversion

We present preconditioned non‐linear conjugate gradient algorithms as alternatives to the Gauss‐Newton method for frequency domain full‐waveform seismic inversion. We designed two preconditioning operators. For the first preconditioner, we introduce the inverse of an approximate sparse Hessian matrix. The approximate Hessian matrix, which is highly sparse, is constructed by judiciously truncating the Gauss‐Newton Hessian matrix based on examining the auto‐correlation and cross‐correlation of the Jacobian matrix. As the second preconditioner, we employ the approximation of the inverse of the Gauss‐Newton Hessian matrix. This preconditioner is constructed by terminating the iteration process of the conjugate gradient least‐squares method, which is used for inverting the Hessian matrix before it converges. In our preconditioned non‐linear conjugate gradient algorithms, the step‐length along the search direction, which is a crucial factor for the convergence, is carefully chosen to maximize the reduction of the cost function after each iteration. The numerical simulation results show that by including a very limited number of non‐zero elements in the approximate Hessian, the first preconditioned non‐linear conjugate gradient algorithm is able to yield comparable inversion results to the Gauss‐Newton method while maintaining the efficiency of the un‐preconditioned non‐linear conjugate gradient method. The only extra cost is the computation of the inverse of the approximate sparse Hessian matrix, which is less expensive than the computation of a forward simulation of one source at one frequency of operation. The second preconditioned non‐linear conjugate gradient algorithm also significantly saves the computational expense in comparison with the Gauss‐Newton method while maintaining the Gauss‐Newton reconstruction quality. However, this second preconditioned non‐linear conjugate gradient algorithm is more expensive than the first one.     

Simulation of Vortex-Induced Vibrations of A Cylinder Using ANSYS CFX Rigid Body Solver

This article simulates the vortex-induced oscillations of a rigid circular cylinder with elastic support using the new ANSYS CFX rigid body solver. This solver requires no solid mesh to setup FSI (Fluid Structure Interaction) simulation. The two-way case was setup in CFX only. Specific mass of the cylinder and flow conditions were similar to previous experimental data with mass damping parameter equal to 0.04, specific mass of 1 and Reynolds number of 3800. Two dimensional simulations were setup. Both one-degree-of-freedom and two-degree-of-freedom cases were run and results were obtained for both cases with reasonable accuracy as compared with experimental results. Eight-figure XY trajectory and lock-in behavior were clearly captured. The obtained results were satisfactory.