ALBERT

Notes: Numerical simulations are performed to investigate quantitatively density effects of a contaminant plume on its movement in time and space. The numerical model used is a characteristics/finite difference method. The density of the solute is described by an equation of state similar to sea water or lead nitrate. The results of a large number of simulations do not allow us to establish a general empirical law for predicting the fate of a density-dependent plume. Whether density effects are important or not depends on a variety of hydraulic parameters of the aquifer model, such as the permeability (isotropic or anisotropic), flow gradient, the hydrodynamic dispersivity, and the time-scale considered. Following some theoretical ideas of previously derived analytical scaling laws for buoyant plumes, the concept of a near-source and a far-source region of the plume has been found very useful. The modeled plume centerlines compare favorably with the predictions of these scaling laws in the intermediate-source region, but deviate significantly in the far-source region where diffusion processes become important or necking instabilities at the plume edges occur. It is found that the combined influence of the various model parameters above can be very different, depending on whether the plume is still within the near-source or has already extended into the far-source region. In spite of the large dependency of the density effects on these model parameters, in some cases variable density might have an effect on the plume migration for already moderate density contrasts of~0.3% (which corresponds to a concentration of~4000 ppm for a leachate of salt or lead nitrate). Hydrodynamic dispersion tends to reduce the density effects. For sufficiently small values of the dispersivity, convective instabilities and fingering phenomena occur at the horizontal plume boundaries. For a lighter-than-water contaminant, such as acetone or methylethylketone, significant buoyant movements occur only for (unrealistically) high concentration of ~ 20,000 ppm. In conclusion the results of the simulations do not provide a generally applicable guideline for the evaluation of density-dependence transport. Therefore, the individual numerical modeling of a particular site will often be indispensable.

Notes: A new technique for the simultaneous inversion for three-dimensional (3-D) seismic structure and hypocentres (SSH) is developed and validated. the seismic forward problem is solved with a new non-linear 3-D ray tracing procedure that includes direct (as first or later arrivals), refracted and reflected phases from various crustal discontinuities. the non-linear inversion problem is formulated in terms of a modified, iterative Levenberg-Marquardt (LM) technique. It is demonstrated that this method, in spite of its computational inexpediencies, has various properties that make it best suited for the solution of both the general non-linear inverse problem (near-quadratic convergence, due to the approximate restoration of the full Hessian of the objective function) and its linearized subproblems [where LM is equivalent to classical damped least squares (ridge regression)]. Therefore LM is able to play a dual role for the optimal regularization (OR) of both the non-linear and the linear ill-posed SSH problem. the SSH method is validated through simulated inversions of local traveltimes from the Rhine Graben region. the results demonstrate that the usual trade-off between focal depths and seismic velocities can be reduced strongly through the combined use of all crustal phases. A new non-linear statistical F-test shows that the Newton-like LM method gives a quasi-linear ‘appearance’ of the SSH problem: i.e. convergence is essentially obtained already in the first iteration. This is further confirmed from the results of the OR performed within both the non-linear and the linear model space employing the regularization techniques (RT's) of Tikhonov, the ridge regression, the stochastic inverse, the method of Backus & Gilbert, and a new method (Backus subjective). Some of these RTs rely on various forms of a priori model information so that they can, in principal, be derived from a general Bayesian formulation. However, the results of the OR illustrate the limitations of this approach, which is attributed to difficulties in specifying the appropriate covariance matrices in model and data space and discrepancies between the theoretical optimal model and its numerical realization. Therefore, those ORTs have been found the most useful, that rely on some form of graphical trade-off curves to systematically explore the model and data space. Based on their theoretical foundations and practical performances, the ORTs of Backus (subjective) and of Tikhonov are being chosen as the reference for the other RTs. Using the ORT of Backus, the minimum of the true error (MSE) is computed, after an a priori upper bound on the model has been selected. This allows one to estimate the statistical bias of the model which is proved to be formally equivalent to the resolution error, as epitomized in the Backus & Gilbert formalism. the Tikhonov ORT, which is used in its original form (the objective one) and as a new version (the subjective approach), allows to constrain best the optimal solution from both the model- and data viewpoints. All of the other Bayesian ORT's and that of Backus & Gilbert have not been found satisfactory, because they are not able to delimit the optimal model space appropriately.

Notes: The new technique of simultaneous inversion for hypocentres and crustal structure (SSH) using direct, refracted and reflected crustal phases is applied to the northern Rhine Graben/Rhenish Massif region. P- and S-wave arrival times of about 100 seismic events are inverted for locations and crustal structure. the issue of the coupling between crustal structure and hypocentre locations is investigated by comparing SSH models where the hypocentres have been fixed a priori (pure velocity inversion) with ‘full’ SSH inversion models. Although this computationally expedient variant of SSH leads to smaller reductions in the residuals than the corresponding ‘full’ SSH, their features compare surprisingly well. Improvements of over 100 per cent in the non-linear residual fit are obtained for the P-wave 3-D models and somewhat less when S phases are included which hints of variations in the assumed vp/vs ratio. Some of the structural results corroborate findings from previous deep-seismic-sounding experiments while others deliver new information on the petrology and tectonics of this region. For the uppermost crustal layer the SSH models show positive velocity anomalies that reflect the gneiss and granite basements found under most of the stations. the seismic velocities of the 3-D models for the Odenwald suggest a continuation of the gneiss outcrops down to the middle crust. Both the 1-D model and sections of the 3-D models reveal a small velocity decrease in the middle crust, clarifying an ambiguity of earlier refraction models. the lowermost crustal layer of the 3-D model is characterized by large positive anomalies (up= 7.3-7.4 km s-1) that are interpreted as a crust-mantle transition zone. For the upper mantle consistently high Pn velocities ∼8.4 km s-1 are found for both the 1-D and 3-D models. the structural results under the graben proper suggest the absence of many of the thermo-mechanical characteristics of a typical rift zone in the northern Rhine Graben. the simultaneously relocated hypocentres manifest some dependency upon the parametrization of the crustal model. Although the hypocentral movements are generally larger for the 1-D than for the 3-D SSH models, they are not sufficiently large to warrant a reinterpretation of the seismotectonics of the region. Overall the SSH results give evidence for a local correlation between decreased crustal velocity and reduced seismic activity in the middle and lower crust. This appears to reflect some general seismo-, thermo-mechanical and rheological concepts which postulate a ductile, aseismic flow regime for various anomalous portions of the middle and lower crust.

Notes: The new technique of simultaneous inversion for hypocentres and crustal structure (SSH) is applied to the southern Rhine Graben. P and S wave first and later arrival times of direct, refracted and reflected phases of 350 seismic events are used in the study. Substantial improvements of over 100 per cent in the non-linear residual fit are obtained for the 3-D and less for the 1-D models. Many of the structural results of the 3-D SSH models are consistent with major findings from other seismic refraction experiments and fit into the general geological, petrological and geodynamical frame of this area. Thus the thick sedimentary layer in the Rhine Graben proper manifests itself by large negative seismic velocity anomalies. For the middle crust the SSH models show a strong seismic differentiation between sections of the graben proper and the areas under its western and eastern shoulders of the Vosges and the Black Forest, respectively. Using a new a priori Bayesian inversion technique it has been attempted to substantiate the refraction-seismic low velocity zone of Gajewski & Prodehl (1987) in the middle crust under the Black Forest. the results demonstrate that such a velocity low is compatible with the observed traveltimes only if one assumes it as a more local crustal phenomenon in this area. In the lower crust the SSH models are able to clarify some controversies from earlier refraction experiments in the region. the models reveal many seismic features which are typical for continental rift zones such as high transitional velocity anomalies (∼7.4 km s-1) under parts of the graben proper (‘rift-cushion’). In the upper mantle, the models show a ring-like high velocity structure of 8.30-8.40 km s-1, centred around a low velocity area (∼7.9 km s-1) beneath the Kaiserstuhl. I conjecture this to be a ‘thermal fingerprint’ of a partially molten upwelling asthenospheric diapir bulging under the Mono. the simultaneously relocated hypocentres for the 1-D models show some systematic downward movements for the events in the lower crust of the southern Black Forest area, but otherwise do not differ too much from the initial ones to alter the present seismotectonic picture of the southern Rhine Graben. Thus the hypothesized phenomenon of the seismic gap along the southern section of the Graben Black Forest wedge can both structurally and seismically be substantiated. the relocated hypocentres suggest optically even a widening of this seismic gap. the later has thus to be accepted as a, possibly more general, characteristic of a graben formation.