Wave Processes in Inhomogeneous Nonlinear-Dissipative Media

Several problems for nonlinear localized wave processes are analysed. Wave solutions of the kink type, concentrated in the vicinity of some curve l, are considered. Both the solution and the curve l are unknown. It is shown that the determination of l may be realized without knowledge of the solution. For one class of problems, a variational principle for finding l, similar to the Fermat principle, is obtained. Types of waves are found which exist due to the inhomogeneity of the medium or due to the initial front curvature only.     

NEW WAYS FOR THE INTERPRETATION OF GEOELECTRICAL RESISTIVITY MEASUREMENTS IN THE SEARCH FOR AND DELIMITATION OF AQUIFERS

Abstract

Geoelectric resistivity measurements by means of direct current for solving hydrogeological problems have become increasingly significant in recent years. Measurements on the surface according to the four-point-method (SCHLUMBERGER or WENNER arrangement) result in so-called “apparent” resistivities ? α as a function of the electrode distance L. The evaluation of these measuring data, here in form of sounding graphs ? α(L/2), consists of the determination of true resistivities as a function of the depth z. Since a direct computation of ? (z) from α (L/2) is not possible in practice, theoretically computed master curves constitute the essential auxiliary means for the evaluation.

New simplified calculation techniques allow to establish accurately computed master curves for an underground consisting of more than three layers. By means of such standard graphs special problems of hydrogeology can quantitatively be solved by applying geoelectrical methods. The procedure is demonstrated on hand of complicated cases of aquifers devided into several storeys.     

Approaches indG/G-determinations

Summary Whereas observations of planets and solar satellites are more promising for detecting possible variations of Newtonian gravitational constant,G, with time the application of additional methods which are substantially different might be useful. It is discussed to what extent the tidal problems can be solved in connection with lunar orbit tracking for detectingG; further a relativeG-experiment at the earth surface is outlined.     

Evaluating Groundwater Interbasin Flow Using Multiple Models and Multiple Types of Data

The groundwater interbasin flow, Q_y, from the north of Yucca Flat into Yucca Flat simulated using the Death Valley Regional Flow System (DVRFS) model greatly exceeds assessments obtained using other approaches. This study aimed to understand the reasons for the overestimation and to examine whether the Q_y estimate can be reduced. The two problems were tackled from the angle of model uncertainty by considering six models revised from the DVRFS model with different recharge components and hydrogeological frameworks. The two problems were also tackled from the angle of parametric uncertainty for each model by first conducting Morris sensitivity analysis to identify important parameters and then conducting Monte Carlo simulations for the important parameters. The uncertainty analysis is general and suitable for tackling similar problems; the Morris sensitivity analysis has been utilized to date in only a limited number of regional groundwater modeling. The simulated Q_y values were evaluated by using three kinds of calibration data (i.e., hydraulic head observations, discharge estimates, and constant‐head boundary flow estimates). The evaluation results indicate that, within the current DVRFS modeling framework, the Q_y estimate can only be reduced to about half of the original estimate without severely deteriorating the goodness‐of‐fit to the calibration data. The evaluation results also indicate that it is necessary to develop a new hydrogeological framework to produce new flow patterns in the DVRFS model. The issues of hydrogeology and boundary flow are being addressed in a new version of the DVRFS model planned for release by the U.S. Geological Survey.     

Role of in situ cosmogenic nuclides 10be and 26al in the study of diverse geomorphic processes

The central premises of applications of the in situ cosmogenic dating method for studying specific problems in geomorphology are outlined for simple and complex exposure settings. In the light of these general models, we discuss the information that can be derived about geomorphic processes, utilizing concentrations of in situ produced cosmogenic radionuclides ¹⁰Be (half-life=1·5 ma) and ²⁶A1 (half-life=0·7 ma) in a variety of geomorphic contexts: glacial polish and tills; meteorite impact craters; alluvial fans; paleo-beach ridges; marine terraces; sand dunes; and bedrock slopes. We also compare ¹⁰Be-²⁶Al data with results obtained by other dating methods. We conclude that the technique of measuring in situ cosmic ray produced nuclides holds promise for quantitative studies of processes and time-scales in a wide range of geomorphological problems.     

Seismic zoning for initial‐ and total‐cost minimization

We consider two design criteria to study seismic zoning. In the first, codes require that structures be designed for some specified values. Zoning is then optimal when it minimizes the expected present value of the initial costs of all structures to be built in the region being zoned. In the second criterion, it is designed so that the present value of the total cost is minimized, including initial and maintenance costs as well as losses due to damage and failure. We will call these criteria zoning for the initial‐ and total‐cost minimization, respectively. It is shown that under certain conditions, the boundaries coincide with isoparametric curves and the problem may be solved in one dimension. We also deal with problems not reducible to a single dimension. Different methods are proposed to solve the various kinds of problems. The work ends with some illustrative examples. Copyright © 2000 John Wiley & Sons, Ltd.     

Two notes on the modern theory of inverse problems in geophysics

On the basis of comparison of the approaches to the solution of inverse problems in information theory and geophysics, it is shown that results, obtained in information theory, are suitable to supplement the theory of geophysical inverse problems. The conditions of the existence and uniqueness of the solutions of inverse problems in their practical discrete statement are specified. The terms of ɛ-entropy H _ɛ and informational capacity C _ɛ, characterizing “volumes” of unknown and observed data, are introduced. It is shown, that the instability of the solution of the inverse problem decreases with increase in H _ɛ, (increase in the “complexity” of studied section), if the relation H _ɛ ≤ C _ɛ is maintained.     

BAYESIAN ESTIMATION IN SEISMIC INVERSION. PART I: PRINCIPLES1

This paper gives a review of Bayesian parameter estimation. The Bayesian approach is fundamental and applicable to all kinds of inverse problems. Its basic formulation is probabilistic. Information from data is combined with a priori information on model parameters. The result is called the a posteriori probability density function and it is the solution to the inverse problem. In practice an estimate of the parameters is obtained by taking its maximum. Well-known estimation procedures like least-squares inversion or l₁ norm inversion result, depending on the type of noise and a priori information given. Due to the a priori information the maximum will be unique and the estimation procedures will be stable except (in theory) for the most pathological problems which are very unlikely to occur in practice. The approach of Tarantola and Valette can be derived within classical probability theory. The Bayesian approach allows a full resolution and uncertainty analysis which is discussed in Part II of the paper.