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A solute flux approach to transport in heterogeneous formations: 1. The general framework

It is common to represent solute tranport in heterogeneous formations in terms of the resident concentration C (x, t), regarded as a random space function. The present study investigates the alternative representation by q , the solute mass flux at a point of a control plane normal to the mean flow. This representation is appropriate for many field applications in which the variable of interest is the mass of solute discharged through a control surface. A general framework to compute the statistical moments of q and of the associated total solute discharge Q and mass M is established. With x the direction of the mean flow, a solute particle is crossing the control plane at y = η, z = ζ and at the travel (arrival) time τ. The associated expected solute flux value is proportional to the joint probability density function (pdf) g 1 of η, ζ and τ, whereas the variance of q is shown to depend on the joint pdf g 2 of the same variables for two particles. In turn, the statistical moments of η, ζ and τ depend on those of the velocity components through a system of stochastic ordinary differential equations. For a steady velocity field and neglecting the effect of pore‐scale dispersion, a major simplification of the problem results in the independence of the random variables η, ζ and τ. As a consequence, the pdf of η and ζ can be derived independently of τ. A few approximate approaches to derive the statistical moments of η, ζ and τ are outlined. These methods will be explored in paper 2 in order to effectively derive the variances of the total solute discharge and mass, while paper 3 will deal with the nonlinear effect of the velocity variance upon the moments of η, ζ and τ

Water Resources Research↗

Recent advances in understanding the interaction of groundwater and surface water

The most common image of the interaction of groundwater and surface water is that of the interaction of streams with a contiguous alluvial aquifer. This type of system has been the focus of study for more than 100 years, from the work of Boussinesq (1877) to the present, and stream-aquifer interaction continues to be the most common topic of papers discussing the interaction of groundwater and surface water. However, groundwater and surface water interact in a wide variety of landscapes from alpine to coastal. Within these landscapes, ground-water systems range in scale from local to regional, and the types of surface water include streams, lakes, wetlands, and oceans. Given the broad spectrum of the topic of groundwater and surface water interaction, an overview of studies of this topic could be organized according to surface water type, landscape type, scale of hydrologic systems, or field and analytical methods. All these factors are discussed, but this paper is organized according to landscape type because of the great increase in studies of the interaction of groundwater and surface water in landscapes other than riverine systems in the last 15 years. Furthermore, discussing studies by landscape type facilitates comparison of methods and results from different geologic and climatic settings. The general landscapes discussed are mountain terrane, riverine systems, coastal terrane, hummocky terrane, and karst terrane.

Reviews of Geophysics↗

Estimating 14C groundwater ages in a methanogenic aquifer

This paper addresses the problem of 14 C age dating of groundwaters in a confined regional aquifer affected by methanogenesis. Increasing CH 4 concentrations along the groundwater flow system and 13 C and 14 C isotopic data for dissolved inorganic carbon, dissolved organic carbon, and CH 4 clearly show the effect of methanogenesis on groundwater chemistry. Inverse reaction path modeling using NETPATH indicates the predominant geochemical reactions controlling the chemical evolution of groundwater in the aquifer are incongruent dissolution of dolomite, ion exchange, methanogenesis, and oxidation of sedimentary organic matter. Modeling of groundwater 14 C ages using NETPATH indicates that a significant part of groundwater in the Alliston aquifer is less than 13,000 years old; however, older groundwater in the range of 15,000–23,000 years is also present in the aquifer. This paper demonstrates that 14C ages calculated using NETPATH, incorporating the effects of methanogenesis on the carbon pools, provide reasonable groundwater ages that were not possible by other isotopic methods.

Water Resources Research↗

High-resolution Monte Carlo simulation of flow and conservative transport in heterogeneous porous media: 1. Methodology and flow results

In this, the first of two papers concerned with the use of numerical simulation to examine flow and transport parameters in heterogeneous porous media via Monte Carlo methods, various aspects of the modelling effort are examined. In particular, the need to save on core memory causes one to use only specific realizations that have certain initial characteristics; in effect, these transport simulations are conditioned by these characteristics. Also, the need to independently estimate length scales for the generated fields is discussed. The statistical uniformity of the flow field is investigated by plotting the variance of the seepage velocity for vector components in the x , y , and z directions. Finally, specific features of the velocity field itself are illuminated in this first paper. In particular, these data give one the opportunity to investigate the effective hydraulic conductivity in a flow field which is approximately statistically uniform; comparisons are made with first- and second-order perturbation analyses. The mean cloud velocity is examined to ascertain whether it is identical to the mean seepage velocity of the model. Finally, the variance in the cloud centroid velocity is examined for the effect of source size and differing strengths of local transverse dispersion.

Water Resources Research↗

The age of scarplike landforms from diffusion-equation analysis

The purpose of this paper is to review developments in the quantitative modeling of fault-scarp geomorphology, principally those since 1980. These developments utilize diffusionequation mathematics, in several different forms, as the basic model of fault-scarp evolution. Because solutions to the general diffusion equation evolve with time, as we expect faultscarp morphology to evolve with time, the model solutions carry information about the age of the structure and thus its time of formation; hence the inclusion of this paper in this volume. The evolution of fault-scarp morphology holds a small but special place in the much larger class of problems in landform evolution. In general, landform evolution means the evolution of topography as a function of both space and time. It is the outcome of the competition among those tectonic processes that make topography, erosive processes that destroy topography, and depositional processes that redistribute topography. Deposition and erosion can always be coupled through conservation-of-mass relations, but in general deposition occurs at great distance from the source region of detritus. Moreover, erosion is an inherently rough process whereas deposition is inherently smooth, as is evident from even casual inspection of shaded-relief, digital-elevation maps (e.g., Thelin and Pike, 1990; Simpson and Anders, 1992) and the current fascination with fractal representations oferoding terrains (e.g., Huang and Turcotte, 1989; Newman and Turcotte, 1990). Nevertheless, large-scale landform-evolution modeling, now a computationally intensive, advanced numerical exercise, is generating ever more realistic landforms (e.g., Willgoose and others, 1991a,b; Kooi and Beaumont, 1994; Tucker and Slingerland, 1994), although many of the rate coefficients remain poorly prescribed

Book chapter↗

Pre‐Cambrian and Paleozoic vulcanism of interior Alaska

The history of vulcanism in Alaska is a topic of great universal interest, but one which has had no adequate treatment. For some years the writer has been accumulating comparative data on this subject, and it is hoped that this information may some time be sufficiently amplified and coordinated to justify a general description of the sequential igneous history of Alaska. The scope of such an undertaking, however, can well be appreciated from the statement that Alaska is nearly a fifth the size of the United States, and that geologic studies have shown that igneous rocks have originated in Alaska in every geologic period, excepting perhaps the Cambrian and the Silurian. Therefore, in the present paper, it has seemed best to present only a part of this interesting record, and perhaps in subsequent papers to expand the areal and geologic limits of discussion. ©1935. American Geophysical Union. All Rights Reserved.

Eos, Transactions, American Geophysical Union↗

The channel‐storage method of determining effluent seepage

Some years ago the senior author, in collaboration with Norah Dowell Stearns, undertook to make a monthly inventory of the water‐supply of the Pomperaug River Basin, in Connecticut, from a study of data obtained by A. J. Ellis from 1913 to 1916. For this purpose approximate determinations or estimates were made of the ground‐water runoff, that is, of the part of the daily discharge of the river that consisted of water derived from the zone of saturation by effluent seepage. The determinations or estimates were essentially based on the assumption that after a week of fair weather the storm‐water was all discharged and that until the next rain the runoff was essentially all ground‐water (U.S. Geol, Surv. Water‐Supply Paper 597, pp. 107–116 and pi. 19, 1929). In the discussion of the methods and results of this investigation, the following statement was made (Water‐Supply Paper 597, pp. 145–146): “In this investigation the estimates of ground‐water runoff were based on the discharge of the Pomperaug at Bennetts Bridge—that is, on the discharge during the periods between rains, when there was virtually no direct runoff left in the stream‐system. Much better results could be obtained by basing the estimates on periods beginning as soon after rains as all of the direct runoff has reached the streams. With this method the ground‐water runoff during any particular day would be the total runoff minus the decrease in stream‐storage. The decrease in stream‐storage could be estimated by maintaining gages at several points on the trunk‐stream and on selected tributaries and making surveys of the stream‐system showing the approximate water‐areas of different parts of the system at different gage‐heights.”

Eos, Transactions, American Geophysical Union↗

Part I—History and activities of the section of geophysics of the United States Geological Survey

From the beginning of time, all ingenuity of mankind has been concentrated upon the methods of finding gold and unusual deposits in the earth. An illustration (Fig. 1) from the old treatise by Agricola, “De Re Metallica,” published in 1580, will serve to show the implicit faith of that generation in divining methods. However, it was not until 1920 that real progress was made in prospecting by using the latest advances of the physical sciences. The public interest was stimulated by the successes of these methods on the part of commercial operators, and governmental agencies received many requests for information concerning their reliability. There were also, in the late 1920's, high‐pressure mine‐promotion schemes which used geophysical methods in a very questionable manner, symbolized in Figure 2 as of 1928 by an electrified forked stick. Authoritative information concerning such practices for public protection was needed to curb such notorious undertakings. Dr. Scott Turner, then Director of the United States Bureau of Mines, thoroughly understood the situation and was first in the governmental departments to recognize the possible value of a study of modern prospecting methods. The Bureau of Mines began this investigation by employing Drs. A. S. Eve and D. A. Keys of McGill University for short periods in the summer in 1927. Their first publication [see 1 of “References” at end of paper] served to illustrate the fundamental scientific principles which underlie geophysical prospecting. This was followed by a second publication [2] giving the results of field‐tests. In the light of the rapid improvements during the intervening ten years, these two papers take a historical position.

Eos, Transactions, American Geophysical Union↗

Report of committee on relation of inch and meter

Those of you who attended the annual meeting of this Section on April 27, 1938, heard a paper entitled “A method for introducing a new standard of length” that was presented by Professor Philip Klssara, calling attention to the Bill then in Congress proposing to redefine the length of the inch. The paper has been published in the “Transactions of the American Geophysical Union“ [19th Annual Meeting, 1938, pp. 94–96]. Its closing paragraph is as follows: “As the American Geophysical Union has as one of its functions the duty of offering advice to the Congress on technical matters, I move, Mr. Chairman, that the Chairman be empowered to appoint a committee to study the matter and to report what recommendations should be made to Congress by the Union.”

Eos, Transactions, American Geophysical Union↗

Some features of the Livingston Formation near Nye, Montana

The Livingston Formation is a series of pyroclastic rocks several thousand feet thick cropping out on the north side of the Beartooth Mountains. These pyroclastic rocks grade laterally into the Claggett, Judith River, Bearpaw, and Lennep formations of the Montana Group, according to Stone and Calvert [see 1 of references at end of paper], showing that they were being deposited during much of Montana time; they are therefore of Upper Cretaceous age and antedate the Laramide orogeny. The purpose of this paper is to describe briefly several significant features of the Formation where it is exposed in the Nye No. 2 Quadrangle (Fig. 1) along the southeast edge of its outcrop. It is concluded that much of the Formation was formed by mudflows, and that certain chloritized beds were deposited by hot mudflows.

Montana↗

Early history of the Mexican volcano Parícutin

Owing to the good fortune of being stationed near the new volcano Parícutin when it first erupted, I was able to visit it when it was only a week old. As my observations have been recorded in full in a previous article [see 1 of “References” at end of paper], only a few of the more pertinent features are repeated here, in order to give a setting for the succeeding papers in this symposium.

Michoacan↗

Correlation of ground‐water levels and precipitation on Long Island, New York

A brief though concise statement of the history of ground‐water studies on Long Island, beginning with the early water‐level observations in Brooklyn by STODDARD in 1854, was given by THOMPSON [see 7 of “References” at end of paper]. These and other early data were considered later by LEGGETTE [8]. He evaluated them by means of a graph of the cumulative departure of precipitation. More recent studies by LEGGETTE [9] and by the writer have lead to the procedure outlined in Part I of this paper [10], which was founded upon an empirical approach suggested by LEGGETTE and was later justified by analysis based on the theory of BOUSSINESQ [11].

New York↗

Report of Committee on Runoff—1944–1945

The membership of the committee has been selected to afford good representation of geographic sections and of organizations engaged in runoff research. Some new members were added during the year in order to strengthen the representation of the committee in certain phases of runoff research. Norbert H. Leupold submitted his resignation in April because his work is no longer directly related to runoff‐research. At the beginning of the year members of the committee met to discuss its setup and plans for the future. The committee has two subcommittees, one dealing with floods and the other with subsurface‐flow. The question was considered whether progress might be facilitated by the addition of one or more additional committees dealing with logical classifications of the subject of runoff. The confusion in nomenclature and terminology relating to runoff was discussed,but it was thought that the present time was not fitting for comprehensive consideration of standardization. It was considered important that the writer of a paper dealing with runoff should make clear the usage of terms he follows In his paper. It was emphasized that there is still an important need for better understanding or liaison between groups dealing with the influence of land use on stream‐flow and those dealing with control and development of streams.

Eos, Transactions, American Geophysical Union↗

The glacial anticyclone theory examined in the light of recent meteorological data from Greenland—Part I

The glacial anticyclone theory, which William H. Hobbs propounded in 1910, is today still the only definitely formulated theory concerning the atmospheric movements that take place over an ice sheet of large extent. It stands chiefly on deductive grounds and contains several features that to climatologists as well as to glaciologists have always seemed questionable. Aside from the need of its verification for scientific reasons, there is now also urgent practical need for reliable information about the weather conditions that prevail over the ice sheet of Greenland, for Greenland lies athwart several of the great air routes of the future. In this paper, accordingly, the glacial anticyclone theory is first analyzed and then confronted with the facts of observation that are now at hand, especially those reported from the fixed meteorological stations which were maintained in the interior of Greenland during the 1930s. In this, the first part of the paper, the meteorological data from the Eismitte station of the German Wegener Expedition are reviewed. The second part will cover the areological data of that expedition and the similar material from the other ice‐cap stations. The conclusions reached are that there is no evidence of a virtually permanent “glacial anticyclone” centered over the Greenland ice sheet. On the contrary, there is consistent evidence from all parts of Greenland that the weather over the ice sheet is controlled by alternating cyclonic and anticyclonic movements. Cyclonic activity is most intense in southern Greenland and weakest in northern Greenland. The entire ice sheet is supplied with snow brought by rising maritime air masses, not by air descending from the upper troposphere. Aviators need not expect so much as a fifty‐fifty chance of meeting with good weather on flights across central Greenland, except for a few weeks in midsummer.

Eos, Transactions, American Geophysical Union↗

Discussion of “tide‐producing forces and artesian pressures”

I was an employee of the Texas State Board of Water Engineers in charge of the Fort Stockton field office at the time that the data for this paper were gathered. Since I have done both extensive and detailed ground‐water work in the Fort Stockton area, including the setting and maintaining of the water‐stage recorder at the Gonzales well, I believe I can add some pertinent hydrologic remarks about this paper. The authors state that the principal water‐bearing formation is a limestone. This opinion is not shared by myself and most likely the majority of other geologists in this area. Adkins [1927] favored the basal Cretaceous sands as the principal source of water to Comanche Springs. I believe that the most extensive and the principal water‐bearing formation is a sand and sandstone. The crevices and channels reported in wells and exposed at the springs are only a localized condition resulting from structural weakness and solution caused by a high water surface. The piezometric surface in sand and crevice wells is essentially identical; this suggests that there exists but one principal aquifer in this area. W.N. White, former District Geologist in Texas for the U.S. Geological Survey, in a personal communication to me in 1948, reported Comanche Springs to be the most reliable springs in Texas. This reliable flow strongly supports the concept of a sand aquifer, whose catchment area, or source, is of vast and varied extent, and a great distance from its outlet.

Eos, Transactions, American Geophysical Union↗

Montana earthquakes noted in pennsylvania mine‐water pools

A recent paper by daCosta [1959] reported water ‐level fluctuations caused by the Montana earthquake of August 18, 1959, and mentioned the fluctuations registered in three mine ‐ water pools of the Northern anthracite field in northeastern Pennsylvania , ten miles north of Wilkes‐Barre. This paper will discuss the water ‐level phenomena of these pools in more detail. Most of the coal mines near Wilkes‐Barre are idle, and ground water is forming extensive mine ‐ water pools in the underground mine openings. Some of the pools are interconnected by boreholes, tunnels, and other openings through the barrier pillars between adjacent mines.

Montana↗

The U. S. Geological Survey's gravity program in Washington, Idaho, Montana, and Wyoming

The following summary of the U . S . Geological Survey gravity program in Washington , Idaho , Montana , and Wyoming is one of a series of short papers that outline Geological Survey gravity projects in the western United States. The substance of this summary is a list of references of published papers on U . S . Geological Survey gravity projects in the northwestern states together with an index map (Figure 1) showing the location of the project, the approximate a real coverage reported in the publication, and the contour map given in the publication. Areas in Figure 1 are related to the References (part 2) by a number code. In addition, the gravity projects in progress are listed in Table 1, indicating the area in which the work is being done and the person in charge of the project. Capital letter relate the locations of the projects in Figure 1 to the list of projects in Table 1. No attempt has been made to indicate the areal coverage or contour interval of the projects in progress.

Washington, Idaho, Montana, Wyoming↗

Field determination of the three-dimensional hydraulic conductivity tensor of anisotropic media: 1. Theory

A field method is proposed for determining the three-dimensional hydraulic conductivity tensor and specific storage of an anisotropic porous or fractured medium. The method, known as cross-hole testing (to distinguish it from conventional single-hole packer tests), consists of injecting fluid into (or withdrawing fluid from) packed-off intervals in a number of boreholes and monitoring the transient head response in similar intervals in neighboring boreholes. The directions of the principal hydraulic conductivities need not be known prior to the test, and the boreholes may have arbitrary orientations (e.g., they can all be vertical). An important aspect of the proposed method is that it provides direct field information on whether it is proper to regard the medium as being uniform and anisotropic on the scale of the test. The first paper presents theoretical expressions describing transient and steady state head response in monitoring intervals of arbitrary lengths and orientations, to constant-rate injection into (or withdrawal from) intervals having similar or different lengths and orientations. The conditions under which these intervals can be treated mathematically as points are investigated by an asymptotic analysis. The effect of planar no-flow and constant-head boundaries on the response is analyzed by the theory of images. The second paper describes the field methodology and shows how the proposed approach works in the case of fractured granitic rocks.

Water Resources Research↗