EIN AUTOMATISCHES VERFAHREN ZUR INTERPRETATION MAGNETISCHER ANOMALIEN NACH DER METHODE DER KLEINSTEN QUADRATE*

The interpretation of magnetic anomalies on the basis of model bodies is preferably done by making use of “trial and error” methods. These manual methods are tedious and time consuming but they can be transferred to the computer by making the required adjustments by way of the method of least squares. The general principles of the method are described. Essential presumptions are the following:

• 1 the assumption of definite model bodies
• 2 the existence of approximation values of the unknown quantities (position, dip, magnetization, etc.)
• 3 a sufficiently large number of measuring values, so that the process of adjustment can be carried out.

The advantages of the method are the following:

• 1 substantial automatization and a quick procedure by using computers
• 2 determination of the errors of the unknown quantities.

The method was applied to the interpretation of two-dimensional ΔZ- and ΔT-anomalies. Three types of model bodies are taken as basis of the computer program, viz. the thin dyke, infinite resp. finite in its extension downward and the circular cylinder. Only the measuring values are given to the computer. The interpretation proceeds in the following steps:

• 1 calculation of approximation values
• 2 determination of the model body of best fit
• 3 iteration in the case of the model body of best fit.

The computer produces the end values of the unknown quantities, their mean errors, and the pertaining theoretical anomalies. These end results are given to a plotting machine, which draws the measured curve, the theoretical curve and the model bodies. Interpretation examples are given.     

A MAN/COMPUTER INTERPRETATION SYSTEM FOR RESISTIVITY SOUNDINGS OVER A HORIZONTALLY STRAFIFIED EARTH*

The proposed system works as follows:

• 1 By a trial-and-error procedure using a graphic display terminal a geologically relevant layer sequence with parameters (ρ_j, d_j) is adjusted to yield roughly the measured curve.
• 2 The resulting layer sequence is used as starting model for an iterative least squares procedure with singular value decomposition. Minimization of the sum of the squares of the logarithmic differences between measured and calculated values with respect to the logarithms of the resistivities and thicknesses as parameters linearizes the problem to a great extent, with two important implications:

• a) a considerable increase in speed (the number of iterations goes down), thus making it cheap to achieve the optimum solution;
• b) the confidence surfaces in parameter space are well approximated by the hyper-ellipsoids defined by the eigenvalues and eigenvectors of the normal equations.

Since these are known from the singular value decomposition we do in fact know all possible solutions compatible with the measured curve and the geological concept.

• 3 It is possible to “freeze” any combination of parameters at predetermined values. Thus extra knowledge and/or hypotheses are easily incorporated and can be tested by rerunning step (2). The overall computing time for a practical case is of the order of 10 sec on a CDC 6400.

     

GEOPHYSICAL ANOMALY INTERPRETATION OF POTENTIAL FIELDS BY MEANS OF SINGULAR POINTS METHOD AND FILTERING*

The calculation of potential field anomalies on different levels below the measuring level permits to localize the singular points related to the sources of anomalies. It is possible to achieve considerable improvement of the resolution of this method

• 1) filtering of analytical downward continuation,
• 2) the use of the magnitude of the gravitational vector,
• 3) calculation of physe changes.

The numerical examples confirm these assumptions.     

IMPEDANCE OF A PLANE ELECTROMAGNETIC WAVE AT THE SURFACE OF A LAYERED CONDUCTING EARTH WITH DIPPING ANISOTROPY*

The problem of a plane wave incident on a non-isotropic dipping layer lying over an isotropic conducting substratum has been studied and some numerical results are presented to show the effects of

• 1) degree of anisotropy m,
• 2) conductivity contrast between the substratum to the upper layer b,
• 3) angle of inclination of the axis of anisotropy α,

on the variation of amplitude and phase difference of the wave impedance with the normalized skin-depth (d/δ₁).     

A generalized continuum method for dynamic analysis of asymmetric tall buildings

The paper presents a continuum method for dynamic analysis of asymmetric tall buildings with uniform cross-section in which the horizontal stiffness is provided by shear walls and columns of arbitrary shape and layout, coupled by horizontal beams. The equations of motions are formulated in variational terms, including axial strain energy. Numerical solutions, obtained by using finite time differences and infinite polynomials, are presented for the response of a twenty-storey building with six shear walls to an impact load and earthquake accelerations. It is shown that omission of the axial deformations results in a substantially distorted pattern of behaviour, some of its effects being:

• 1 Overestimation of the bending stiffness of the coupled shear walls, with corresponding changes in their stiffness ratios.
• 2 Underestimation of the periods of the principal modes, with a corresponding change in the dynamic response.
• 3 Distortion of the magnitude, form, time of onset and coupling of the maximum displacements.
• 4 Pronounced change in the shear force and moment diagrams for the shear walls, the beams and the building as a whole.

     

Analysis of riverbank instability due to toe scour and lateral erosion

This paper provides instruction in the use of the computer spreadsheet to undertake the calculations necessary to apply the Osman–Thorne bank stability analysis for steep, eroding riverbanks. The guide explains how to input the necessary parameters into the LOTUS 123 spreadsheet in order to:

• 1 find the initial factor of safety of the bank with respect to slab-type failure;
• 2 test the sensitivity of bank stability to changes in the engineering properties of the bank material;
• 3 analyse the response of bank stability to toe scour and/or lateral erosion and find the critical condition;
• 4 find the geometry of the failure surface and failure block;
• 5 analyse the response of bank stability to further toe scour and/or lateral erosion;
• 6 find the geometry of the failure surface and failure block in subsequent failures.

     

Studies on the Toxicity of a few Pesticides on Colisa fasciatus and Notopterus notopterus with Reference to Histopathology and Histochemistry. Part 1: Bioassay Studies

An attempt has been made to study the toxicity of two commonly used pesticides aldrin (organochlorine) and ethyl-parathion (organophosphorus) to the fish Colisa fasciatus (Anabantidae) and Notopterus notopterus (Notopteridae). During bioassay studies, the behaviour of the fishes was recorded. The aldrin concentration used lies between 0.021 mg/1 and 0.042 mg/1 for C. fasciatus and 0.00056 mg/1 and 0.00135 mg/1 for N. notopterus. The ethyl-parathion concentration used lies between 1.8 mg/1 and 3.7 mg/1 for C. fasciatus and 0.49 mg/1 and 1.00 mg/1 for N. notopterus.

• – The effect of lethal aqueous concentrations of pesticides on the Fishes prior to death are usually manifested by excitation, erratic swimming ability, difficulty in respiration, increasing in ventilation rate, jerky movements of body and fin fast, up- and downward movements, convulsions, loss of equilibrium, loss of the original colour of the body skin and the excess secretion of mucus by the gills and the body wall.
• – the TL_m values for 24, 48 and 96 hours of exposition are determined for both species of fish and both pesticides at the following variables:

• ? three levels of temperature,
• ? three levels of dissolved oxygen,
• ? three levels of pH,
• ? three fish sizes.

• – statistical analysis of variance shows, that all variables have a significant effect on the TL_m values of both pesticides for both fish species;
• – Aldrin (chlorinated hydrocarbon) is more toxic than ethylparathion (organophosphate) at all variables;
• – Colisa fasciatus is the more resistant species than Notopterus notopterus.
• – the relationship between the total number of the fishes N₀, survival numbers N and time t can be expressed by a mathematical formula as:
• – the harmless concentration to C. fasciatus ranged from 0.0049 mg/1 to 0.0161 for aldrin, 0.54 mg/1 to 0.99 mg/1 for ethyl-parathion and to N. notopterus from 0.00012 mg/1 to 0.00045 mg/1 for aldrin, 0.10 mg/1 to 0.21 mg/1 for ethyl-parathion;
• – the aldrin should be diluted at least 4000 times and ethyl-parathion 320 times of its actual concentration.

     

RELATIVE CONTRIBUTION TO SIGNAL BY GROUND ELEMENTS IN TWO-COIL INDUCTION LOGGING SYSTEM*

A two-coil induction logging system in an infinite homogeneous medium has been theoretically analysed for the relative contributions of various ground elements to the total signal at the receiver. Unlike an earlier approximate treatment by Doll (1949), the present analysis takes skin effect into account (while neglecting displacement currents). Contour diagrams depicting relative contributions from every ground point and diagrams for vertical and radial/lateral investigation characteristics are presented. The results differ significantly from Doll's in the following points:

• 1 The relative contribution is frequency and conductivity dependent;
• 2 It does not show symmetry with respect to the center of coil system;
• 3 It alternates between positive and negative values with distance;
• 4 Real and imaginary contributions for a given conductivity and frequency are different from each other.

The possibilities of a horizontal-horizontal sonde is briefly examined and found to be inferior to the usual sonde because of its higher sensitivity to the mud column and the invaded zone.     

Hysteresis‐based flood‐wave analysis using the concept of strain

Hysteresis represents a loop in a rating curve and is a phenomenon which closely resembles that occurring in stress–strain curves used for studying the elastic properties of solid substances in engineering mechanics. Earlier hysteresis‐based studies used for defining floodwave propagation in open channels have qualitatively shown that hysteresis is an index of energy loss during floodwave propagation. Using the concept of elasticity, this paper introduces a new term called flow strain (defined as the ratio of change in discharge to the initial discharge) for investigating hysteresis. The usefulness of this new term is evaluated with use of four dam‐break studies. The study reveals that:

• 1 flow strain is a function of three wave speeds, Seddon speed, Lagrange speed, and elastic speed;
• 2 a single linear reservoir concept frequently used in flood routing is a specific variant of the Seddon speed formula;
• 3 the non‐linear storage–discharge relationship, widely used in overland flow modelling, is a variant of the kinematic wave representation;
• 4 the discharge ordinates on the recession part of a hydrograph follow a simple first‐order autoregressive form;
• 5 the hysteresis, phase difference and logarithmic decrement all define attenuation and are indices of energy loss during floodwave propagation.

Copyright © 2001 John Wiley & Sons, Ltd.     

Observed Drawdown Pattern Around a Well Partially Penetrating a Vertically Extensive Water-Table Aquifer

In order to understand the flow pattern around a pumping well partially penetrating a vertically extensive aquifer, a specially designed pumping test was carried out in Pakistan. In this paper salient features of the test have been described. The spatial distributions of drawdown have been shown graphically. Some of the preliminary conclusions made from the drawdown pattern include:

• • The distance beyond which the flow is likely to be horizontal increases with decrease in the degree of aquifer penetration.
• • In equidistant observation wells open at different depths, (1) the drawdowns tend to merge at larger times, provided the observation point is located within the screened section of the aquifer; (2) the less the depth of penetration is, the earlier the drawdowns start merging; and (3) the initial rate of drawdown near the aquifer top is slow but catches up with time to exceed those at deeper points.

     

Phylogenetic systematics of chelonioid sea turtles

Abstract Chelonioid sea turtles (Order Testudinata; Superfamily Chelonioidea) first appear in the early Cretaceous (Aptian-Albian). Their long fossil record is excellent compared to most marine tetrapods. Nonetheless, there has been no inclusive attempt to provide an analysis of cladistic relationships among this group. In this paper, the following chelonioid classification is proposed, based on 76 characters among 20 fossil and six living well- represented genera:

• 1 Family Cheloniidae (Coniacian to Recent); Toxochelys, Ctenochelys, Osteopygis, Erquelinnesia, Allopleuron, Argillochelys, Puppigerus, Eochelone, Syllomus, Natator, Eretmochelys, Chelonia, Caretta, Lepidochelys
• 2 Family Protostegidae (Aptian to Maastrichtian?); ‘Santana new protostegid’,Rhinochelys, Notochelone, Desmatochelys, Chelosphargis, Protostega, Archelon
• 3 Family Dermochelyidae (Santonian? to Recent); Corsochelys, ‘HMG new dermo-chelyid’, Eosphargis, Psephophorus, Dermochelys.

     

Earthquake response of steel-framed multistorey buildings with set-backs

A study is made of the dynamic behaviour of multistorey steel rigid-frame buildings with set-back towers. The effects of set-backs upon the building frequencies and mode shapes are examined. Then the effects of set-backs on seismic response are investigated by analysing the response of a series of set-back building frame models to the El Centro ground motion. Finally, the computed responses to the El Centro earthquake are compared with some code provisions dealing with the seismic design of set-back buildings. The conclusions derived from the study include the following:

• 1. The higher modes of vibration of a set-back building can make a very substantial contribution to its total seismic response; this contribution increases with the slenderness of the tower.
• 2. Some of the important response parameters for the tower portion of a set-back building are substantially larger than for a related uniform building.
• 3. For very slender towers, the transition region between the tower and the base may be subjected to very large storey shears.

     

DEVELOPMENT OF MORE EFFICIENT AIRGUN ARRAYS: THEORY AND EXPERIMENT*

Source strength of an airgun array may be increased by:

• — utilizing higher pressure,
• — increasing total array volume,
• — employing more guns,
• — improving gun efficiency.

One measure of gun efficiency is “specific source strength”, P_a*, defined as source strength per unit quantity of air used. Typical units are MPa m/l. Most developments are directed toward increasing gun pressure and/or gun volume to increase source strength of the array. These efforts require that more air compressors be installed onboard the ship. Consequently, a larger ship may be needed for the additional compressors, guns, and auxiliary equipment. A development program was initiated in 1976 to increase source strength of the array without using a larger ship. New guns were designed and built—one for 41.4 MPa and 7.37 liter (6000 p.s.i./450 in³) operation and another with 13.8 MPa and 4.92 liter (2000 p.s.i./300 in³) capability. Experiments were conducted with these new guns (and existing guns) over a range of pressures from 13.8 to 41.4 MPa (2000 to 6000 p.s.i.). Design of the new guns was aided by a mathematical model. The model relates physical dimensions of the airgun to acoustic pressure in the water. It consists of four nonlinear differential equations relating

• — shuttle motion,
• — bubble pressure,
• — chamber pressure,
• — bubble radius.

The last equation is the “free-bubble-oscillation equation” and represents the ideal case of a pressurized bubble released instantaneously in water. The three other equations modify this ideal case; the four equations together model an airgun of the type manufactured by Bolt Associates, Inc.     

RADON DEPTH MIGRATION1

A depth migration method is presented that uses Radon-transformed common-source seismograms as input. It is shown that the Radon depth migration method can be extended to spatially varying velocity depth models by using asymptotic ray theory (ART) to construct wavefield continuation operators. These operators downward continue an incident receiver-array plane wave and an assumed point-source wavefield into the subsurface. The migration velocity model is constrained to have longer characteristic wavelengths than the dominant source wavelength such that the ART approximations for the continuation operators are valid. This method is used successfully to migrate two synthetic data examples:

• 1 a point diffractor, and
• 2 a dipping layer and syncline interface model.

It is shown that the Radon migration method has a computational advantage over the standard Kirchhoff migration method in that fewer rays are computed in a main memory implementation.     

Detection of underground cavities with monofrequency electromagnetic tomography between boreholes in the frequency range 100 MHz to 1 GHz1

In order to detect underground cavities, we have designed a geophysical method based on the interaction of a monochromatic electromagnetic wave in the frequency band 100 MHz to 1 GHz with the ground situated between two boreholes. Three different approaches are involved in the design of this EM tomographic method.

• 1 The application of an ‘exact’ theory is used to calculate artificial data, based on an integral equation method. These data are inverted using a tomographic algorithm whose basic assumptions are rather coarse. The results show that, however, cavities can very well be detected and their position recovered.
• 2 Data are obtained with a physical reduced-scale model in a water tank, in which all parameters are known in advance. The inversion process confirms the validity of the method.
• 3 Underground cavities are actually detected.

The above approaches are described and discussed and results are shown. The equipment involved and its operation is quite simple: the surface devices are commercially available and only the transmitter and receiver antennae must be specially built. The method is shown to be quite efficient and its cost should be reasonably low.     

Partitioning of rainfall in a eucalypt forest and pine plantation in southeastern australia: IV the relationship of interception and canopy storage capacity,the interception of these forests,and the effect on interception of thinning the pine plantation

A study of partitioning of rainfall into throughfall, stemflow, and interception was conducted in a dry sclerophyll eucalypt forest and an adjacent pine plantation over a period of seven years, on a rainfall event basis. The following three issues are discussed: (1) the relationship between canopy storage capacity and interception of continuous events, (2) interception, throughfall, and stemflow, and (3) the effect on interception of thinning the pine plantation.

• 1 The canopy storage capacity/interception interaction for the eucalypt forest was assessed by comparing a gravimetric estimate of canopy storage capacity with interception. The maximum possible value for canopy storage capacity was found to be a small proportion of interception for events of all sizes. This suggests that evaporation of intercepted water during the continuous events was responsible for most of the interception. This ‘within event’ evaporation appears to be responsible also for the net rainfall/gross rainfall estimate of canopy storage capacity being four times the gravimetric value. For the pines the regression estimate was more closely related to interception.
• 2 Interception, throughfall, and stemflow of these forests were measured for four years. Data are presented for each year with overall average interception being 11-4 per cent of precipitation for the eucalypt forest and 18-3 per cent for the pine plantation. Topography and rainfall event type are considered in the comparison.

Species composition and tree type are considered when comparing these results with published studies from similar forest types in southeastern Australia. The periodic (annual) variations of interception in this and the other studies makes comparison difficult.

• 3 The effect of thinning on the throughfall, stemflow, and interception in a Pinus radiata plantation is examined. Throughfall increased, interception decreased but not in proportion to the removed biomass; stemflow decreased on an area basis, but increased on a per tree basis. A positive relationshiip is established between interception and stemflow on the thinned plantation but not in the unthinned. Reasons for this are suggested. The results are compared to those reported from similar experiments in other forests.
• 4 The periodic variations in interception and errors inherent in its estimation suggest that caution should be exercised when using average interception figures in water balance studies.

     

Recursive evaluation of interaction forces of unbounded soil in the time domain from dynamic-stiffness coefficients in the frequency domain

The interaction forces of the linear unbounded soil in a non-linear soil-structure-interaction analysis can be calculated recursively, starting directly from the dynamic-stiffness coefficients in the frequency domain. Two possibilities of choosing a recursive equation are discussed.

• (i) The recursive equation in the frequency domain. For each frequency, the interaction force at a specific time station is expressed as a function of the corresponding interaction force at the previous time station and of the displacements at the current time station and at the two most recent past time stations. This recursive evaluation of the convolution integral. which can be derived using the z-transformation, is rigorous. By using interpolation in the frequency domain, an approximate procedure results, which leads to a significant reduction in computational effort.
• (ii) The recursive equation in the time domain. By approximating the dynamic-stiffness coefficients as the ratios of two polynomials in frequency using a curve-fitting technique based on the least-squares method and by applying the partial-fraction expansion and using the z-transformation, the recursive coefficients can be determined explicitly. Alternatively, the ratio of two polynomials can also be transformed to an ordinary differential equation together with the initial conditions.

The recursive equations using interpolation in the frequency domain and based on a ratio of two polynomials lead to a reduction in the computational effort of one and up to three orders of magnitude, respectively.     

A COMPARISON BETWEEN WIENER FILTERING,KALMAN FILTERING,AND DETERMINISTIC LEAST SQUARES ESTIMATION*

The least squares estimation procedures used in different disciplines can be classified in four categories:

• a. Wiener filtering,
• b. b. Autoregressive estimation,
• c. c. Kalman filtering,
• d. d. Recursive least squares estimation.

The recursive least squares estimator is the time average form of the Kalman filter. Likewise, the autoregressive estimator is the time average form of the Wiener filter. Both the Kalman and the Wiener filters use ensemble averages and can basically be constructed without having a particular measurement realisation available. It follows that seismic deconvolution should be based either on autoregression theory or on recursive least squares estimation theory rather than on the normally used Wiener or Kalman theory. A consequence of this change is the need to apply significance tests on the filter coefficients. The recursive least squares estimation theory is particularly suitable for solving the time variant deconvolution problem.     

SIGNATURES FROM SINGLE AIRGUNS*

The far-field signatures from a comprehensive and systematic airgun pulse test have been analyzed. Empirical relations between the characteristic signature parameters and depth (5–12 m), pressure (100–137 bar = 10–13.7 MPa) and total chamber volume (0.65–9.5 l) have been derived. Also, the influence of using waveshape kits in different positions within the chamber has been tested. The results indicate that:

• 1 The amplitude is proportional to chamber pressure to the power 3/4.
• 2 The bubble period is nearly independent of the position of the waveshape plate.
• 3 The increase in primary/bubble amplitude ratio is inversely proportional to the chamber volume above the waveshape plate.
• 4 The amplitude is independent of airgun depth.

Suggestions and comments regarding this work from Dr B. Ursin and Dr A. Ziolkowski are appreciated. The field work was supported by the Norwegian Petroleum Directorate through the Continental Shelf Project at the Seismological Observatory, University of Bergen. An airgun allowing for continuous variation of the chamber volumes was supplied by GECO (Geophysical Company of Norway). The purchase of two airguns was financed by Norske Getty Exploration A/S.     

Discrete model for dynamic through-the-soil coupling of 3-D foundations and structures

An efficient discrete model for predicting the dynamic through-the-soil interaction between adjacent rigid, surface foundations supported by a homogeneous, isotropic and linear elastic half-space is presented. The model utilizes frequency-independent springs and dashpots, and the foundation mass, for the consideration of soil–foundation interaction. The through-the-soil coupling of the foundations is attained by frequency-independent stiffness and damping functions, developed in this work, that interconnect the degrees of freedom of the entire system of foundations. The dynamic analysis of the resulting coupled system is performed in the time domain and includes the time lagging effects of coupled dynamic input due to wave propagation using an appropriate modification of the Wilson-θ method. The basic foundation interaction model is also extended to the evaluation of coupled building-foundation systems. © 1998 John Wiley & Sons, Ltd.