ALBERT

Notes: Income redistribution studies on the macro–economic level have been undertaken in Denmark for the years 1938–39, 1949, 1955, and 1963. By use of national accounts figures and all other available statistics, it was on certain assumptions possible to distribute public sector income and expenditure by income groups.A quite different approach is used in a Danish redistribution study on the micro-economic level for 1971, which relies solely on the comprehensive data from the family budget survey for that year. Unfortunately this study only relates to employee households.This paper deals with the 1963 and 1971 studies. First it describes and discusses the differences in methodology between the two studies and indicates some ideas for future studies in this field in Denmark. In the following sections some main results of the two studies are given, briefly for the 1963 study and more comprehensively for the 1971 study. The studies show the great and growing strength of the policy of redistribution through public sector income and expenditure in Denmark.It is the opinion of the authors that the appearance of redistribution studies based on comprehensive family budget surveys makes for a substantial improvement of redistribution figures, and that the purely micro-level frame of reference makes it possible to interpret the results in a more satisfactory way than before. Furthermore, the appearance of detailed input-output based national accounts data should bring about further improvements in redistribution figures through better data on indirect taxes and subsidies as well as supporting data which are necessary to link the micro and macro levels in a consistent way.

Notes: It is often discussed that inflation introduces a substantial, arbitrary and regressive redistribution of income and wealth under even mild inflation. But after a quarter century of experience with inflation in postwar Japan, very little is known about these costs of inflation on an empirical basis. Due to the complexity of the evaluation of the redistributional impact on Japan, the present paper analyzes the effects of inflation on individuals or groups as wage earners, debtors and creditors, taxpayers, and holders of real estate.The main results of the present investigation suggest that the Japanese inflation for 1955–75 did not seem to introduce much inequality in the income (flow) account in the economy, but that the inequality between households has appeared more in the wealth (stock) account, especially between the house-owner groups and non-house-owner groups. These observations are mainly derived from the following investigations; (i) the wage lag hypothesis about inflation, even if not wrong, does not seem acceptable when applied to the entire period (1955–75) as well as to each of the five sub-periods; (ii) there has been a substantial transfer of real purchasing power from households to non-financial corporations, and, to a lesser extent, to government entities in the debtor-creditor redistribution; (iii) among households, the most substantial redistribution takes place from the non-houseowners to houseowners with land, because of the huge amount of capital gains from the rapid increase in the price of real estate relative to the prices of other assets or the consumer price index, except for the last three years of rampaging inflation.

Notes: Preliminary estimates of the total incomes system of accounts (TISA) are provided for 1959 and 1969. They extend conventional accounts to include all consumption services produced by government and households as well as by enterprises, but define household purchases of durable and semi-durable goods as investment. Acquisitions of capital throughout the economy, intangible as well as tangible, and not only in the business sector, are included in capital accumulation along with, for tangible capital, net revaluations, that is capital gains net of increases in the general price level. Imputations are offered for non market consumption and capital accumulation, most prominently in unpaid household work and education. Much of government output, particularly police services and defense, is recalculated as intermediate, along with expenses related to work, while media services, treated by the United States Bureau of Economic Analysis (BEA) as business purchases of intermediate product, enter into TISA consumption. Subsidies are included in the value of product, as are services of volunteers and imputations for the underpayment of military conscripts and of jurors. Separate accounts are offered for the national income and product, business, nonprofit institutions, government enterprises, government and households.The ratios of BEA to TISA Net National Product were 81.4 percent and 76.5 percent in 1959 and 1969, respectively. BEA national income was 74.1 percent of the corresponding TISA net national income in 1959 and 69.6 percent in 1969, reflecting a greater per annum rate of growth of TISA net national income, 7.49 percent, as against 6.82 percent for the corresponding BEA national income.BEA gross private domestic investment, restricted to business acquisitions of tangible capital at original cost, was estimated as only approximately 22 percent of comprehensive TISA gross domestic capital formation in 1959 and some 20 percent in 1969. The BEA net private domestic investment growth rate of 7.32 percent per annum from 1959 to 1969 may be compared with a TISA net domestic capital formation growth rate of 9.42 percent.

Notes: This paper describes a study designed to provide quarterly estimates of the real capital stock of the United States by sector and industry, which is being undertaken by the Conference Board. It surveys the history of wealth estimation in the United States, and goes on to describe work now in progress both in the Bureau of Economic Analysis and by private researchers. It then continues with a description of the methodology being used in the Conference Board study.

Notes: This paper is in 7 sections. Section 1 gives as background a chronological account of the steps taken in the United Kingdom, from 1974 to late 1977, towards the development of a new system of accounting in company reports which would allow for the effect of changing costs and prices on the measurement of profit and of capital employed in the business. Section 2 discusses the main features of the system, known as current cost accounting, as it is seen in the United Kingdom. Section 3 surveys the relationship between current cost accounting and the national income and expenditure statistics, and the likely implications of the introduction of current cost accounting upon the quality of macro-economic statistics, including estimates of national and sector balance sheets. Section 4 describes some of the problems of implementing current cost accounting, particularly in special situations, and outlines the solutions which were proposed in the “Exposure Draft” published in 1976 by the accountancy profession in the United Kingdom. Section 5 considers the definition of distributable profit in relation to the need to maintain capital, considering the concept of gain, the system of valuing assets and liabilities, and the enterprise's capacity to take on additional debt as a means of financing its assets. Section 6 briefly surveys the implications for taxation, price control and price setting. Section 7 concludes by surveying the scene at the end of 1977 and by looking at likely future developments.

Notes: This article explores the assumptions underlying present definitions of national income in its principal uses, and considers the alterations that would be needed to allow for the inclusion of environmental quality. A numerical example illustrates the impact of alternative measures. The discussion concludes that if we want national income to conform more closely to theoretical concepts of welfare indices, then we need to include a proxy for those environmental services that would not be completely free goods if it were possible to overcome their inherent non-marketability. The least unsatisfactory proxy would be the spending on environmental protection.

Notes: This paper examines the causes and consequences of the inflationary process in terms of its impact upon the national accounting flows, illustrated by the case of France during the period 1966–76. The first section of the paper discusses the apparent causes of inflation, and lays out the circuits through which inflation is propagated. The second section looks behind the apparent causes to examine more closely the reasons for the observed behavior. The final section considers the consequences of inflation in terms of factor allocation, and in turn its impact upon unemployment, the balance of payments, and the rate of growth.

Notes: In the June 1977 issue of the American Economic Review extraordinary attention was given to the statistical problem of measuring the effect on inequality in current income arising from differences associated with age. The method adopted by Paglin was severely criticized although everyone recognized the value of Paglin's unusual, if not original, emphasis on the importance of the underlying issue.This paper is not primarily concerned with the statistical problem of correcting data on current income distributions for income-age differences. It is concerned mainly with the lifetime income perspective itself-with ways of viewing the long-term path of persons and of ways of viewing inequalities in that path as they develop within and among different generations.The paper discusses issues of measurement on a birth-cohort or longitudinal basis, recent trends for selected cohorts, intra-and inter-cohort variances in lifetime income, and various policy issues, for example, the equity of the U.S. Social Security System viewed on a lifetime dimension.

Notes: This paper is about the theory of the measurement of real income. By “theory of measurement” I mean the characterization of statistical terms as variables in a model, just as real consumption is characterized as an indicator of utility and the consumer price index is characterized as the cost of attaining a given level of utility in the economic theory of index numbers developed by Konus, Frisch and others half a century ago. I identify five logically distinct and internally-consistent concepts of real income: maximum sustainable consumption, consumption plus the output of new capital goods, consumption plus the increase in the capital stock where capital can be measured in two quite separate ways, and the sum of actual consumption and consumption forgone in the investment process. The last of these concepts is the most appropriate as a guide to producing long time series of real income for measuring a country's rate of economic growth.

Notes: This paper gives a general description of the principles and methods in connection with making estimates of capital stock and capital consumption in the Swedish National Accounts, with breakdowns into industries and purposes of government services. The first section of the paper deals with definitions, principles and related questions. The major part of the estimates have been made according to the perpetual inventory method. The principles of this method are summarized. A number of problems relating to price indices are also described, as well as problems of valuation of capital for net worth and capital consumption estimates. The second section describes the methods of estimation and sources of data. The calculations have been made on a level of disaggregation into 41 industries and 13 purposes of government services. Three methods are used, i.e., direct estimates for capital objects, where some form of current stock data has been available, insurance values as proxy for replacement values, and perpetual inventory estimates. Comparisons between estimates according to the various methods are made in a number of cases.In the third section a few special problems regarding the quality of the estimates and the possibilities of improving the estimates are explored. The main problems refer to the lack of gross fixed capital formation data, in the form of detailed series which are consistent, cover a long period, and are deflated with an adequate set of price indices. The lack of information on survival curves and durabilities of various types of capital objects is also a severe set-back. Direct inventories would improve the level of the estimates, but they would also be difficult and costly to undertake. The change in capital stock would in any case have to be determined on the basis of gross fixed capital formation data.

Notes: This paper examines the data base available in four South Asian countries, India, Pakistan, Bangladesh, and Sri Lanka, for the examination of trends in real inequality and poverty. Taking the position that sample surveys of household income and consumption are the only really adequate bases on which size distributions of income for a less developed country can be constructed, the paper examines in Section I the reliability of the surveys available in the four countries. Section II evaluates available price data. Section III looks at directions for future development of data collection. The conclusion is reached that sample surveys regularly conducted in these countries do not provide a particularly good basis for this type of analysis. Needed alterations include permitting access to the primary data (or redesign of published tabulations to meet the needs of this type of analysis), use of per capita rather than total household income and consumption, better coverage of regions and occupations, and exploitation of the price data implicit in the survey data collected. Further, the surveys themselves need to be overhauled, especially with regard to timing of interviews. The paper concludes with a short discussion of alternatives to estimates of inequality that can be used to measure absolute deprivation, such as the QUAC stick for identifying nutritional insufficiency.

Notes: This article reports on the plans of the member countries of the Council for Mutual Economic Assistance (CMEA) in the area of the purchasing power parity comparisons of national product and similar aggregates. A series of comparisons of the U.S.S.R. with other individual member countries was made for 1959,1966, and 1973. A new series will be undertaken for the year 1978. The scope of the program will be expanded to cover several new aggregates, including productivity concepts and total consumption of the population. The article discusses the conceptual and methodological problems and plans. Among other matters, attention is being given to the possibility of reducing the number of specifications priced, without sacrificing accuracy.

Notes: The problem of identification and classification of off-shore financial flows and extra-territorial funds is discussed with special reference to the case of the “captive” insurance market in Bermuda. The problem is examined in the context of the UN SNA definitions relating to the evaluation of insurance activities and the difficulty of gaining access to relevant and complete data. The conclusion is reached that the conduct of off-shore financial operations by local institutions and the resulting surpluses generated remain essentially extranational and thus contribute very little to the domestic value added of the tax haven concerned. Furthermore, by its very nature, information relating to the transactors involved, as well as the value of their transactions, is difficult to obtain. This raises a much wider issue, however, as to whether such surpluses are ever identified in any country's national income estimates.

Notes: This paper has two main points. First, the usefulness of the industry detail called for in the SNA would be increased if it were altered to facilitate the construction of price and quantity aggregates classified by stage-of-process sectors. Second, the price and quantity data so arranged should be augmented by data on behaviorally related variables classified the same way. The feasibility of the stage-of-process approach is demonstrated by a table showing the high degree to which the U.S. input-output table for 1967 can be triangularized. The analytical usefulness of the approach is demonstrated through analysis of changes in prices, output, unfilled orders and finished goods inventories for primary and for finished goods manufacturers.

Notes: This article proposes a method of characterizing the growth process using two parameters, a production index measuring growth, and a structural change index measuring the changes in the composition of output. It discusses the properties of the structural change index that is developed, including its relation to the bias in growth rates measured by conventional index numbers. It then applies the measure to an examination of Yugoslav industry for the period 1952–71.

Notes: Expanding a conventional national accounting framework in order to include activities that are not produced or consumed via ordinary markets requires the accountant to adopt some procedure for assigning unit values to these activities. Often, as is the case with governmental services, unit values are equated with unit costs of production.This paper argues that the appropriate valuation generally differs depending on whether the activity is viewed from the perspective of the producer, the consumer, or society. The theoretical justification for this position is developed first for the case of nonmarketed environmental services and then for in-kind governmental transfers.Rather than choosing a single unit value, the paper argues for and outlines an accounting system that will permit the simultaneous adoption of more than one valuation. Techniques for implementing the system for the environment and for in-kind transfers are discussed.Finally, drawing on the experience of the authors, the paper argues for the importance of developing data sets with more than one valuation. The authors claim that the effort to implement the system has generated valuable ancillary data sets even though data limitations and unresolved methodological questions have precluded complete implementation.

Notes: The paper presents some estimates of the imputed dollar value of household work (HW)for Canada in 1961 and 1971, finding this to be about $16 and $38 billion respectively, equal to 40 percent of GNP. From the results we derive some implications about five questions raised in the relevant literature. First, no clear evidence of a downward trend for the ratio HW/GNP is found, contrary to U.S. results. Second, addition of HW to GNP as a welfare measure does not affect the general pattern of past growth estimates. Third, a cost–by-function method of estimating HW is found superior in its theoretical support and the detail it provides, but the opportunity-cost method, despite doubts on its theoretical validity, gives a good approximation in the aggregate, and, being simpler, is likely to remain popular. Fourth, disaggregation does matter if detail by region or family type is required, in which case data by number and ages of children and market-employment status of females are needed; for the total, a reasonable estimate (6–7 percent error)is given by further aggregated data. Fifth, sensitivity of HW to accuracy in the data used is large only for female wages chosen, in particular for the function “cooking”. Finally, though available data must be manipulated to fit the needs of HW, especially for earlier years, the extent of this is not all that much more than is commonly found for GNP estimations.

Notes: This paper discusses the problem of valuing the time spent on household production and presents estimates of that production for the United States in 1960 and 1970. The estimates are derived by using both opportunity cost and market cost valuations of household time. A comparative analysis of these estimates concludes first that opportunity cost estimates exceeded market cost estimates by 1.0 to 3.0 percent of the GNP. Second, the ratio of household production to the GNP, although declining slightly between 1960 and 1970, may in the long run tend to be relatively stable. These conclusions do not support the popular views that over time household production will decline in relative magnitude, or that the opportunity cost method of valuing household time, relative to the market cost method, is significantly upward biased.

Notes: Construction has traditionally constituted one of the problem areas in the preparation of industry price and quantity statistm with in the system of national accounts of most countries. The difficulty stems from what is considered to be the unique character of construction projects. This has unnecessarily impeded the calculation of output price indexes and has resulted in the use of various input-based prices as proxies for output prices.One of the objectives of the development of the system of construction price statistics described in this paper is to permit deflation of the outputs of construction industries in order to produce industry output data in constant prices in a manner consistent with measures for the rest of the economy. This is a more promising approach to improving constant price industry and expenditure measures within the SNA framework than attempting such improvements through the collection of a vast array of quantity data.Construction industries sell specified configurations of materials-in-place which are, to borrow the jargon of other fields, sub-assemblies of some total system. As in other areas of industrial pricing, some of these products are simple and some are complex. Trade contractors sell these sub-assemblies or commodities mainly to an owner-builder or to a general contractor who, in turn, resells the trade contractors’ commodities along with whatever sub-assemblies the general contractor has produced. These sub-assemblies, when combined with, for example, the relevant outputs (or sub-assemblies) of manufacturers, the design services of service industries and the purchasers’ own contributions, yield the wide variety of plant and structures which constitute the various classes of gross fixed capital formation, which are not typically solely the outputs of the construction industries.The resulting contractors’ selling price indexes will provide deflators for the whole range of outputs of the various construction industries. These will become part of the system of industry selling price indexes from which relevant indexes for the various goods and services can be selected and combined with appropriate weights to yield arrays of deflators for the highly complex capital expenditures of business, institutions and government.Ultimately this integrated system of construction industry statistics will permit the preparation of gross output and value added measures, in both current and constant prices, to be calculated for the construction industries as an integral part of the Canadian System of National Accounts, as well as provide a key element for improving the deflation of fixed capital formation.

Notes: The general problems of distinguishing between theoretical concepts and practical measures concerning capital are considered and the difference between various stock and flow measures of capital and their respective uses is defined. The qualifications and limitations to these measures in the interpretation of output changes are also discussed. Attention is concentrated on the initial, basic problem of how to measure gross capital stock and the special difficulties involved in using the perpetual inventory simulation method and census procedures in less developed countries to derive such estimates are broadly defined. Some of the special problems encountered in an attempt to undertake an inventory of industrial capital assets in Lesotho are also referred to and the paper concludes by expressing the view that there are at present far more important issues demanding higher statistical priority in less developed countries than the evaluation of capital stocks.

Notes: This paper examines several nonmoney components of economic welfare in both a theoretical and an empirical framework, computes the distributional ranking of aged families arising from such a measure, and subsequently examines the target effectiveness of eleven programs of the U.S. federal government aimed at the aged. While the theoretical discussion attempts to cover all factors contributing to the economic welfare of the aged, the empirical measure is somewhat less comprehensive, excluding the value of nonmarket productive activities and leisure time as well as benefits derived from direct government expenditures and some in-kind transfers and taxes. The study makes use of a subsample of the 1967 Survey of Economic Opportunity data composed of all families with at least one aged member. Specific attention is devoted to dissaving from net worth, in-kind transfers, incidence of taxes, and intrafamily transfers. Government cash and in-kind transfers are found to constitute a third of the total measured economic welfare of the aged, and the impact of each of these programs is examined individually. As might be expected, public assistance and public housing are the programs of most benefit to the aged poor. Medicaid and Medicare are substantially less so, and Social Security is distributionally neutral. Such programs as unemployment insurance are of little benefit to the aged. Tax expenditures, finally, provide no benefits to even the lower half of the distribution.

Notes: The constant price method is used here to evaluate transfers related to inflation either between households and other economic agents (essentially enterprises) or among groups of households defined by occupation, age class and so on. The results obtained are only fragmentary due to a lack of many pieces of information. The method requires in fact the splitting up of every value variation into a price component and a size component.Nevertheless, some interesting results are shown. In recent years, if the total productivity surplus has always been positive, the wealth surplus of households is sometimes positive, sometimes negative. Concerning the distribution of the productivity surplus among household groups, it has not been possible to find significant distortions, other than those which are related to differences in the propensity to save. On the contrary, marked distortions appear in the distribution of the wealth surplus due to wide differences in estate composition and indebtedness level.

Notes: As a basis for judging how public policy affects the poor, this article explores how “poor” families may be defined and how well such families can be distinguished from other families in the less developed countries. This is done by seeking proxies for poverty which are relatively easy to measure, accurate in discriminating between the poor and the non-poor, and relevant to public policy. To this end, a highly parsimonious model is developed, based on truncation and regression procedures, using only family size and number of wage earners in addition to either income or an education-age combination. Application of this model to data from household surveys in three major cities of Latin America shows that the model is highly effective in pinpointing poverty households, although the pattern of errors is not random, the most frequent type of error being to classify poverty households as non-poor.Especially significant is that the model is nearly as effective for discriminating poverty households from others when financial variables are excluded as when they are included. This would suggest that a good deal of flexibility exists in deciding what variables to include in future studies of this type. The results also suggest that even better results should be possible if more complete information is obtained on the employment status of the different members of the household and on the contribution of each to household income. Ideally, the data collection and model development should proceed in an iterative manner since there are numerous possible variables as well as alternative model formulations.

Notes: Unlike most developing countries, the Philippines has had several (four) reasonably comparable family income and expenditure surveys, covering a reasonable period of time (15 years). This study draws on those surveys and on wage data in an attempt to judge how, if at all, the distribution of income has been changing. The household survey data shows a declining share of both income and consumption for the top income groups; for the bottom quintile the share of recorded income fell while that of recorded consumption rose. When possible biases of the data are allowed for, it is hard to argue that either a narrowing or widening of income differentials occurred over these years. Real wages of a number of important occupations appear to have fallen, however. Only a partial reconciliation of the trends indicated by these wage series and the income trends for various occupational groups implicit in the household survey data was possible, indicating either data problems or the need for more subtle interpretations of the data. Since structural change in the labour force has been rapid (an increasing share being found in the high income occupations as time passed), declining wage rates for certain lower income groups cannot be taken to imply a general worsening of distribution. Our final conclusion is that distribution has probably changed little, and is about as likely to have changed one way as the other.

Notes: The paper reports on several results from a comprehensive study of the household incidence of public expenditure in Peninsular Malaysia in 1974. The results for education show a pro-poor distribution of expenditure when measured as a share of household income. Using however the criterion of each according to his needs (that is the number of school-age children per household) reverses this outcome. In agriculture, because of the importance of land settlement, benefits from public expenditure distribute predominantly in favor of the poor.The research differs from the usual study of this kind in that individual government outputs such as school years, or fertilizer loans, were defined, and in the case of education their unit costs estimated and their distribution across households measured. In the case of education, both the costs of services from capital and the households’ out-of-pocket educational costs were added to the current subsidies. As one consequence, it was seen that total expenditure for education in Malaysia exceeds one-eighth of GNP, nearly double the conventional estimate. Equally important, for the poor the burden of private costs for education even within a public system were seen to be very high.The contrasts between the strong results for education, a broad based social service, and the less conclusive results for agriculture, an economic service which impacts directly on production, were instructive in suggesting the limitations of such research in measuring the effects of government budget activity on distribution.

Notes: To adjust business accounting for inflation, one current proposal is to convert all dollar figures in existing financial statements to units of fixed general purchasing power. A widely offered alternative is to retain the dollar units but replace the historical-cost figures by current values. The two alternatives would yield very different results. After reviewing these and variant proposals, the analysis concentrates on certain major issues: the unit of measurement; the treatment of capital gains; the concept of capital maintenance; and the treatment of changes in the purchasing power of debt. Current value accounting would not correct for changes in the general price level and would involve far more difficult problems of concept and measurement than general purchasing power accounting. The latter is therefore preferable.

Notes: In this paper, we reclassify U.S. input-output data along functional lines by analyzing the use of products represented in the detailed coefficients of the 1967 interindustry study. Our new categories comprise 11 producing “industries,” services (nonproduction), energy (nonproduction), marketing, distribution, other general, crude materials, semi-finished materials, energy production, service production, and machinery replacement, furnishing products to 80 consuming industries. This functional input-output system is then used to analyze postwar structural change in the American economy. Distinct shifts in the uses of different types of inputs are indicated and the implications of these results are discussed.

Notes: This paper is divided into two parts. In the first part the consequences of permanent differences in the rates of productivity growth between economic activities are dealt with. Special attention is given to the substitution of self-service activities for marketed services. The former are tentatively defined as activities carried out outside the market having the following principal inputs: consumer's time, industrial products (mainly durables), and energy. The emergence of self-service activities challenges the conventional division of man's time into work for market and leisure, which should be replaced by a more detailed breakdown. Consumers’preference for self-service results mainly from high taxation, high real wages and equality in the distribution of personal income. Because of the growth of self-service activities in industrialized countries a non-negligible part of the population's productive effort will be difficult to record, since it will neither appear on the market nor have market value. The need to record self-service activities would be most strongly felt in statistics on private consumption, but would also have consequences in the measurement of the nation's welfare. One should make a distinction between consumption of marketed services and their self-service substitutes in order to provide information on the complementarity of the energy, time and material inputs into various self-service activities and on the substitutability between them and marketed services. This could perhaps be done with the help of extended commodity-private expenditure matrices. The recording as well as the valuation of non-market working time would probably cause great difficulties. Self-service activities are also becoming sufficiently important to warrant their inclusion in the debate on the measurement of the nation's productive effort and of the nation's welfare. But any recording of self-service activities would be a controversial measure since it would require recourse to imputations on a large scale.

Notes: The history of national accounting in Argentina is presented in brief. The use of the production method as a basis for GDP estimates is explained and sources and methods of deriving the estimates for different sectors are commented on in some detail. Next the reliability of the estimates is examined for sectoral product, national income by factor shares and the components of final expenditure in terms of the comparison of two different estimates for the period 1950–1963. The degree of accuracy is judged to be generally sufficient, but the importance of economic censuses in the process of estimation is stressed. The importance of detailed studies on several different aspects of the economic structure (input-output, personal and family income by size and regional accounts) is also stressed as a basis for improving the reliability of estimates.

Notes: Is it expedient or possible to modify the content of the national accounting aggregates like GDP so that they reflect also the effect of environmental changes like pollution and noise–this is the question the author tries to answer. He points to some analogies with other national accounting problems, where the basic question is also how far should we go in modifying our measuring scale, the market price, in order to get closer to the measurement of some kind of economic welfare.Reviewing the various possibilities for modifications of the national accounting concepts, the author does not propose any substantial changes. The harm done to the environment as such cannot be measured in monetary terms. The cost of prevention is not a good approximation of the harm done to the environment, since the correlation between these two variables is not strong enough. Nor is the cost of restoration a good measure of the disfunction. Some damages, like noise, lung cancer caused by air pollution, cannot be restored. If–as proposed by some authors–the compensation for the disfunction (e.g. a swimming pool built to compensate for the water pollution) were deducted from GDP, this would not provide a good solution either, since the trouble is the disfunction itself and not the remedying action. (If no swimming pool is built, there is nothing to be deducted?) On the whole, there is no sufficiently sound basis for evaluating the monetary value of environmental damages.The author attaches great importance to getting more information on environmental phenomena. However, he prefers to supplement the national accounting information by a series of physical, chemical, biological, etc., indicators, instead of changing the national accounting concepts themselves.

Notes: In December 1973, the so-called 2nd Perspective Plan was published by the Danish Ministry of Finance. It included some 5 and 15 year forecasts of investments in the private sector, based on the projected development of production and labour. The forecasts were made by use of a simple Cobb-Douglas production function, taking as capital-input the stock of buildings and machinery, using the perpetual inventory method (assuming sudden death).Since the publication of these forecasts, an attempt has been made to refine the capital concept, measuring its services as factor input. Thus, it has been necessary to introduce an exogenous rate of interest. Inspired by Danish findings for private cars, depreciation functions for stocks and utility of machinery are developed. These functions may not seem very realistic for the heterogenous class of durables called machinery, but other possibilities appear even less convincing.Together with an assumption of exponential decay for buildings, it is possible to produce alternative time-series for changes in input of capital in the production process. Some of the resulting estimates of parameters in the Cobb-Douglas function give a better fit than the original version. But no value of the elasticity of production of capital is firmly established, e.g. it is obviously dependant upon the period of estimation, and therefore of no great value in forecasting. No firm connection between labour productivity and capital input (in short as well as the long run) has so far been revealed in Denmark, so no measure of capital is yet of great use in forecasting, except when future growth in production resembles that of the past fairly closely.

Notes: The method of finite differences is applied to the computation of multi-dimensional synthetic seismograms. This paper gives a study of the mathematical and numerical formulations of the problem, the boundary conditions, the convergence conditions and how to simulate the source in both one solid or a liquid. It is shown that the numerical formulation chosen is valid both for direct and inverse problems (i.e. for modeling and migration). This formulation makes it possible to use the normal incidence reflection coefficients for P and S waves, whether they travel horizontally or vertically. The examples shown have been chosen on purpose in order to be easily interpreted. They do not give a full idea of the possibilities of the algorithm which allows to consider non-planar interfaces, except close to the vertical axis.

Notes: Finite difference migration has been developed and popularized by J. F. Claerbout of Stanford University and is now widely used in seismic processing. For most sections finite difference migration gives results comparable to those obtained by conventional Kirchhoff migration and, where events are not dipping too much, a cleaner appearance is often apparent. However, there are two practical limitations to the method, and these occur in regions of very steep dip and where there is a large variation of the velocity in the lateral direction.It is possible to develop successively more accurate equations to deal with the steep dip problem, but above third order these schemes become prohibitively expensive to implement. The finite difference method itself introduces errors and so imposes further limitations on the angle of dip. For the effective treatment of steeply dipping beds there appears to be no method available in the time domain which does not suffer from dispersion inaccuracies. However, by developing wavenumber migration, an exact one-way wave equation can be used, and this eliminates any error except that caused by finite sampling.The other difficulty with wave migration is the correct migration in regions with lateral velocity variation. A number of approaches are possible of which three are discussed here. The first uses an exact theory, the second is based on the deviation from a depth stratified model, and the third uses a transformation to a depth co-ordinate system. All methods are discussed with their advantages and limitations. Finally, some examples are shown of wave migration applied to synthetic and real data.

Notes: In seismic refraction surveys, in particular those using first arrival recording techniques, the hidden layer problem occurs where energy from a refractor of higher velocity arrives at the surface before energy from an overlying refractor. The maximum thickness of the hidden layer is referred to as the blind zone.Hypothetically, every recorded refractor has an associated blind zone which may or may not contain a hidden layer. For an assumed earth model of plane constant-velocity layers and stepwise increase of velocity with depth, the effect of a blind zone on an interpreted depth section may be evaluated by defining an intercept time for a blind zone of assumed or known velocity and by using standard time-term equations for layer thicknesses and depths.The treatment covers an arbitrary number of blind zones embedded within a multilayer sequence of horizontal or dipping refractors. Model calculations affirm the benefits of this approach compared with previous methods which, in general, have been restricted to the case of two horizontal layers with one intermediate blind zone.

Notes: For a thin highly-conducting layer with given longitudinal conductance the recurrence formulae for an n-fold horizontally stratified subsoil are established for d.c. resistivity and magnetotelluric soundings. Similarly, a thin low conductivity layer with given transverse resistance is treated in the d.c. case and a non-conducting intermediate bed in magnetotellurics. Model curves for a thin high- or low-conductivity intermediate layer in the three-layer case have been carried out, which may serve as an extension of the well-known three-layer diagrams for a Schlumberger configuration. The corresponding model curves in magnetotellurics are given.By numerical comparison of these curves with real three-layer curves some diagrams have been developed to show the allowed thicknesses of the intermediate layer in the Schlumberger case and in the case of magnetotelluric sounding.

Notes: Four radar systems at three different frequencies are described which are useful in probing into salt for finding information of interest to miners. Ranges in salt to (a) the edge of a salt dome, (b) the top of the salt dome, (c) boreholes in salt, or (d) faults or hazards ahead of mining can be determined using one or more of these radar systems. Radar wave velocities in salt are determined by radar probing through pillars of known length, and then used to determine ranges in salt to timed radar reflections. Radar probing results are shown obtained in different salt mines probing upwards and downwards. Enclosed areas in the mine are the best radar station locations to probe into salt as air reverberation of radar energy is shortened.

Notes: A simple extension of our previous work in which digital filters were developed to transform dipole resistivity measurements over layered earth to Schlumberger ones leads us to the development of filters for transforming the latter to the former. As in the previous work we use a sampling interval of 1/6 In 10 in designing the filters that are both accurate and fast in operation.

Notes: Seismic facies analysis makes use of different seismic parameters in order to get other than structural information. A review is given of possibilities and usefulness of seismic facies analysis in oil exploration.A seismic facies unit can be defined as a sedimentary unit which is different from adjacent units in its seismic characteristics. Parameters that should be taken into consideration in the seismic facies analysis are as follows: reflection amplitude, dominant reflection frequency, reflection polarity, interval velocity, reflection continuity, reflection configuration, abundance of reflections, geometry of seismic facies unit, and relationship with other units.Interpretation of seismic facies data may be either direct or indirect. The purpose of the direct interpretation is to find out geological causes responsible for the seismic signature of a seismic facies unit. So, the direct interpretation may be aimed at predicting lithology, fluid content, porosity, relative age, overpressured shales, type of stratification, geometry of the geological body corresponding to the seismic facies unit and its geological setting. The indirect interpretation is intended to reach some conclusions on depositional processes and environments, sediment transport direction, and some aspects of geological evolution (transgression, regression, subsidence, uplift, erosion).The results of the seismic facies analysis may be shown on seismic facies cross-sections and seismic facies maps. Depending on the available seismic data and geological conditions in the area under consideration, the seismic facies maps may be of different types such as general seismic facies maps showing distribution of different seismic facies units, sand-shale ratio maps, direction of cross-bedding and paleo-transport maps etc.Several kinds of seismic facies units and their geological interpretation are discussed as examples of seismic facies analysis.

Notes: The reflectivity method for computing synthetic seismograms can be applied to seismic prospecting problems with special focus on coal-mining problems. The method allows the calculation of reflected waves for point-source excitation and non-vertical incidence. It automatically includes all possible conversions of wave types and all inner multiple reflections. Synthetic horizontal- and vertical-component seismogram sections are given for a simple two-seam model and for a realistic seam sequence which is represented by 48 layers; the source-receiver distances range from 100 m to 1000 m. These seismograms show prominent PS reflections already at moderate source-receiver distances. These waves complicate the vertical-component records by producing arrivals of similar strength as the PP reflections. From this it is concluded that PS reflections in strongly layered media can cause problems in routine CDP stacking. On the horizontal-component records the PS reflections are dominant. Because of the lower velocities of S waves the time resolution of PS reflections is better than that of PP reflections. This suggests that horizontal-component recording may be useful in the investigation of subsurface regions with strong velocity contrasts, even with conventional energy sources producing mainly P waves.

Notes: Expressions for the I. P. activity coefficient for an inhomogeneous sphere with the conductivity increasing/decreasing from the core towards the periphery according to a power law have been derived.In certain geometrical situations of the electrode configurations a negative I. P. signal is obtained. The negative I. P. may be understood as due to modifications in the discharge current from the polarized medium during the discharge process.The results of the investigation may be useful for more accurate interpretation of I. P. anomalies due to isometric inhomogeneous bodies.

Notes: Magneto-telluric experiments were performed in August 1974 in the Muhos Jotnian sedimentary formation and the Koillismaa Precambrian basement complex by the Centre de Recherches Géophysiques, Garchy, and the Department of Geophysics, University of Oulu, employing the “Résistivimètre magnéto-tellurique”, an instrument which permits apparent resistivity values to be observed at eight pre-selected frequencies between 8–1700 Hz.Preliminary soundings were made on the Muhos formation and on its surroundings, after which a magneto-telluric profile was measured involving eleven sites on a line 13 km long extending across the formation. Some further soundings were made at certain sites of known stratigraphy. The resistivity values in the sedimentary formation were found to vary between 10 ωm and 200 ωm, while those in the basement were markedly higher. This resistivity contrast suggests that the method seems to be suitable for delimiting the sedimentary formation.Soundings made on the basement at Koillismaa show apparent resistivity values in the range 1000–20000 ωm. The interpretation of these soundings was in agreement with other, independently obtained geophysical results.

Notes: Multispectral recordings used for remote sensing are not without analogy with seismic records from CDP field set-ups. These seismic data may be regarded as “photographs’ of deep regions of the earth taken from various angles.The Karhunen-Loève (K.L.) transformation is commonly used for multispectral data processing, where it helps emphasize some features of remote sensing information. The same method may be applied to seismic data processing. Signal-to-noise ratio is improved on synthetic or field examples when K.L. transformation is applied instead of conventional CDP stacking. Residual statics seem to be diminished by a significant factor.

Notes: A horizontally layered non-absorptive system of homogeneous layers may be specified by giving the reflection coefficients at each interface. Provided the layers have equal vertical travel time and a perfect reflector as a free surface, the reflection coefficients are generally reconstructed from the reflected pulses by way of solving simultaneous equations of the Toeplitz matrix form with the Levinson recursion method. There exists an alternative approach to solving this problem which by simple reasoning immediately turns out the (Levinson) recursion scheme. The method is based on formulas that relate to solving the forward problem. It resembles Kunetz's (1962) original inverse solution in as much as the computation of the reflection coefficients is based on the idea of separating the contribution of a primary from the sum of all multiples.

Notes: The magneto-telluric and telluric-telluric profiling techniques are presented, and then a new method which combines these two techniques for mapping a parameter defined as the “apparent pseudo-resistivity”.The results obtained for the uranium structures in the Cluff Lake district (Saskatchewan Canada) indicate the use of these different techniques in the detection of zones of conduction for surface zones and for deeper zones, and demonstrate the advantages of these methods over the usual electrical methods in problems of structural research.

Notes: The geological sequence rock-coal-rock represents a seismic low-velocity channel. Channel waves generated in a coal seam and their reflections from discontinuities can be used for proving the minability of the seam. To investigate the process of reflection, two-dimensional models of the sequence rock-coal-rock have been investigated by means of the ultrasonic transducer technique. Two-dimensional models have the advantage that the wave field can be observed at an arbitrarily chosen point of the model plate. Thus, by means of these models the direct and the reflected Rayleigh channel wave can be observed along their path of propagation.From the geophysical point of view the various types of discontinuities of a coal seam can be divided into two basic types: one is restricted to the seam, the other includes in addition a fractured zone in the adjoining rock.The investigation of the symmetrical Rayleigh channel wave reflected by a discontinuity yields the following results:For dip angles γ between approximately 90° and approximately 60° the reflectivity is virtually independent of the type of discontinuity. This does not hold for the limiting case of γ= 90° (vertical dip) for which the reflectivity increases with increasing influence of the fractured zone. For dip angles γ between approximately 60° and approximately 40° the reflectivity is still independent of the fractured zone but the shape of the reflected wave deteriorates with increasing influence of the fractured zone.For dip angles γ below approximately 40° the reflected wave deteriorates such that the application of the in-seam seismic reflection method will be difficult or even impossible.The conversion of the direct wave of the symmetrical fundamental mode into a reflected wave of the antisymmetrical fundamental mode has been observed.

Notes: Analytical solutions exist for the potential of a Point Source in media with depth dependent conductivity of the form σ(z) =σ0(1 +αz)n.Of particular importance is the case of the linear gradient (n= 1). More general distributions of conductivity with depth can be approximated by equivalent sequences of homogeneous layers. Comparison between such approximations and the analytical solution for media with linear gradient of conductivity indicates that already a coarse step function yields a reasonably good approximation.

Notes: An approximate method of interpretation of resistivity sounding is presented, which may be described as a very crude manner of application of the exact direct interpretation method. The accuracy of this method is fairly low, the errors being in the order of 25%. The method is very fast in application and well suited for application to multilayer cases. The main advantage of the method is that it is in close and clear relation to the exact theory.

Notes: Dip selective migration velocity determination calculates coherency of energy migrating into an output trace or ‘MVD-axis’ as a function of the three variables time, velocity, and dip. In doing so, it provides additional information, the dip information, relative to standard MVD.

Notes: It is well known that interval velocities can be determined from common-reflection-point moveout times. However, the mathematics becomes complicated in the general case of n homogeneous layers with curved interfaces dipping in three dimensions.In this paper the problem is solved by mathematical induction using the second power terms only of the Taylor series which represents the moveout time as a function of the coordinate differences between shot and geophone points. Moreover, the zero-offset reflection times of the nth interface in a certain area surrounding the point of interest have to be known. The n—I upper interfaces and interval velocities are known too on account of the mathematical induction method applied. Thus, the zero-offset reflection raypath of the nth interface can be supposed to be known down to the intersection with the (n—1)th interface.The method applied consists mainly in transforming the second power terms of the moveout time from one interface to the next one. This is accomplished by matrix algebra.Some special cases are discussed as e.g. uniform strike and small curvatures.

Notes: The least squares estimation procedures used in different disciplines can be classified in four categories:〈list xml:id="l1" style="custom"〉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.

Notes: The use of arrays to separate primary reflections from unwanted coherent seismic events is common practice in land seismic surveys. Very long source and receiver arrays have been used recently to reduce the effects of waterbottom multiples on marine seismic data.The source array consists of five uniformly spaced identical subarrays, each with five different airguns, where the distance between the subarrays may vary from 20 m56 m. The volume of each subarray is 10.3 1 (630 cu.in.) which gives a total volume of the array of 51.5 1 (3150 cu.in.) operated at a pressure of 14 MPa (2000 psi). In order to have a flexible receiver system it was decided to implement the extended receiver array in data processing by computing a weighted sum of two to five traces. The hydrophone cable consists of fifty-four channels with a group length of 50 m.Data shot with the superlong airgun array are processed by a combination of standard techniques and special procedures. In particular, the quality of the stack section is improved by using a weighted stack. The stack weights are computed by a program which takes into account the primary-to-multiple ratio.Comparisons with conventional data show significant improvements in data quality obtained by using the superlong airgun array. Examples show that the waterbottom multiples have been strongly attenuated and the deep seismic events have been enhanced.The combined array response function for dipping events is given in an appendix.

Notes: We start from the Hankel transform of Stefanescu's integral written in the convolutionintegral form suggested by Ghosh (1971). In this way it is possible to obtain the kernel function by the linear electric filter theory. Ghosh worked out the sets of filter coefficients in frequency domain and showed the very low content of high frequencies of apparent resistivity curves.Vertical soundings in the field measure a series of apparent resistivity values at a constant increment Δx of the logarithm of electrode spacing. Without loss of information we obtain the filter coefficient series by digital convolution of the Bessel function of exponential argument with sine function of the appropriate argument. With a series of forty-one values we obtain the kernel functions from the resistivity curves to an accuracy of better than 0.5%. With the digital method it is possible to calculate easily the filter coefficients for any electrode arrangement and any cut-off frequency.

Notes: Most of the data recorded at seismological observatories are essentially noise, not signal. One way to achieve a higher information density is to trigger the seismograph, as in strong-motion accelerographs. This approach loses the first motion—not important for earthquake-engineering studies, but very important for studies of focal mechanism. To eliminate this defect, various cumbersome techniques have been used, such as closed-loop tape-recording.Here we describe a seismograph that records only the signals and does not lose the first motion. Our procedure uses a microprocessor (MC6800) to monitor the energy level adaptively, uses a solid-state memory like a large shift-register, and has the microprocessor trigger recording from the solid-state memory onto a tape cassette whenever a signal (as defined by energy level) is recognized by the microprocessor.A field station consists of a crystal clock, seismometer, amplifier, analog-to-digital converter, Parallel Interface Adapter (PIA), MC6800 microprocessor, 8K solid-state memory, Asynchronous Communications Interface Adapter (ACIA), cassette tape-recorder, and battery. The duration of operation depends upon the frequency content of data, the sampling rate used, and the frequency of events. The design criteria used for the stations of the first field system are a 1 Hz to 10 Hz bandpass amplifier, 8-bit digitization, 5 samples per cycle of highest frequency content, and quality tape cassettes. These requirements are appropriate for exploring for magma chambers in subduction zones—the motivation for developing this system. A playback facility uses the DEC LSI-11 computer, which has an assembly language set very similar to that of the MC6800.This equipment, or a slight modification thereof, would be suitable for recording strong-motion earthquakes, for monitoring quarry blasts, or for any seismological effort in which the triggering criterion can be specified as an algorithm for programming into the microprocessor firmware. The resulting data are digital and only include significant signals, thus the data reduction facilities may properly concentrate on analysis and interpretation. Because the parameters of the system can be easily modified in firmware or software, the system is very flexible and can be considered the Universal Geophysical Recorder. An adaptation to recording transient EM phenomena is in progress. In this application, the source is controlled, but the use of the self-triggering approach eliminates the need for a radio-control system to activate the recorders, HIG Contribution no. 753.

Notes: The problem of detecting discontinuities which interrupt coal seams is of great importance to the coal mining industry. One possible method of detecting such discontinuities is that of in-seam seismology where both source and detectors are placed under- ground on the coal face. In this paper the propagation of SH waves from a line source in the seam is investigated. There exists a particular set of waves–channel waves–, confined to the coal seam. These waves are dispersive and have an associated Airy phase whose geometrical attenuation is least. However, if absorption of energy within the coal is included then the Airy phase is the dominant wavegroup only for distances less than a certain maximum. If a detection criterion proposed by Dresen and Freystätter applies, then there is a lower limit to the frequency that should be used for exploration. This requirement may be in conflict with attenuation considerations.

Notes: Reflections and refractions from curved interfaces were studied on two dimensional scale models. Time of arrival, amplitude and character of reflected, converted, and refracted waves were mainly used for this study. Some reflected refractions, refracted reflections and diffractions were also considered. It was possible to separate PS and SP waves and to study their amplitude and character separately. From the amplitude study of refracted arrivals it was concluded that the refracted ray path penetrates into the high velocity layer rather than propagating along the interface. Although most of the results are interesting from the theoretical point of view, a few applications to exploration problems are suggested.

Notes: The results of specific processing of seismic sections on an actual oil field have proved that it is possible to find a link between a seismic parameter (amplitude of a reflecting horizon) and petrophysical characteristics of a reservoir whose changes modify well productivity.A good correlation appears between the values of good oil productivity and the weakness of the amplitudes of one horizon close to the oil producing layers.

Notes: The expressions for quasi-static electromagnetic fields of a horizontal electrical dipole placed on the surface of a polarizable half-space have been derived for low and high values of induced polarization parameter and presented along with numerical results. It has been observed that the polarity of the mutual impedance function is negative for low values and positive for high values of the induced polarization parameter in the entire time domain, whereas the induced voltage function is positive for low values of induced polarization parameter and becomes negative for high values. In the case of low values of induced polarization parameter the transient electromagnetic field in the beginning increases with time, later on it starts to decay with time. The present study shows that the decay rate of electromagnetic field is highly dependent upon the induced polarization parameter. In the light of the present study the conductivity of the polarizable medium may be determined more accurately.

Notes: Stratigraphic models are usually oversimplified by petroleum geologists, and the result is that the principles which we use for interpreting geophysical data are also over-simplified or even incorrect.Based on the marine seismic data from the Adriatic Sea, an example of prediction of a rather complex sedimentation model of detrital sediments is shown. On the basis of the stratigraphic interpretation using seismic techniques only for this some very important characteristics are discussed:— paleotopography of the valley and conditions which have given opportunity to map accurately the pre-depositional surface,— seismic signatures of the sedimentary section of the ancient valley in which we have recognized aluvial sequence and marine one.The conclusion is that there is a real opportunity for exploration of stratigraphic traps in this part of the Mediterranean Basin.

Notes: Boreholes present a potential hazard to mining in rock salt mines. The only rock salt mine in England was almost lost when they mined into an unknown borehole open to an aquifer. Rock salt is a good transmitter of VHF radar waves, so a good method of detecting boreholes is by using radar probing. This paper investigates theoretically the detection of a borehole in advance of mining using two different radar systems, Bravo II and Charlie II. Bravo II has a peak power of 20 kW at 230 MHz and Charlie II has 3 W at 440 MHz. The borehole detectability depends critically on the radar wave attenuation in salt, which is characterized by its loss tangent, tan δ. The backscattering cross section σ of the borehole is also important. These parameters are related in the radar signal-to-noise equation which determines the signal-to-noise ratio (S/N) for a given range in salt to the borehole. Theoretically, in salt with a tan δ of 10-3, Charlie II can detect (S/N= 3 dB) a 12.7 cm borehole 225 m in advance of mining while Bravo II, using only 100 W, can detect the same borehole 680 m ahead. These values are with the antenna E field parallel to the axis of the borehole. Theory shows this antenna orientation to be optimum for maximum detection probability. For salt with a tan δ of 2 × 10-5, the smallest value measured for salt, Bravo II can detect the borehole up to 15.3 km using maximum power of 20 kW.

Notes: The electromagnetic surface detection of underground quarries by classical methods becomes difficult when they are situated at depths greater than ten meters and when the thickness and conductivity of the superficial layers are irregular.The problem is tackled in two stages: at first using successive approximations, characteristics of the miscellaneous layers of a stratified medium are identified, and the quarries are then detected by observation of the conductivity changes of one of the lower layers. Computer interpretation, however, is necessary.The chances of detection of the quarries are considerably improved by a field localization method developed by us: computer interpretation is eliminated. The new aspect is an auxiliary transmitter which annuls the currents induced by the principal transmitter in the uppermost—generally more conductive—layers.The theoretical and experimental results show that the probability of detection of the quarries by this method are four times as high as by the classical one.

Notes: This final part of our study of the resistivity sounding method in the presence of transitional layers deals with the direct application of the theoretical developments, previously reported, to both theoretical and field examples. The former are used to explain in more detail all steps of the direct procedure of interpreting resistivity measurements, when transitional layers with different dispositions are present in the assumed earth section. An alternate sequence of uniform and transitional layers is at first considered, then the case of a random sequence of these layers, and finally a sequence of only transitional layers. Then we give some logical considerations about the best fields of application of the new interpretation theory, with particular reference to hydrogeological, geological- structural, and mining exploration problems. Representative field examples are finally presented and discussed in detail for each of the exploration fields above listed. The comparison of the geophysical models obtained with the old interpretative scheme and the new system shows the greater resolving power of the new theory, provided that preliminary geological considerations, and where existing–borehole evidence justify the use of the new approach.

Notes: During the last few years many airgun arrays have been designed with the objective of generating a short signature of high amplitude. For linear arrays of non-interacting airguns two rules have been derived that may help in the design or evaluation of airgun arrays. To achieve a short pressure pulse, the total available air volume has to be distributed over the individual guns in such a way that the tail of the signal, owing to the added bubble signals, becomes as flat as possible.When we think of ordering airguns according to volume, this flat signal tail can be achieved by designing the volumes such that the difference in bubble times of two adjacent guns is proportional to their volume to the power 2/3.The amplitude expected from a linear array of non-interacting airguns is limited by the physical length of the array.A graph of measured values tends to confirm this relation.No relation has been found between the total volume of an array and its amplitude.The graph also detects inefficient use of available array length of existing arrays.

Notes: A graphical interpretation method is presented by which separately the depth and the product of conductivity and thickness of a vertical plate-shaped conducting orebody can be determined. The method is based on the result of model experiments.

Notes: The Fourier transform of a square-shaped section of a magnetic survey, digitized in a square grid, forms a rectangular matrix of coefficients which can be condensed to a series of average amplitudes dependent only on their frequency and no longer on the direction of the respective partial waves. These average amplitudes together represent a spectrum which–when plotted in a semilogarithmic coordinate system (log amplitude versus frequency)–often shows straight segments which decrease with increasing frequency. By continuing the given field downwards these straight segments become horizontal at a certain depth, the so-called “white depth”. This white depth may be used as a first estimate for the depth of magnetic sources producing the respective part of the field. It is shown that the sources which correspond to such use of the white depth can be expected to be “randomly distributed with some positive autocorrelation”.As an example for such a depth estimation the interpretation of the aeromagnetic survey of NW-Germany by a relief in 8–16 km depth is given. The relief divides the subsurface in an upper nonmagnetic layer and a lower layer with magnetization M= 2 Am−1.

Notes: The combination of layer resistivity and thickness in the so-called Dar Zarrouk parameters S and T may be of direct use in aquifer protection studies and for the evaluation of hydrologic properties of aquifers.The protective capacity of a clayey aquifer overburden is proportional to its longitudinal unit conductance S which, in terms of aquifer protection, gets a dimension of time (e.g. infiltration time). Aquifer storage in fissured reservoirs may be determined from differential conductance measurements (ΔS). Combination of the expression for ΔS with an empirical expression for electric conduction in fissured media yields a simple formula for water content per unit surface area. Both principles and possible developments are illustrated for a set of carboniferous limestone basins.

Notes: The difficulty to use master curves as well as classical techniques for the determination of layer distribution (ei, ρi) from a resistivity sounding arises when the presumed number of layers exceeds five or six.The principle of the method proposed here is based on the identification of the resistivity transform. This principle was recently underlined by many authors. The resistivity transform can be easily derived from the experimental data by the application of Ghosh's linear filter, and another method for deriving the filter coefficientes is suggested.For a given theoretical resistivity transform corresponding to a given distribution of layers (thicknesses and resistivities) various criteria that measure the difference between this theoretical resistivity transform and an experimental one derived by the application of Ghosh's filter are given. A discussion of these criteria from a physical as well as a mathematical point of view follows.The proposed method is then exposed; it is based on a gradient method. The type of gradient method used is defined and justified physically as well as with numerical examples of identified master curves. The practical use for the method and experimental confrontation of identified field curves with drill holes are given. The cost as well as memory occupation and time of execution of the program on CDC 7600 computer is estimated.

Notes: The spectrum of a magnetic or a gravity anomaly due to a body of a given shape with either homogeneous magnetization or uniform density distribution can be expressed as a product of the Fourier transforms of the source geometry and the Green's function. The transform of the source geometry for any irregularly-shaped body can be accurately determined by representing the body as closely as possible by a number of prismatic bodies. The Green's function is not dependent upon the source geometry. So the analytical expression for its transform remains the same for all causative bodies. It is, therefore, not difficult to obtain the spectrum of an anomaly by multiplying the transform of the source geometry by that of the Green's function. Then the inverse of this spectrum, which yields the anomaly in the space domain, is calculated by using the Fast Fourier Transform algorithm. Many examples show the reliability and accuracy of the method for calculating potential field anomalies.

Notes: Several new features are described which facilitate an automatic, more meaningful, and more accurate interpretation of gravity anomalies associated with approximately two-dimensional mass distributions. These include a provision for fixed points on the bounds of a distribution, outward dipping boundaries, calculation of the gravity effect at individual elevations of stations, smoothing of models and end-corrections for distributions of limited strike length. It is possible to obtain distributions about a median plane; these distributions are sensitive to shape and allow estimates of optimum depths and minimum density contrasts for the anomalous masses.

Notes: The utility of electrical resistivity and magnetic measurements to locate suitable wellsites in hard-rock terrains intruded by dykes is illustrated. The example is taken from a highly hilly terrain of Karnataka State situated in the Western Ghat hills of Peninsular India. Electrical resistivity profiles and soundings, S.P., and total magnetic field measurements are discussed. Of the fifteen recommended sites, nine have been drilled, eight of which are reported to yield between 6–12 m3/hr (1500 to 3000 gals./hr), which is considered satisfactory in this region.

Notes: The relative time shift of CDP reflections, caused by long period statics, is treated as the result of a filtering process. The shape of the filter is that of a comb having the magnitude and spacing of its teeth determined by the CDP spread geometry. Convolution of a near surface anomaly with a comb filter representing the CDP spread geometry produces the same time fluctuations at CDP reflections (CDP statics) as the stacked traces across the anomaly. Conversely, the near surface time anomaly is given by the convolution of the CDP statics with the inverse of the comb filter. Provided that CDP statics can be separated from noise, dip, and residual normal moveout, it is pcissible to determine long period statics with a relative wavelength of between half a spreadlength and five spreadlengths.The object of this paper is to present the theory and practical applications of the method. Several examples based on synthetic and real data will also be discussed.

Notes: Various Dix-type formulae are derived, which are useful to approximate travel time functions that can be observed while modeling the common depth point (CDP) technique for 3-D isovelocity layers of varying dip and strike. All formulae can be used to compute interval velocities and recover the depth model from surface measurements. They are established by making use of the concept of wavefront curvature. Many similarities with known formulae valid for the 2-D plane isovelocity layer case exist.

Notes: The main problem in seismic prospecting is to infer from the observed reflection response the distribution of density and seismic velocity with depth. This process is generally called the inversion of the reflection data.For plane waves propagating through plane parallel stratification, it can be shown that at any depth the ratio between the amplitude of the transmitted and reflected wave satisfies the Riccati equation. Based on this equation we have formulated an iterative inversion method, which is found to be suitable for numerical computations. We have applied this method on synthetic reflection data, and found that it provides a very fast and accurate inversion.

Notes: In-situ seismic measurements on shear waves propagation both in soft formations (clays) and in hard formations (calcareous rocks), using several field techniques did not result in clear S arrivals.Particular digital approaches were then used, based on spectral analysis of records, for the selection of the seismic events and the calculation of their propagation velocity.The actual application of these numerical procedures are described and to some records obtained using the “crosshole” field technique show that the suggested procedures are a substantial contribution to the identification of transverse waves.

Notes: The problem of the propagation of acoustic waves in a two-dimensional layered medium can be easily solved in the frequency domain if the Dix approximation is used, i.e. when only the primary reflections are considered. The migrated data at a depth z are obtained by convolving the time section with a proper two-dimensional operator dependent on z. The same result can be obtained by multiplying their two-dimensional spectra and summing for all the values of the temporal frequency.The aspect of the operator in the time-space domain has the classic hyperbolic structure together with the prescribed temporal and spatial decay.The main advantages of the frequency domain approach consist in the noticeable computer time savings and in the better approximation. On the other hand lateral velocity variations are very difficult to be taken into account. This can be done if a space variant filter is used in the time-space domain.To reduce computer time, this filter has to be recursive; the problem has been solved by Claerbout by transforming the hyperbolic partial differential equation into a parabolic one, and using the latter to generate the recursion operator.In the presentation a method is given for the generation of recursive filters with a better phase characteristics that have a pulse response with the requested hyperbolic shape instead of the parabocli one. This allows a better migration of steeper dips.

Notes: A spatial analysis of both continuous and discrete operators for upward continuation help us realize the problems and limitations which have been encountered before (Henderson 1960, Kontis 1971) but remained unsolved in practical application of upward continuation computation due to the finite length of data and operator in spatial domain. Various numerical examples show that an improvement of accuracy of continuation computations can be achieved through proper sampling and sufficient length of data.

Notes: In marine gravity interpretation, the density required for the Bouguer correction is not easily measured, and, therefore, one often uses either standard values or extrapolates density from a station or a profile to an entire survey. If the real density varies, this leads to inconsistencies. In this paper a method is proposed to eliminate as much as possible the gravimetrical effects of real density variations. The principle is to apply Nettleton's method to the whole space, but also to use a continuously variable density in the Bouguer gravity computation. It is possible to avoid affecting real gravity anomalies by using stations situated on suitable area elements the optimal size of which is determined by the program. The density that is obtained is called “processing density’ because it is not a real one, but rather the resultant of the densities affect on each station. Use of the method is demonstrated on an example from the southeastern part of Bay of Biscay.

Notes: In western Canada, the near surface weathered zone has variable velocity and is underlain by more uniform subweathering material. The uphole time is often used to compensate for the weathered zone, but there are limitations to its use.A method is proposed using the refraction delay time which is exactly proportional to the weathering correction time for several commonly assumed weathering velocity functions. The method does not require accurate determination of velocities or weathering depth nor even the depth of shot, yet is theoretically exact. A strip off time tr is used to replace the weathered zone mathematically with high velocity material where tr= zD/F, where D is the delay time and F the Blondeau factor.An algorithm using first break times is proposed that is amenable to computer use for determining D for each geophone point. F might be constant in some areas but is more likely a variable to be solved in an automatic static program. Thus, structure and residual statics can be handled at once.