ALBERT

Notes: Within the last two decades, national accountants wondered whether they were able to solve problems that in many respects were of the squaring the circle type: how could they embellish their representation of the economy without having their instrument grow heavier and less flexible? How could they elaborate synthetic frameworks in fields of collective concern that could both be specific and insure a dialogue with macroeconomics? How to keep consistent with the central framework and at the same time experiment with some freedom and flexibility. Satellite accounts are an answer to these questions. Much experience has been accumulated on satellite accounts in both national statistical offices and in international organisations. This paper provides a survey of this work. After an introduction (Part 1) devoted to stating the question, we try to propose a classification for the different types of satellite accounts (Part 2). Then we show their common characteristics (Part 3). However, this exercise would still remain abstract if we did not present samples of currently produced accounts. That is what we do in Part 4 with four examples. These examples have purposely been chosen in fields where many countries and international organizations have heavy investments, thus insuring the specific results will be obvious.

Notes: This paper is presented as a general contribution to discussions underway with respect to the revision of the SNA. The author argues that underlying premises in the current (1968) version of the SNA tend to favour quantitative aspects of production and that the treatment of certain financial items such as interest and valuation of inventory change have been compromised in regard to their effects on production.The need for alternative approaches to these components in the subaccounts of the SNA is emphasized, the rationale involved is explained and modifications to some of the subaccounts are proposed. The alternative approaches affect the boundaries of production and it is argued that the new boundaries would provide a more realistic representation of current values of gross domestic product. It is also noted that the modified production accounts are more compatible with the balance sheet subaccounts.The author shows that production subaccounts on input-output and productivity are based on the need for quantitative measures in analysing growth in the volume of goods and services produced and of productivity to determine efficiency of factor utilization. It is argued that the existing conceptual structure of these two subaccounts meet these needs and should be retained in their present form.

Notes: This paper presents survey results on the size and structure of the hidden labour market in The Netherlands. According to the results total income from hidden work is at least 1 percent of national income. The hidden income is shared by more than one million participants (nearly 12 percent of the corresponding population). This result is lower than various other estimates of the magnitude of the hidden economy. Some definitional and methodological issues are discussed in order to explain the difference from the other estimates.The most notable results of the survey refer to the structure of the hidden labour market. At one end of this market are people with a high wage rate, working relatively few hours. They have the characteristics which given them a favourable position in the formal labour market. At the other end are people with low hidden wages, who work more hours. They have difficulty in finding a formal job. The income from hidden labour is distributed in very much the same way as income from formal activities. There is no evidence that the hidden labour market compensates those who are worse off in the formal economy.

Notes: The paper shows the relationship between microbusiness accounting based on double-entry bookkeeping and macroeconomic accounting based on quadruple-entry bookkeeping. In order for microaccounts to successfully aggregate into macroaccounts (i.e. preserve macro/micro linkages), quadruple-entry bookkeeping requires that the traditional double entries, recorded by transacting microbusiness units, be “consistent” with each other. In fact national economic accounting implicitly assumes that such consistency is maintained when national “aggregates” are uniquely extracted from national accounts and when national “identities” are claimed to hold true.The main purpose of the paper is to show important examples where quadruple-entry consistency is not satisfied. These examples typically involve “complex” economic transactions between business units in which the legal form of the transactions do not necessarily represent their economic substance. When this occurs, different business units have genuinely divergent conceptions and perceptions with respect to their mutual economic transactions. Therefore, microbusiness accounts cannot be successfully aggregated into macroeconomic accounts without violating the integrity of microdecision making records.The conclusion of the paper introduces a new theory called Perpetual Imbalanced Accounting. The theory shows that inconsistent (or imbalanced) economic accounting does tend to become consistent (or balanced) over sufficiently long time periods. Therefore, we must adopt a more dynamic view of national accounting if we desire to preserve successful macro/micro linkages. However, the problems of imbalanced macroaccounting and its statistical consequences cannot be entirely avoided no matter how long the accounting time period is taken. All of the above have important implications for the revision of the United Nations System of National Accounts.

Notes: This paper seeks to forge a link between Canadian macro and micro data relating to the household sector. The analysis is in three parts. The first part begins with National Accounts data on the personal sector. These data are adjusted to remove transactions relating to non-biological persons, so that the result is income and expenditure for the household sub-sector. The second part starts with the annual household survey used to collect income distribution data. These survey data are augmented in various ways to account for under-reporting and to add information from other micro data sets particularly the periodic survey of household expenditure patterns and a sample of individual income tax returns. The result is a comprehensive, albeit partially synthetic, household micro data set. In the final part of the paper these two largely independent data sets are compared, and the general quality of the results is discussed.

Notes: Poverty is a much used term by politicians, economists, sociologists, the media and interest groups. Although there is some common consensus that the word poverty means some type of deprivation, there is a lack of comprehensive measures to quantify this term. Although deprivation can relate to a number of areas such as health and education, the focus in policy development has been aimed at economic deprivation or more specifically, income adequacy. Even in this perspective, the availability of comprehensive measures are limited. The United States is the only major industrial nation that has an official poverty line. Several unofficial poverty lines have been developed in Canada, but the poverty measures have not gone beyond head counts of people who fall below these lines. In an environment where the goal is to further progressive social development constrained by inadequate public resources, the emphasis has been on first directing scarce resources to those “most in need”. To get a better perception of economic need, this paper provides a micro analysis of the size and distribution of the poverty gap so that meaningful comparisons can be made between demographic groups. The results of this analysis yield some interesting findings. For example, there are virtually no poor elderly couples and although there are a large number of poor single elderly, their income shortfalls are relatively small and are highly concentrated near the poverty line; the poverty rate among families with children is quite low but their incomes on average fall well below the poverty line and are widely dispersed; and single parents fare badly on all measures.

Notes: This paper presents original estimates of the distribution of personal wealth in Nova Scotia, Canada in 1871 using the estate multiplier technique and discusses the sensitivity of estimates of the wealth distribution to the assumed wealth holdings of non-probated decedents. We examine, in particular, the implications of assuming: (1) that non-probated decedents had zero wealth, (2) that the wealth distribution was quasi-Paretian (with parameters that can be estimated from the distribution of wealth of probated decedents) or (3) that the wealth distribution had the form assumed by A. H. Jones in her analysis of wealth inequality in the Thirteen Colonies in 1774. We conclude that it is unlikely that large estates escaped the probate process in Nova Scotia, but it is also unlikely that all non-probated decedents had equal wealth-thus our “best guess” is that the wealth distribution of non-probated decedents was quasi-Paretian. However, a methodology similar to Jones' would have implied considerably less measured inequality in the wealth distribution and greater average wealth in 1871– and would therefore have altered our perception of long term trends in the distribution of wealth and in the rate of accumulation of wealth. The measurement of wealth inequality in a society with a significant slave population, such as the thirteen colonies in 1774, is also highly sensitive to the treatment of slavery. Our preferred estimates of wealth inequality in Nova Scotia in 1871 and in the Thirteen Colonies in 1774 indicate a much higher inequality in the distribution of personal wealth than exists today.

Notes: A new set of international comparisons covering the period 1950–85 is developed here for 121 market and 9 centrally planned economies. This new so-called Penn World Table (Mark 4), a completely revised and updated expansion of an equivalent table published by the authors in 1984, draws on the data of two previously unavailable international comparison benchmark studies. This article presents a detailed description of all estimation procedures, and excerpts from the overall DATA TABLE covering two years, 1980 and 1985. Three computer diskettes accompanying this article (and also available from the authors) contain the complete 36–year, 60,000 entry DATA TABLE in a form that economizes on scarce journal space and is immediately machine-readable. For the 121 market economies, the DATA TABLE gives annually, in addition to population and exchange rates, real product and price level estimates for four different national income concepts, and for the major subaggregates, consumption, investment, and government. Only population and real gross domestic product estimates are given for the nine centrally planned economies, however.This new table is one more step toward the goal of establishing a new worldwide System of Real National Accounts.

Notes: The next UN System of National Accounts (SNA) should have two basic characteristics. First, it has to be a modulary system. Its core is an institutional system without imputations and attributions. Next to that there are several modules. By means of imputations and attributions they transform the core into alternative systems. Second, it has to be an integrated meso-system. There is a need for a more detailed breakdown of households and enterprises than the present SNA provides. At the same time a description of all interrelations between activities and sectors is necessary. This requires a linkage between input-output tables and sector accounts at a detailed level. The paper shows the synoptic structure of such a system. The heart of this structure is the three-dimensional generation of value added table. It shows not only how much of each component of value added is generated by the establishments in each activity, but it also provides the breakdown of each of these cells according to the sector of the enterprise to which the establishments belong. The paper shows how the synoptic Structure clarifies the delineation of imputations and attributions.

Notes: Because wealth estimates from survey data have usually fallen substantially short of independent aggregate estimates, survey data have not been seen as adequate for assessing questions dependent on a good representation of the entire distribution of wealth, such as estimates of wealth concentration. The 1983 Survey of Consumer Finances (SCF), which contains a supplementary sample of very high income households drawn from a tax-file sample frame, is the first U.S. survey since the 1963 Survey of Financial Characteristics of Consumers that offers hope of accurately measuring the entire wealth distribution. In this paper, we discuss the design of the survey, the critical issue of proper weighting to merge the supplementary sample with an area probability sample, and the role of imputation. We show that the use of ordinary area probability samples alone leads to probable bias in the measurement of highly concentrated assets such as stocks and bonds. We compare the SCF data with aggregates derived from the flow-of-funds accounts of the Federal Reserve Board. While methodological issues cloud exact comparisons, it appears overall that the SCF estimates are at least as credible as other aggregate measurements. Finally, we use the data to assess the change in concentration of wealth from 1963 to 1983. We estimate that the concentration of wealth in terms of households did not change significantly over this period.

Notes: In the Dutch statistics on government finance a micro/macro link is established. The paper describes why and how this has been done. It appears to be of relevance to the users of the statistics to present two different data sets: one according to an accounting/administrative point of view and one fitting in the National Accounts. The main features of the way in which these data sets are derived from the underlying bookkeeping documents are given and it is shown how they relate to the accounting and juridical structures of the various government agencies. It appears that in order to arrive at homogeneous data sets, adaptations are in order, mainly bearing on the entries; for the National Account data further transformations, relating to transactions as well as transactors, will appear necessary. It will be enunciated how the relation between these data sets is shown in the statistics on government finance and how, in the same course a micro/macro link is provided for.

Notes: The Luxembourg Income Study (LIS) database on which this article is based offers researchers exciting new possibilities for international comparisons based on household income microdata. Among the choices the LIS microdata allows a researcher, e.g. income definition, income accounting unit, etc., is the choice of family equivalence scale, a method for estimating economic well-being by adjusting income for measurable differences in need.The range of potential equivalence scales that can and are being used in the ten LIS countries and elsewhere to adjust incomes for size and related differences in need span a wide spectrum. The purpose of this paper is to review the available equivalence scales and to test the sensitivity of various income inequality and poverty measures to choice of equivalence scale using the LIS database. The results of our analysis indicate that choice of equivalence scale can sometimes systematically affect absolute and relative levels of poverty; and inequality and therefore rankings of countries (or population subgroups within countries). Because of these sensitivities, one must carefully consider summary statements and policy implications derived from cross-national comparisons of poverty and/or inequality.

Notes: This paper analyses the Kapteyn and Van Praag method of estimating equivalence scales with respect to the way family size and age composition are incorporated into the scales according to rank and age of each family member. It becomes evident that the Kapteyn/Van Praag procedure fails to distinguish between household size and individual age effects with the result that personal weights can not be used for recomposition of household types other than wife and husband families, nor can they be interpreted as showing real age dependence of personal income equivalence. For these reasons another specification of the general approach, separating both effects, is outlined. This specification distinguishes between several consumption classes within each household. Within each class, economies of scale are attached to similar individuals while differences in individual need are obtained by comparing individuals with the same rank in the different classes.

Notes: There has been considerable public debate in Canada on the merits of proposals to extend coverage under the public earnings-related pension system (the Canada and Quebec Pension Plans or C/QPP) to homemakers. This paper presents an analysis of one such proposal put forward by a Parliamentary Committee in 1983. The analysis considers both the likely costs and the redistributional impact of this homemaker pension proposal, based on a Monte Carlo lifecycle microsimulation model. The main results are first that the proposal tends to be mildly redistributive from higher to lower lifetime income groups. Secondly, the proposal is of not as much benefit to women as might be expected-it is almost equal in value to men and women. This later conclusion is the result of the fact that the homemaker pension provision was part of a package tl at also included splitting of pension credits accrued during marriage.

Notes: The purpose of this article is to add 12 Latin American countries to the Phase III of the United National International Comparisons Project (ICP). The data for Latin America was obtained through ECIEL. It has been demonstrated that the exchange rates do not usually reflect the relative purchasing power of currencies. When low-income countries are compared to higher income countries the exchange rate conversion tends to understate the relative income of the lower income countries. This is true for the total GDP and even more so for the GDP components. In per capita terms it is found that for low income countries their income is more than twice as great as is indicated by the exchange rate conversion.

Notes: The first Swedish historical national accounts were compiled in the 1930s, and that pioneering work formed the main basis for later estimates until now. In this paper, an attempt to construct new historical accounts for 1800–1980 is presented. First, the methodology is discussed, particularly concerning series in constant prices adapted for analysis of growth and structural changes. In principle Paasche deflators should be used, but for such a long period they are inadequate due to the huge changes in the goods composition of production as well as of consumption and investment. Instead, a division of the whole period into shorter subperiods is made and within these, Paasche deflators are applied. Then the series for the deflation periods can be linked in order to arrive at longer series. Second, some findings of the work (still in progress) are reported. The new series show a slower growth rate in the second half of the nineteenth century than the earlier ones, and Sweden can internationally no longer be seen as the country where this period's economic miracle took place. Instead, concerning rate of growth of GDP per capita as well as its level, Sweden seems to have been a middle-way country compared to other European countries. In the first half of the 20th century, on the other hand, the growth rate was high in an international comparison. The Swedish sectoral changes followed a general pattern with decreasing agricultural and increasing industrial shares. The service share was not unusually high in the nineteenth century. Within this service production a very distinct pattern of structural change is evident. Finally, a plea is made for a regional breakdown of the national GDP data in order to obtain a better understanding of the economic growth and modernization process.

Notes: The increasing number of countries for which a Social Accounting Matrix (SAM) has been compiled testifies to the usefulness of this integrated data framework. Considerable resources are always involved in the construction of a SAM, for it provides a comprehensive description of an economy with emphasis on distributive aspects. This means that, unlike other data systems, incomes and expenditures of several categories of households and their relation to the production structure, the balance of payments and transactions by other institutions are shown.However, apart from this minimum requirement, no standardized concepts and guidelines for SAM construction are as yet available. Although a SAM should stay as close as possible to the specific (institutional) reality of the economy it describes, some general remarks as to its design and compilation are in order. This paper represents a first attempt in that direction. After a general introduction to SAMs, each stage of the construction process is reviewed in turn.The construction process begins with the overall design of the system and various options are discussed. This section includes a schematic representation of a fairly extensive SAM. Next, the sources for the SAM need to be identified, and a provisional checklist is given here. After an overview of considerations regarding the choice of a reference year, the topic of classification in the SAM is reviewed in detail. Finally, the paper describes how the different data sets might be integrated and reconciled for consistency.The guidelines may also aid in designing a time schedule and in organizing the work when constructing a SAM.

Notes: A new time-domain method is introduced for the calculation of theoretical seismograms which include frequency dependent effects like absorption. To incorporate these effects the reflection and transmission coefficients become convolutionary operators. The method is based on the communication theory approach and is applicable to non-normal incidence plane waves in flat layered elastic media. Wave propagation is simulated by tracking the wave amplitudes through a storage vector inside the computer memory representing a Goupillaud earth model discretized by equal vertical transit times. Arbitrary numbers of sources and receivers can be placed at arbitrary depth positions, while the computational effort is independent of that number. Therefore, the computation of a whole plane-wave vertical seismic profile is possible with no extra effort compared to the computation of the surface seismogram. The new method can be used as an aid to the interpretation of plane-wave decomposed reflection data where the whole synthetic vertical seismic profile readily gives the interpreter the correct depth position of reflection events.

Notes: A parameter estimation or inversion procedure is incomplete without an analysis of uncertainties in the results. In the fundamental approach of Bayesian parameter estimation, discussed in Part I of this paper, the a posteriori probability density function (pdf) is the solution to the inverse problem. It is the product of the a priori pdf, containing a priori information on the parameters, and the likelihood function, which represents the information from the data. The maximum of the a posteriori pdf is usually taken as a point estimate of the parameters. The shape of this pdf, however, gives the full picture of uncertainty in the parameters. Uncertainty analysis is strictly a problem of information reduction. This can be achieved in several stages. Standard deviations can be computed as overall uncertainty measures of the parameters, when the shape of the a posteriori pdf is not too far from Gaussian. Covariance and related matrices give more detailed information. An eigenvalue or principle component analysis allows the inspection of essential linear combinations of the parameters.The relative contributions of a priori information and data to the solution can be elegantly studied. Results in this paper are especially worked out for the non-linear Gaussian case. Comparisons with other approaches are given. The procedures are illustrated with a simple two-parameter inverse problem.

Notes: For converted waves stacking requires a true common reflection point gather which, in this case, is also a common conversion point (CCP) gather. We consider converted waves of the PS- and SP-type in a stack of horizontal layers.The coordinates of the conversion points for waves of PS- or SP-type, respectively, in a single homogeneous layer are calculated as a function of the offset, the reflector depth and the velocity ratio vp/vs. Knowledge of the conversion points enables us to gather the seismic traces in a common conversion point (CCP) record. Numerical tests show that the CCP coordinates in a multilayered medium can be approximated by the equations given for a single layer. In practical applications, an a priori estimate of vp/vs is required to obtain the CCP for a given reflector depth.A series expansion for the traveltime of converted waves as a function of the offset is presented. Numerical examples have been calculated for several truncations. For small offsets, a hyperbolic approximation can be used. For this, the rms velocity of converted waves is defined. A Dix-type formula, relating the product of the interval velocities of compressional and shear waves to the rms velocity of the converted waves, is presented.

Notes: An increase in the grain/pore size can cause the received echo signal to be distorted due to the preferential attenuation of the high-frequency components of the transmitted acoustic signal. Therefore, a rock acts as a low-pass filter and the property of the filter has a linear relation to the grain/pore size. The results have shown that P- and S-wave attenuations can be used to characterize selected internal characteristics of a rock. For example, an increase in the differential stress can cause an increase in the attenuation, due to the sensitivity of the S-wave to microcracks.

Notes: Three-component recordings permit the construction of particle trajectories. These three-dimensional pictures of particle motion show successive predominant directions of polarization and allow wave modes with distinct polarization directions to be recognized. A polarization selection, called ‘spatial directional filtering’, can be accomplished by several methods; four techniques are described. The application of these polarization filters to a noise shot, offset VSPs and CDP stack are also presented. This type of filtering is shown to cancel waves with undue polarization and to enhance the signal-to-noise ratio.

Notes: Gold, as a trace element, is not directly detectable by geophysical borehole logging techniques. Geophysical logging methods have therefore been used to infer the presence of structural features and alteration processes associated with gold. Since these features and processes differ with the style of gold mineralization, a unique relation between geophysical anomalies and gold cannot be established. However, in a particular environment, such an association can be established. We examined geophysical log data (self potential, induced polarization, resistivity, gamma, temperature, and temperature gradient) and drill core from the Barber-Larder property in NE Ontario. The geophysically detectable alteration processes associated with gold were identified as sericitization and pyritization, by means of factor analysis. A linear discriminant function was constructed which allowed the zones of economic mineralization (nominally 0.05 oz/ton or 1.5 ppm) to be identified with a 75% success rate based on geophysical log data alone. This rate was achieved without sophisticated non-linear data transformations.

Notes: A model of parallel slip interfaces simulates the behaviour of a fracture system composed of large, closely spaced, aligned joints. The model admits any fracture system anisotropy: triclinic (the most general), monoclinic, orthorhombic or transversely isotropic, and this is specified by the form of the 3 × 3 fracture system compliance matrix. The fracture system may be embedded in an anisotropic elastic background with no restrictions on the type of anisotropy. To compute the long wavelength equivalent moduli of the fractured medium requires at most the inversion of two 3 × 3 matrices. When the fractures are assumed on average to have rotational symmetry (transversely isotropic fracture system behaviour) and the background is assumed isotropic, the resulting equivalent medium is transversely isotropic and the effect of the additional compliance of the fracture system may be specified by two parameters (in addition to the two isotropic parameters of the isotropic background). Dilute systems of flat aligned microcracks in an isotropic background yield an equivalent medium of the same form as that of the isotropic medium with large joints, i.e. there are two additional parameters due to the presence of the microcracks which play roles in the stress-strain relations of the equivalent medium identical to those played by the parameters due to the presence of large joints. Thus, knowledge of the total of four parameters describing the anisotropy of such a fractured medium tells nothing of the size or concentration of the aligned fractures but does contain information as to the overall excess compliance due to the fracture system and its orientation. As the aligned microcracks, which were assumed to be ellipsoidal, with very small aspect ratio are allowed to become non-fiat, i.e. have a growing aspect ratio, the moduli of the equivalent medium begin to diverge from the standard form of the moduli for flat cracks. The divergence is faster for higher crack densities but only becomes significant for microcracks of aspect ratios approaching 0.3.

Notes: Ray theories are a class of methods often chosen to compute synthetic seismograms due to their efficiency and ability to deal with complex, three-dimensional inhomogeneous media. To deal with the large number of rays needed to compute synthetic seismograms, a ray generation algorithm is given which is capable of generating a numerical code describing each ray. The code describes a subset of all possible rays by considering only pre-critical reflections. In a horizontally plane-layered medium the generation of rays and computation of amplitudes and traveltimes can be efficiently accomplished by grouping the rays into reflection order and dynamic analogue groups. Expressions summing all unconverted rays and rays with a single mode conversion are given for source and receiver located at arbitrary positions within the medium. Examples of zero-offset synthetic VSPs obtained by this method are given.

Notes: The cross-correlation technique for increasing the anomaly-to-noise ratio is applied to the interpretation of resistivity profiles.To verify the method theoretically, resistivity profiles above a body having the shape of a parallelepiped were simulated with correlated and uncorrelated noise. Seven different electrode geometries are discussed. As a practical test, we considered profiles of a geoelectrical survey to locate tombs at a site of archaeological interest.When the shape and dimensions of the anomaly can be foreseen, the cross-correlation method can be applied and it gives a substantial improvement in the signal-to-noise ratio.

Notes: In the quantitative data interpretation for HLEM induction prospecting, a vertical half-plane model in an insulating medium is widely employed. For this assumption to be valid, the steeply dipping massive sulphide dykes must have large strike lengths and depth extents, but small thickness.We report investigations, using the laboratory scale-modelling method, on the response variation of large vertical conductors as the thickness is varied. We conclude that a steeply dipping large dyke can be approximated by a half-plane model only if its thickness is less than half the skin depth. An inductively thick conductor produces larger amplitudes and relatively higher quadrature compared to a thin conductor, even if both have the same induction number.

Notes: A model has been developed to relate the velocities of acoustic waves Vp and Vs in unconsolidated permafrost to the porosity and extent of freezing of the interstitial water. The permafrost is idealized as an assemblage of spherical quartz grains embedded in a matrix composed of spherical inclusions of water in ice. The wave-scattering theory of Kuster and Toksoz is used to determine the effective elastic moduli, and hence the acoustic velocities. The model predicts Vp and Vs to be decreasing functions of both the porosity and the water-to-ice ratio. The theory has been applied to laboratory measurements of Vp and Vs in 31 permafrost samples from the North American Arctic. Although no direct measurements were made of the extent of freezing in these samples, the data are consistent with the predictions of the model. Electrical resistivity measurements on the permafrost samples have demonstrated their essentially resistive behaviour. The ratio of resistivity of permafrost in its frozen state to that in its unfrozen state has been related to the extent of freezing in the samples.Electromagnetic and seismic reflection surveys can be used together in areas of permafrost: firstly an EM survey to determine the extent of freezing and then the acoustic velocity model to predict the velocities in the permafrost. The necessary transit time corrections can thus be made on seismic reflection records to compensate for the presence of permafrost.

Notes: The classical aim of non-linear inversion of seismograms is to obtain the earth model which, for null initial conditions and given sources, best predicts the observed seismograms. This problem is currently solved by an iterative method: each iteration involves the resolution of the wave equation with the actual sources in the current medium, the resolution of the wave equation, backwards in time, with the current residuals as sources; and the correlation, at each point of space, of the two wavefields thus obtained.Our view of inversion is more general: we want to obtain a whole set of earth model, initial conditions, source functions, and predicted seismograms, which are the closest to some a priori values, and which are related through the wave equation. It allows us to justify the previous method, but it also allows us to set the same inverse problem in a different way: what is now searched for is the best fit between calculated and a priori initial conditions, for given sources and observed surface displacements. This leads to a completely different iterative method, in which each iteration involves the downward extrapolation of given surface displacements and tractions, down to a given depth (the‘bottom’), the upward extrapolation of null displacements and tractions at the bottom, using as sources the initial time conditions of the previous field, and a correlation, at each point of the space, of the two wavefields thus obtained. Besides the theoretical interest of the result, it opens the way to alternative numerical methods of resolution of the inverse problem. If the non-linear inversion using forward-backward time propagations now works, this non-linear inversion using downward-upward extrapolations will give the same results but more economically, because of some tricks which may be used in depth extrapolation (calculation frequency by frequency, inversion of the top layers before the bottom layers, etc.).

Notes: Two particular sources of distortion, which may be encountered when applying tomographic imaging techniques to crosshole seismic data, have been investigated.Errors in survey locations of the shots and receivers can produce significant distortions in the images obtained. A simple method for solving simultaneously for the velocity field and shot and receiver location errors is presented and applied to synthetic and real data.Reflection and refraction of rays at velocity interfaces may produce poor density and angular coverage of the rays within the region of interest. It is shown that the effect of the velocity field on the ray coverage can significantly affect the resolution in the velocity image, even if ray bending is taken into account. One consequence of this effect is that, in some cases, little improvement in image quality is achieved by using curvi-ray rather than straight-ray inversion techniques, despite the occurrence of pronounced ray bending.

Notes: The WKB-method is used for the derivation of both the complex dispersion relation and displacement functions for Love channel-waves that propagate in a coal seam of varying thickness. The constant Q-model is used to describe the anelastic friction. With numerical solutions of the absorption-dispersion relation, the influence of thickness changes on the phase velocity and absorption coefficient of Love seam-waves is analysed at various frequencies. It is shown that the changes in the seam thickness can be optimally detected around the average Airy-phase frequency. An equivalence is pointed out between the wave guide structures: homogeneous with varying seam thickness and horizontally inhomogeneous with constant seam thickness.

Notes: Methods of minimum entropy deconvolution (MED) try to take advantage of the non-Gaussian distribution of primary reflectivities in the design of deconvolution operators. Of these, Wiggins’(1978) original method performs as well as any in practice. However, we present examples to show that it does not provide a reliable means of deconvolving seismic data: its operators are not stable and, instead of whitening the data, they often band-pass filter it severely. The method could be more appropriately called maximum kurtosis deconvolution since the varimax norm it employs is really an estimate of kurtosis. Its poor performance is explained in terms of the relation between the kurtosis of a noisy band-limited seismic trace and the kurtosis of the underlying reflectivity sequence, and between the estimation errors in a maximum kurtosis operator and the data and design parameters.The scheme put forward by Fourmann in 1984, whereby the data are corrected by the phase rotation that maximizes their kurtosis, is a more practical method. This preserves the main attraction of MED, its potential for phase control, and leaves trace whitening and noise control to proven conventional methods. The correction can be determined without actually applying a whole series of phase shifts to the data. The application of the method is illustrated by means of practical and synthetic examples, and summarized by rules derived from theory. In particular, the signal-dominated bandwidth must exceed a threshold for the method to work at all and estimation of the phase correction requires a considerable amount of data.Kurtosis can estimate phase better than other norms that are misleadingly declared to be more efficient by theory based on full-band, noise-free data.

Notes: The Offset Wenner resistivity sounding system provides for the extrapolation of the Wenner resistivity curve. The extrapolation technique was applied to data measured in the Solomon Islands and it is shown to be unreliable. An accurate method of predicting the reliability of extrapolation using measured resistances could not be found.

Notes: The concept of multifrequency induction logging simulations in the frequency range of 10 kHz to 1 MHz, applied to two-dimensional, axial symmetric model geometries, is presented. The scalar Helmholtz equation has been solved by a finite-element procedure. The model domain has been discretisized under the condition that the discontinuities in conductivity are represented by the nodes of the adjacent triangular elements. The modification of the signal distribution by the skin effect is illustrated for several models. Several sets of induction logs have been calculated with particular consideration of the frequency-dependent conductivities and permittivities.The improvement of a multifrequency inversion technique, based on standard least-squares methods, is shown for a two-layer model including borehole and invasion zones. Using this improved inversion technique we can state, as an additional inversion parameter, the frequency dependence of each inverted rock conductivity.

Notes: The wavefield in, and at the surface of, a homogeneous, isotropic, perfectly elastic half-space, excited by a traction distribution at the surface of the medium is investigated. The emitted wavefield is a spatial convolution of the surface tractions and the spatial impulse response. The properties of the wavefield in the far-field of the medium are derived and it is shown that the far-field particle velocity is essentially equal to a weighted sum of the time derivative of the integrated surface tractions, that is, of the components of the ‘ground force’. The theory is valid for an arbitrary geometry and orientation of the surface tractions, and is independent of the boundary conditions at the surface of the medium.The surface tractions are related to a source that consists of a mass distribution with an arbitrary force distribution imposed upon it. A boundary condition is introduced that accounts for the mass load and the forces applied to it but neglects vibrations within the mass. The boundary condition follows from the equation of motion of the surface mass load.The theory is applied to the Vibroseis configuration, using a P-wave vibrator model with a uniformly distributed force imposed on top of the baseplate, and assuming that horizontal surface traction components are absent. The distribution of displacement and stress directly underneath the baseplate of a single vibrator and an array of vibrators is investigated. Three different boundary conditions are used: (1) assuming uniform pressure, (2) assuming uniform displacement, (3) using the equation of motion of the baseplate as a boundary condition. The calculations of the distribution of stress and displacement over the plate for different elastic media and several frequencies of operation show that only the results obtained with the mixed boundary condition agree with measurements made in the field.The accuracy of three different phase-feedback signals is compared using synthetic data. Baseplate velocity phase-feedback leads to huge deviations in the determination of the far-field wavelet; reaction mass acceleration phase-feedback looks stable but neglects the differentiating earth filter; and phase-feedback to a weighted sum of baseplate and reaction mass accelerations becomes unstable with increasing frequency. The instability can be overcome using measurements over the whole baseplate.The model can be extended to a lossy layered earth.

Notes: This paper describes a method of generating pseudovelocity logs using measurements of electrical resistivity. A theoretical relation between electrical resistivity and transit time, which is applicable to a wide range of lithologies, has been developed. The application of this relation using a method which defines lithoresistivity zones as lithological intervals related to the same formation and showing small resistivity variations, has been tested in the Recôncavo sedimentary basin in Bahia, Brazil. A comparison of derived pseudovelocity logs with actual sonic logs for five wells whows the validity of the present approach.

Notes: Determination of petrography and pore fluid content is an ultimate goal of an integrated seismic-petrophysical study. For lack of a general inversion technique, forward modelling is useful in studying the relations between lithology, stratigraphy, pore fluid content and the seismic response. This report describes a study of two clastic sequences in Utah, from which 32 rock samples were analysed. A detailed petrographic study was done. Laboratory measurements were made of ultrasonic compressional- and shear-wave velocity as a function of pressure. We computed the velocities at seismic frequencies for the samples when dry, over-pressured, brine saturated, and oil saturated. The velocities were sensitive to the porosity, carbonate cementation and the depositional facies. We generated velocity profiles for hypothetical reservoirs for a range of saturation states. The velocity profiles were used to generate synthetic seismic shot gathers to study the seismic response of these clastic reservoirs. The fluid-saturation strongly affects the seismic respone, as does the presence of a coal seam. An amplitude change with offset is often observed. However, stratigraphy appears to have a stronger effect on the seismic response.

Notes: Two-dimensional VSP surveys are often conducted to provide structural illumination of the subsurface away from the borehole. The illumination is achieved through offsetting the source with respect to the downhole geophone. This inevitably gives rise to mode-conversions in both downgoing and upgoing wavefields.Migration of mixed-mode wavefields is complex because the velocity profile used for wavefield extrapolation is valid only for a particular propagation mode; the other mode always propagates at a different velocity. It is therefore advisable to separate the wave-types (P-wave and SV-wave) prior to migration. This may be achieved through wavemode filtering, a multichannel process which exploits the relation between propagation velocity, slowness of events at the recording array and particle motion. The necessary information about particle motion is available only if the VSP data are acquired with a three-component downhole geophone assembly.The wavemode filter partitions wave-types at the recording array; it provides no information about the various changes of propagation mode experienced by the energy as it travels from source to geophone. For the purpose of migration, the intermediate modes of propagation must be deduced.Much of the energy arriving at the receivers is P-wave which has followed the P-wave velocity profile from the source. It can therefore be imaged by conventional (Kirchhoff) migration. As an example of SV-wave imaging, a common mode-code is P-wave from source to reflector and SV-wave from reflector to geophone. Migration of such data calls for back-propagation of the geophone array wavefield, at SV-wave velocity, to the point in the subsurface where it is time-coincident with the forward propagated downwave, at P-wave velocity.

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

Notes: A triple axis borehole magnetometer is described that consists of a Förster-probe (fluxgate) triplet (sensitivity 1 n T), a Förster-probe gradiometer (sensitivity 2 nT/40 cm), a gyro unit (mean angular drift approx. 0.5°/h) which is equipped with accelerometers (sensitivity 1/100°), and a data transmission unit (with multiplexer and 16-bit AD converter). The sensitive fluxgate-magnetometer can detect weakly magnetic or small source bodies. Data from the gyro and the accelerometers allow the 3-component magnetic field values to be transformed to north, east and vertical components. Since they do not rely on magnetically-determined directional data, the results are not disturbed by local anomalies of the magnetic declination. Furthermore, the magnetometer can also be used in vertical boreholes. 3-component measurements are carried out at discrete points in the neighbourhood of a source body to locate its position, and within the source body to determine the direction of magnetization. The strength of magnetization and information on magnetic classification are obtained by continuous measurement of one or more components within the source body. Calculation algorithms and computer programs are available to simplify data processing and interpretation. Survey examples are discussed.

Notes: Resistivity measurements were carried out in a survey area in the south of Germany. This area is characterized by complicated subsurface geology. Schlumberger full-arrays and their respective half-arrays were recorded simultaneously. The results obtained by the one-dimensional (1D) interpretation of the full-array measurements were incorrect because of a resistivity discontinuity. This discontinuity, under a relatively thick overburden, could only be located by the half-array soundings. Its exact location and the resistivity distribution in the subsurface were ascertained by comparing the sounding curves with 2D model curves, which are calculated by a finite-difference method.

Notes: A novel process is used to coat glass spheres with a polymerizing thermo-setting resin, only microns thick. Synthetic rocks of known grain size distribution and pore space characteristics are then made by heating the resin-coated glass spheres under compression in a special mould. The dynamic Young's moduli of these rocks are found to be affected by the percentage of resin content (cement) and the synthetic diagenesis rather than the grain size and permeability.

Notes: Broad-band ultrasonic impulses and the attenuation spectral ratio technique have been used to investigate the characteristics of synthetic rocks for different saturants, by obtaining the attenuation coefficients in the frequency range of 0.1-1.0 MHz.The general trend of the data indicates that the experimental attenuation coefficient increases with an increase in the grain/pore size. Results show that large grains/pores can increase the attenuation coefficient in all mechanisms, and water-saturated synthetic sandstone rocks result in a higher attenuation coefficient than similar oil-saturated rocks.

Notes: It is now believed that the negative transients observed in coincident-loop transient electromagnetic (TEM) measurements are caused by polarizable bodies (bodies whose conductivity increases as a function of frequency). Ordinarily the TEM response of polarizable bodies is obtained by calculating the frequency-domain response at many frequencies and transforming it to the time domain via Fourier, Laplace or Hankel transforms. This is normally a computationally laborious task. However, for some simple non-polarizable bodies the time-domain response is analytical and can be computed easily. When these simple bodies are weakly polarizable an approximate response can be obtained by convolving the easily-calculated, non-polarizable response with the impulse response of the polarization. The approximate response is found to be very similar to the exact response for the polarizabilities normally seen in geological materials.

Notes: Migration of zero-offset data from a point diffractor gives an elliptic or hyperbolic ‘smile’ when the velocity is too high or too low, respectively (over- and undermigration).The phase-shift within the smile is positive (approximately +π/4) when the velocity is too high, and negative (approximately –π/4) when the velocity is too low. The phase-shift is calculated from the stationary phase approximation of the Kirchhoff integral.

Notes: Media containing aligned cracks show anisotropy with respect to elastic wave propagation. There are several models describing the wave propagation in cracked media, most of them only valid for cracks with small aspect ratios. One of these models (Crampin's model) is compared with a model valid for all aspect ratios (Nishizawa's model). The elastic constants and the group velocities are compared for both dry and liquid-filled inclusions with aspect ratios ranging from 0.0001 (flat cracks) up to 1 (spheres). The difference between both models is small for small aspect ratios but becomes larger for increasing aspect ratios. At a crack density of 0.05 both models give-within an error of 5%–the same results for aspect ratios up to 0.3. Therefore Crampin's model can be applied to a large range of cracked media even if the aspect ratio of the inclusions is not small. The variation of the anisotropy as a function of the aspect ratio can be studied using Thomsen's dimensionless parameters δ, E and y. They show how inclusions with large aspect ratios result in elliptical anisotropy.

Notes: The theory by which the Surface Integral Equation method may be applied to the solution of electromagnetic transmission boundary value problems is presented. For a 3D target of arbitrary electrical property contrast with its host medium excited by an arbitrary time-harmonic source, two integral equations are derived which need to be simultaneously solved for tangential electric and magnetic source density on the target's surface. If the target is 2D, though still excited by an arbitrary source (the 2½ D case), the problem is best solved in the transform domain for a number of different wavenumbers in the target's strike direction. Then a set of four simultaneous scalar integral equations needs to be solved for the components of the surface source density transforms in the target's strike direction and in the direction of the tangent vector to the target's cross-sectional contour.Examples are presented in which the 2½D problem is solved numerically using the method of moments with piecewise linear basis functions. Although the results generally compare well with analytical solutions, or solutions obtained numerically by other means, errors appear in the calculation of the real response of these targets to excitation by a magnetic dipole source at low frequencies. This is attributed to ill-conditioning of the system resulting from a non-unique solution at zero frequency.

Notes: A plasma gun source has been successfully used to obtain sub-bottom profiles. The profiles show better penetration than with a 3-5 kHz source and more resolution than with an air gun. The plasma gun source is compact, self-contained, and requires no complex auxiliary equipment. The device was deployed from large research vessels and a small boat. The plasma gun produces sufficient acoustic energy and with its characteristically short pulse length and broad bandwidth it is an attractive sub-bottom profiler, especially in shallow fresh or salt water.

Notes: Electromagnetic scale modelling for most conductors encountered in prospecting requires models of conductivity in the range 10-1000 S/m. A polyester composite filled with aluminium fillers is used to design the required materials. The fillers are chosen with a high aspect ratio to achieve the desired conductivities without altering mechanical properties. The design process, consisting of a chemical reaction, is simple, repeatable and easy to realize in a geophysical laboratory.The conductivity of the designed material is estimated by an inductive method based upon the variation of the quality factor of a coil in which the samples are inserted. This method is much less influenced by the distribution and orientation of fillers in the resin matrix than a galvanic method.The conductivities obtained fill the major part of the interval 10-1000 S/m without requiring unreasonable mixing ratios. The homogeneity of the material was tested and the anisotropy was low at high conductivities. The electrical properties do not vary with time in free air or when immersed in salt water.We propose standard curves giving conductivities of composites filled with aluminium fibres and flakes. A large cylindrical model of fixed resin-to-filler ratio was made to show the capability of the technique to produce models of useful size. Its measured conductivity agrees well with the expected conductivity from the established standard curves. A scale modelling experiment with the horizontal loop technique was carried out over a horizontal thin sheet made of the material, and again the conductivity obtained from the results agrees reasonably well with the expected value.The noted difference between the inductively and galvanically measured conductivities of the proposed material presently restricts the use of the technique to EM scale experiments for which the host rock is considered very resistive.

Notes: Determination of impedance or velocity from a stacked seismic trace generally suffers from noise and the fact that seismic data are bandlimited. These deficiencies can frequently be alleviated by ancillary information which is often expressed more naturally in terms of probabilities than in the form of equations or inequalities.In such a situation information theory can be used to include ‘soft’information in the inversion process. The vehicle used for this purpose is the Maximum Entropy (ME) principle. The basic idea is that a prior probability distribution (pd) of the unknown parameter(s) or function(s) is converted into a posterior pd which has a larger entropy than any other pd which also accounts for the information. Since providing new information generally lowers the entropy, this means that the ME pd is as non-committal as possible with regard to information which is not (yet) available. If the information used is correct, then the ME pd cannot be contradicted by new, also correct, data and thus represents a conservative solution to the inverse problem.In the actual implementation, the final result is, generally, not the pd itself (which may be quite broad) but rather the expectation values of the desired parameter(s) or function(s).A general problem of the ME approach is the need for a prior pd for the parameter(s) to be estimated. The approach used here for the velocity is based on an invariance criterion, which ensures that the result is the same whether velocity or slowness is estimated. Unfortunately, this criterion does not provide a unique prior pd but rather a class of functions from which a suitable one must be selected with the help of other considerations.

Notes: Moving source profiling is a modification of walk-away vertical seismic profiling in which the source is moved along a line across a well while the signal is recorded in the well at a certain depth. The method was designed to better predict the target horizon below the drill bit and away from the well location. The method has several advantages in areas of complicated overburden.In overthrust regions, the receiver is placed below much of the complicated structure to minimize distortion of the reflected signal. The final seismic image is a depth presentation of the subsurface structure and stratigraphy based on wavefront calculations. This depth estimation is obtained without extensive processing of the recorded data. The final result is available within a few days and can help interpreters to decide if and where to sidetrack the well. The method is demonstrated using an example from the overthrust zone of the Lower Saxonian Basin and the Pompeckj's well in Northern Germany.

Notes: Most seismic data is processed using a sample interval of 4 ms two-way time (twt). The study of the statistical properties of primary reflection coefficients showed that the power spectrum of primaries can change noticeably when the logs are averaged over blocks of 0.5, 1 and 2 ms twt (block-averaging). What is a suitable block-averaging interval for producing broadband synthetics, and in particular how should the power spectrum of primaries be constructed when it is to be used to correct 4 ms sampled deconvolved seismic data for the effects of coloured primary reflectivity?In this paper we show that for a typical sonic log, a block-averaging interval of 1 ms twt should satisfy some important requirements. Firstly, it is demonstrated that if the reflection coefficients in an interval are not too large the effect of all the reflection impulses can be represented by another much sparser set at intervals of Δt twt, The coefficient amplitudes are given by the differences in the logarithmic acoustic impedances, thus justifying block-averaging. However, a condition for this to hold up to the aliasing (Nyquist) frequency is that Δt takes a maximum value of about 1 ms twt. Secondly, an event on a log should be represented in the seismic data. For this the acoustic impedance contrast must have sufficient lateral extent or continuity. By making some tentative suggestions on the relation between continuity and bed-thickness, a bed-thickness requirement of 0.15 m or more is obtained. Combining this requirement with the maximum number of beds allowable in an interval in order that multiple reflections do not contribute significantly to the reflections in the interval, again suggests a value of about 1 ms for the block-averaging interval.With this in mind an experiment was performed on three sonic logs. The logs were block-averaged at 1 ms, and primary reflection coefficients calculated. These primaries were then anti-alias filtered and resampled to get a series of primaries at 4 ms, followed by ARMA spectrum fitting. The same logs were also block-averaged at 4 ms directly and primaries computed, followed by ARMA spectrum fitting. In all three cases the first approach gave the ARM A model spectrum with greatest dynamic range, which strongly suggests that direct 4 ms block-averaging introduces significant aliased energy into low frequencies of the primaries spectrum.The conclusion is that routine computation of broadband synthetics (primaries only or primaries plus multiples) should be carried out using a block-averaging interval of 1 ms twt, followed by anti-alias filtering and thinning to the desired final sample interval. In theory it would be advantageous to go to even finer intervals-say 0.5 ms-but in practice at this level the averaging of slowness imposed by the somic logging tool appears to attenuate high-wave number fluctuations, i.e. it interferes with the‘real’data. The 1ms choice is thus a reasonable compromise which will help minimize non-trivial aliasing effects and should give better matches to the seismic data.

Notes: A novel fixed-source electromagnetic system has been developed. The transmitter is a large rectangular loop or grounded dipole. The transmitted waveform consists of up to five superimposed pure sinusoids at well-separated frequencies. The receiver measures the amplitude and phase at two frequencies from a single receiver coil. The amplitude ratio is routinely calculated. Field trials with both surface and downhole configurations show that the method has advantages over the more traditional frequency-domain Turam type and downhole electromagnetic (DHEM) systems. Among such advantages are the use of a single receiver coil and the removal of noise due to free-space variations in transmitter-receiver geometry. The latter is important for DHEM surveys. In terms of field procedures and quantities measured, the system is similar to time-domain methods.

Notes: Expressions are derived for the acoustic pressure in a fluid-filled borehole due to the passage of plane compressional or shear waves propagating in a porous and permeable medium. The derivation is based on a quasistatic description, yielding results applicable at low frequencies. Computations for a plausible sandstone (with porosity of 0.21 and permeability of 300 millidarcies) show accoustic pressure to be a surprisingly distortion-free version of the stress waveform in a plane compressional wave. For a plane shear wave, the pressure waveform is visibly distorted.

Notes: The estimation of velocity and depth is an important stage in seismic data processing and interpretation. We present a method for velocity-depth model estimation from unstacked data. This method is formulated as an iterative algorithm producing a model which maximizes some measure of coherency computed along traveltimes generated by tracing rays through the model. In the model the interfaces are represented as cubic splines and it is assumed that the velocity in each layer is constant. The inversion includes the determination of the velocities in all the layers and the location of the spline knots.The process input consists of unstacked seismic data and an initial velocity-depth model. This model is often based on nearby well information and an interpretation of the stacked section.Inversion is performed iteratively layer after layer; during each iteration synthetic travel-time curves are calculated for the interface under consideration. A functional characterizing the main correlation properties of the wavefield is then formed along the synthetic arrival times. It is assumed that the functional reaches a maximum value when the synthetic arrival time curves match the arrival times of the events on the field gathers. The maximum value of the functional is obtained by an effective algorithm of non-linear programming.The present inversion algorithm has the advantages that event picking on the unstacked data is not required and is not based on curve fitting of hyperbolic approximations of the arrival times. The method has been successfully applied to both synthetic and field data.

Notes: The detection and resolution of a thin layer closely situated above a high-impedance basement are predominantly determined by both the frequency content of the incident seismic wavelet and the existence of the nearby high-impedance bedrock.The separation of the thin layer and the basement arrivals is investigated depending on the low-frequency content of the wavelet. The high-frequency content of the wavelet is kept constant. The initial wavelet spectrum with low frequencies has a rectangular shape. All wavelets used have zero-phase characteristics. Numerical and analogue seismic modelling techniques are used. The study is based on the geology of the Pachangchi Sandstone in West Taiwan.Firstly the resolution of a thin layer between two half-spaces is examined by applying the Ricker and De Voogd-Den Rooijen criteria. The lack of low-frequency components of the incident seismic wavelet reduces the shortest true two-way traveltime by about 20%. In addition, low-frequency components of the wavelet diminish the deviation between true and apparent two-way traveltime by about 65% for layer thicknesses in the transition from a thick to a thin layer.The second step deals with the influence of a high-impedance basement just below a thin layer on the detection and resolution of that thin layer. Reflected signal energies and apparent two-way traveltimes are considered. The reflected signal energy depends on the low-frequency content of the incident wavelet, the layer's thickness and the distance between the basement and the layer. This applies only to layers with thicknesses less than or equal to one-third of the mean wavelength in the layer, and a distance to basement in the range of one to one-half of the mean wavelength in the rock material between layer and basement.The minimum thin-layer thickness resolvable decreases with increasing distance to the basement; i.e. for a layer thickness of one-third of the mean wavelength in the layer the relative error of the two-way traveltime increases from 5% to 30%, if the distance is reduced from one to one-half of the mean wavelength in the material between the basement and the thin layer.Finally, a combination of vertical seismic profiling and downward-continuation techniques is presented as a preprocessing procedure to prepare realistic data for the detection and resolution investigation.

Notes: Numerical wavefield extrapolation represents the backbone of any algorithm for depth migration pre- or post-stack. For such depth imaging techniques to yield reliable and interpretable results, the underlying wavefield extrapolation algorithm must propagate the waves through inhomogeneous media with a minimum of numerically induced distortion, over a range of frequencies and angles of propagation.A review of finite-difference (FD) approximations to the acoustic one-way wave equation in the space-frequency domain is presented. A straightforward generalization of the conventional FD formulation leads to an algorithm where the wavefield is continued downwards with space-variant symmetric convolutional operators. The operators can be precomputed and made accessible in tables such that the ratio between the temporal frequency and the local velocity is used to determine the correct operator at each grid point during the downward continuation.Convolutional operators are designed to fit the desired dispersion relation over a range of frequencies and angles of propagation such that the resulting numerical distortion is minimized. The optimization is constrained to ensure that evanescent energy and waves propagating at angles higher than the maximum design angle are attenuated in each extrapolation step. The resulting operators may be viewed as optimally truncated and bandlimited spatial versions of the familiar phase shift operator. They are unconditionally stable and can be applied explicitly. This results in a simple wave propagation algorithm, eminently suited for implementation on pipelined computers and on large parallel computing systems.

Notes: The attenuation in the vicinity of the geothermal anomaly at Urach was determined by means of two near-vertical reflection profiles. The attenuation in the sediments and in the upper crust (3-4 km depth) was estimated by interpretation of the first (refracted) arrivals. For calculating the attenuation, the amplitude decay with respect to distance was used. Corrections for the spread factor, i.e. the geometric amplitude divergence was deduced from the traveltime curves. Below the anomaly, higher attenuation values (Q−1∼ 0.008) were observed compared with those in the undisturbed crust (Q−1∼ 0.002). This effect is probably due to the cracks and fissures in the upper part of the crystalline basement.The attenuation in the middle and lower crust was determined using near-vertical reflections from this depth interval. The use of the spectral ratio method leads to higher values of the effective attenuation Q−1eff below the heat flow anomaly compared to those of the‘ normal’crust. This zone of high Q−1eff coincides with the low velocity body below the heat flow anomaly. Both effects, the higher attenuation and the lower velocities, could be caused by high temperatures, cracks and fissures in the crust.

Notes: An outline of the provisions of the latest step in the government's ‘step-by-step’ approach to control of union power

Notes: Since the mid-1970s Australian trade unions have conducted a concerted campaign to reduce standard working hours. Part of the logic behind this was to increase employment opportunities for those currently unemployed. This article reviews the economic and industrial relations implications of that campaign by reference to the major studies undertaken in this area and compares them with those from other countries.

Notes: Economic recession has heralded massive job losses in recent years but it is not just financial expediency that has been driving firms’ redundancy programmes. Redundancy has also been a precursor of management attempts to promote the productivity and flexibility of the remaining workforce, enabling many firms to emerge both ‘leaner and fitter’ from the recession.

Notes: Here the author discusses the concept of profit related pay and assesses the practical implications of recent measures to promote this method of payment in Britain through tax relief. The new initiative, it is argued, is unsound in concept and design and unlikely to meet stated objectives.

Notes: Trade union education–a significant area of trade union activity – has been characterised by a tension between the desire to provide a certain ideological, economic and political perspective and the need to develop pragmatic bargaining skills. This comparative study examines the differing ways in which trade union education has developed in France and Britain.

Notes: The annual round of the settlement of disputed transfer fees gave an opportunity for a modest attempt to access the impact of pendulum arbitration, Previous years had clearly indicated the centrifugal impact of arbitration. It appears that pendulum arbitration improves this but at the expense of one side: the club losing the player.