Exact synthetic seismograms for an inhomogeneity in a layered elastic half-space

Summary. The propagation of a pulsed elastic wave in the following geometry is considered. An elastic half-space has a surface layer of a different material and the layer furthermore contains a bounded 3-D inhomogeneity. The exciting source is an explosion, modelled as an isotropic pressure point source with Gaussian behaviour in time.
The time-harmonic problem is solved using the null field approach (the T matrix method), and a frequency integral then gives the time-domain response. The main tools of the null field approach are integral representations containing the free space Green's dyadic, expansions in plane and spherical vector wave functions, and transformations between plane and spherical vector wave functions. It should be noted that the null field approach gives the solution to the full elastodynamic equations with, in principle, an arbitrarily high accuracy. Thus no ray approximations or the like are used. The main numerical limitation is that only low and intermediate frequencies, in the sense that the diameter of the inhomogeneity can only be a few wavelengths, can be considered.
The numerical examples show synthetic seismograms consisting of data from 15 observation points at increasing distances from the source. The normal component of the velocity field is computed and the anomalous field due to the inhomogeneity is sometimes shown separately. The shape of the inhomogeneity, the location and depth of the source, and the material parameters are all varied to illustrate the relative importance of the various parameters. Several specific wave types can be identified in the seismograms: Rayleigh waves, direct and reflected P -waves, and head waves.     

A survey of Earth strain tides in Great Britain

Summary . We report 35 measurements of Earth strain tides at 16 near-surface sites in Great Britain. This is the first widespread survey undertaken specifically to examine the problem of the inhomogeneity of elastic strain fields near the Earth's surface. Some sites were instrumented intensively in order to examine variations of tidal admittance over distances of several hundred metres, while measurements from single instruments at other sites were compared with theoretically predicted strain tides. After allowing for cavity and topographic effects, our data show variations of up to 50 per cent in tidal admittance. We interpret such large anomalies as being due to variations in the regional elastic parameters of wavelength about a 100 m or less. The data indicate that strain measurements from single instrument sites must be interpreted with caution.     

Simulated envelopes of non-isotropically scattered body waves as compared to observed ones: another manifestation of fractal heterogeneity

Envelopes of scalar waves are simulated at various distances from an instant point source embedded in a random uniformly scattering medium by means of direct Monte-Carlo modelling of wave-energy transport. Three types of scattering radiation pattern ('indicatrix') are studied, for media specified by (1) a Gaussian autocorrelation function of inhomogeneities, (2) a power-law ('fractal', k -^α) inhomogeneity spectrum and (3) the mix of case (1) and the isotropic indicatrix (very small + large inhomogeneities). We look for a model that can qualitatively reproduce the two most characteristic features of real S-wave envelopes of near earthquakes, namely (1) the broadening of the 'direct' wave group with distance and (2) the monotonously decaying shape of the coda envelope that does not deviate strongly from that expected in the isotropic scattering case. Both properties are observed for any band over a wide frequency range (1-40 Hz). The well-studied isotropic scattering model realistically predicts the appearance of codas but fails to predict pulse broadening. The model of large-scale inhomogeneity realistically predicts the mode of pulse broadening but fails to predict codas. We have found that, for a particular frequency band, within each class of inhomogeneity studied, both requirements can be qualitatively satisfied by a certain choice of parameters. In the Gaussian-ACF case, however, this match can be obtained only for a narrow frequency range. In contrast, the fractal case (with a value of exponent a of about 3.5-4) reproduces qualitatively the observed wide-band behaviour, and we consider it a reasonable representation of the gross properties of the earth medium.     

SHORT COMMUNICATION DISPLAY ASPECTS IN HIERARCHICAL CLUSTERING

Ultrametric inter-object distances found by hierarchical clustering may be used to generate an appropriateconstellation of points in a plane.A configuration of points which reproduce the ultrametric distancesin a low-dimensional space as closely as possible can be found by Torgerson's method of multidimensionalscaling.The resulting display supports the cognition of clusters very well,and for this purpose it seemsto be superior to,for instance,the frequently applied principal components display.In certain sitt,ationsdedrograms are expected to become simpler to interpret when such complementary 'cluster display' is alsoconsulted.An example from analytical chemistry is presented.     

SCALING TECHNIQUES IN THE ANALYSIS OF ENVIRONMENTAL COGNITION DATA *

The utility of nonmetric, multidimensional-scaling techniques is demonstrated for the analysis and collection of environmental-cognition data. By comparing the multidimensional-scaling solutions of a real-setting map to scaling solutions for sketch maps and two psychophysical, distance-scaling procedures, we demonstrate that magnitude estimation of actual interpoint distances is comparable in accuracy to sketch maps when produced without constraints, or when subjects are given a specified list of landmarks to include on their maps. Triadic comparisons of actual interpoint distances were less accurate than the three other techniques.     

Coseismic and other short-term strain changes recorded with Sacks-Evertson strainmeters in a deep mine, South Africa

Summary. During 1977 March and April, three Sacks-Evertson borehole dilatometers were installed at the ends of boreholes drilled into the sidewall of an experimental tunnel at a depth of 3.1 km in the ERPM gold mine near Johannesburg. In the following year coseismic strain changes ranging from 5 ± 10⁻¹⁰ to values exceeding 5 ± 10⁻⁶ were recorded for hundreds of mine tremors in the magnitude range -1 to 3.7 and at hypocentral distances of 50 m to about 2 km. Hypocentral coordinates and magnitudes were determined from seismograms recorded from an underground array of geophones. Amplitudes and polarities of the coseismic strain steps are generally in excellent agreement with theoretical expectations based on point-source dislocation theory; specifically, the strain steps are proportional to the seismic moment divided by the cube of hypocentral distance. At a strain level of 5 ± 10⁻⁹ or greater the tremors do not appear to be preceded by any short-term indications of instability even for tremors producing coseismic steps greater than 5 ± 10⁻⁶ and for which the strainmeters were within a source radius of the hypocentre. Continuous strain changes observed at the times when the mine excavation, at a distance of about 100 m, is extended are in good agreement with calculated changes based on the theory of elasticity. A similar calculation is consistent with post-seismic strain changes observed to follow some of the closer tremors. These post-seismic strains show a logarithmic dependence on time following the tremor and appear to be due to the interaction of a tremor with the adjacent mine excavation rather than to deformation within the actual seismic source region.     

On the focusing of seismic body waves at the epicentre's antipode

Summary. This note reports on the remarkable focusing of seismic body waves at or near the antipode (Δ= 180°) of an earthquake's epicentre. The particular seismic velocity structure and sphericity of the Earth cause body-wave phases such as P (diff), PKP, PP, PPP, PcPPKP, SKSSKS, SS , etc. to converge individually at antipodal distances after being diffracted, reflected or refracted at discontinuities. This focusing strongly amplifies each signal up to almost one order of magnitude with respect to the normal phase recorded two or more degrees away. Since the signal/noise ratio is enhanced in the same proportion, seismograms at antipodal distances provide clear and strong arrivals of otherwise weak phases. Antipodal monitoring of seismic waves is suggested as a powerful means of exploring the Earth's interior. The study of these 'seismic images' generated at focal points of seismic rays will yield information on the departures from lateral homogeneity and sphericity of the core, as well as stronger constraints on earth models. To interpret the observations correctly, the data must be compared with theoretically generated seismograms. Since the appropriate ray theory equations (see, e.g. Scholte; Gilbert & Helmberger; Richards) are singular at Δ=180°, a corrective measure is taken which provides a formal expression for the wave amplitude that remains finite at the antipode, and reproduces the usual expressions at other distances.     

SCALING TECHNIQUES IN THE ANALYSIS OF ENVIRONMENTAL COGNITION DATA∗

The utility of nonmetric, multidimensional-scaling techniques is demonstrated for the analysis and collection of environmental-cognition data. By comparing the multidimensional-scaling solutions of a real-setting map to scaling solutions for sketch maps and two psychophysical, distance-scaling procedures, we demonstrate that magnitude estimation of actual interpoint distances is comparable in accuracy to sketch maps when produced without constraints, or when subjects are given a specified list of landmarks to include on their maps. Triadic comparisons of actual interpoint distances were less accurate than the three other techniques.     

An improved method for the determination of the tectonic stress field from focal mechanism data

All conventional stress inversion methods, when applied to earthquake focal mechanism data, suffer from uncertainty as to which plane is the true fault plane. This paper deals with several problems in stress inversion brought about by this uncertainty. Our analysis shows that the direction of shear stress on the auxiliary plane does not coincide with the hypothetical slip direction unless the B -axis is parallel to one of the three principal stress directions. Based on this simple fact, we propose a new algorithm dealing with the ambiguity in fault/auxiliary plane identification. We also propose a method to handle the inhomogeneity problem of data quality, which is common and unique for focal mechanism data. Different inversion methods and algorithms are applied to two sets of 'focal mechanism' data simulated from field fault-slip measurement data. The inversion results show that, among the four stress parameters inverted, the stress ratio suffers the most from the ambiguity in fault/auxiliary plane identity, whereas the solutions for the principal stress directions are surprisingly good. The errors in inversion solutions resulting from the fault/auxiliary plane ambiguity can be significantly reduced by controlling subjectively the sample variance of the measurement errors. Our results also suggest that the fault plane cannot be distinguished correctly from the auxiliary plane with a high probability on the basis of the stress inversion alone.     

Interpretation of local two-dimensional electromagnetic anomalies by formalized trial procedure

Summary. An iterative algorithm is presented to be used in the search for the shape of a 2-D local deep geoelectric inhomogeneity lying in a layered medium; an anomaly having been identified in the usual way by observing an alternating time-harmonic electromagnetic field along the surface of the Earth. The normal section parameters (conductivities and thicknesses) and the excess electrical conductivity (inside inhomogeneity) are assumed to be known. The shape of the inhomogeneity is determined by means of a misfit functional minimization technique. A gradient minimization algorithm is constructed and Tikhonov's regularization scheme is applied to achieve stability of the solution. The effectiveness of such an approach is demonstrated by model calculations and by the interpretation of the Carpathian geomagnetic anomaly. Finally, a brief discussion of the problems of the practical application of this formalized trial procedure is presented. Because of the lack of reliable estimates of the excess conductivity, it is proposed to consider a family of models selected for the set of probable values of model parameters. This family can be treated as a generalized solution of the interpretation problem.     

Characterization of landslide ground surface kinematics from terrestrial laser scanning and strain field computation

Assessment and mitigation of the risk induced by landslide activation need an appropriate phenomenon investigation, to obtain useful information about the failure processes. The first step is the complete kinematics characterization of the landslide ground surface, by evaluating the involved displacement and deformation patterns. A dense displacement field can be obtained from comparison of a series of multi-temporal observations performed by means of terrestrial laser scanning. Subsequently, the strain field can be computed from displacement vectors. In this paper, a modified least square technique is employed to compute the strain on the nodes of a regular grid (2D approach) or on the points of a digital terrain model (3D approach). Such a computation takes into account the displacements, their spatial distribution, as well as the measurement and modelling errors. A scale factor is introduced in order to emphasize the contributions of the experimental points on the basis of their distance from each computation point, and to recognize possible scale-depending behaviours. This method has been implemented in Matlab and applied on two landslides located in the northeastern Italian Alps (Lamosano and Perarolo di Cadore). The experiments show that different kinematics can be recognized, and the presence and influence of eventual discontinuities can be revealed.     

Transient electromagnetic field above a permeable and conducting half-space

Summary. The transient fields resulting from an abrupt current switch-off in a vertically oriented finite loop and a magnetic dipole above a permeable and conducting half-space have been investigated by Fourier methods, utilizing an appropriate Green's function. Two partial fields are identified, one 'radiative' and evanescent and one 'diffusive'. Asymptotic formulae for the diffusive field above the interface, applicable for late times, are developed, and from these the effects of height of the transmitting source and the permeability contrast are calculated. It is shown that for 'late enough' times and at sufficient distances the dipole formulae provide adequate approximations to the field due to a finite loop.     

A Review of: “Geographic Information Systems for Geoscientists—Modelling with GIS”

Distances from points to closest shorelines in a given direction are used, for example, in some models for estimating wave exposure. Such distances, also called fetch lengths, can be determined using standard geographic information systems. However, performance may be a problem if these distances are required for a great number of study points. Two new algorithms for determining fetch lengths for study points in the same directions are presented in this paper. It is assumed that the two‐dimensional map is stored in vector format, i.e. shorelines of islands and mainland are stored as polygons. The first algorithm works on a set of undirected line segments derived from the shoreline polygons. The other works on a raster representation of the map. The algorithm saves memory by postponing the rasterisation until necessary. Both of the new algorithms have superior efficiency to a previously reported algorithm when the number of study points is large.     

A new algorithm for distance cartogram construction

A distance cartogram is a diagram that visualizes the proximity indices between points in a network, such as time–distances between cities. The Euclidean distances between the points on the distance cartogram represent the given proximity indices. This is a useful visualization tool for the level of service of transport, e.g. difference in the level of service between regions or points in a network and its improvement in the course of time. The two previously proposed methods—multidimensional scaling (MDS) and network time–space mapping—have certain advantages and disadvantages. However, we observe that these methods are essentially the same, and the merits of both these methods can be combined to formulate a generalized solution. In this study, we first formulate the time–space mapping problem, which includes the key features of both of the above stated methods, and propose a generalized solution. We then apply this solution to the time–distances of Japan's railway networks to confirm its applicability.     

Determination of Geomagnetic Palaeointensities in Vacuum

Summary. Specimens with low and intermediate Curie points from six Hawaiian historic basalt flows were used for the determination of the intensity of the historic geomagnetic field by the Thelliers' method. The specimens were heated either in air or in a vacuum of 10⁻⁵ torr. The regional intensity of the Earth's magnetic field at the time of extrusion of these rocks is known from direct observations. The palaeointensities determined in vacuum from four low and intermediate Curie point flows are correct within the uncertainty caused by the local field anomalies, whereas those determined in air from the same four flows are of lesser quality and accuracy. Unaltered submarine basalts have similarly low Curie points and thus may also be amenable to palaeointensity determination in vacuum. The behaviour of the remaining two flows, which had higher Curie points, was more erratic, and they yielded less accurate palaeointensities regardless of whether they were determined in air or vacuum.     

Electromagnetic response of an arbitrarily shaped three-dimensional conductor in a layered earth—numerical results

Summary. In an earlier work, mathematical formulation on computing the electromagnetic response of an arbitrarily shaped three-dimensional inhomogeneity in a layered earth had been worked out using an integral equation technique. The method has been used to show its efficacy by computing numerical results. Introducing suitable changes of variables the secondary contributions to Green's dyadic are put in the form of convolution integrals and are computed using a digital linear filtering scheme. The matrix equation is solved for the unknown electric fields in the inhomogeneity. The scattered fields are then calculated at the surface of the Earth using the appropriate Green's dyadic. The performance of the computations has been shown by comparing the numerical results with those obtained by analogue modelling as well as by other numerical schemes. The use of digital linear filtering saves an enormous amount of computer time.
The effects of varying excitation-frequency, conductivity of the host medium and that of the overburden have been studied in detail for a horizontal loop system traversing over a two-layered earth with a prismatic inhomogeneity situated in the lower conducting half space.     

An artificial bee colony-based multi-objective route planning algorithm for use in pedestrian navigation at night

Pedestrian navigation at night should differ from daytime navigation due to the psychological safety needs of pedestrians. For example, pedestrians may prefer better-illuminated walking environments, shorter travel distances, and greater numbers of pedestrian companions. Route selection at night is therefore a multi-objective optimization problem. However, multi-objective optimization problems are commonly solved by combining multiple objectives into a single weighted-sum objective function. This study extends the artificial bee colony (ABC) algorithm by modifying several strategies, including the representation of the solutions, the limited neighborhood search, and the Pareto front approximation method. The extended algorithm can be used to generate an optimal route set for pedestrians at night that considers travel distance, the illumination of the walking environment, and the number of pedestrian companions. We compare the proposed algorithm with the well-known Dijkstra shortest-path algorithm and discuss the stability, diversity, and dynamics of the generated solutions. Experiments within a study area confirm the effectiveness of the improved algorithm. This algorithm can also be applied to solving other multi-objective optimization problems.     

Uniqueness of mainly dipolar magnetic fields recovered from directional data

We show that a knowledge of either the signed or the unsigned direction of a potential field on a given smooth surface S , which separates the space into a volume containing the sources and a volume free of sources, sometimes gives enough information for the whole field to be recovered within the free volume, except for a constant multiplier (positive, for the signed case). We show that the best parameter to be considered on the surface S is the number n of loci where the field is known to be either zero (no direction) or normal to the surface. In the case of sources lying outside S ('external-sources' directional problem) we prove that the dimension of the space of solutions is no larger than n –1. This implies uniqueness for the external-sources directional problem when n = 2. In the case of sources lying inside S ('internal-sources' directional problem), we distinguish fields with monopole sources (such as the gravitational field) from those without monopole sources (such as the magnetic field). For gravitational fields, we show that the dimension of the space of solutions cannot exceed n . We note that the only situation of interest is the one for which n = 1, which implies in practice that the surface S is an isopotential and that the problem has a unique solution. For magnetic fields, we show that the dimension of the space of solutions cannot exceed n –1. It follows that the problem has a unique solution when n = 2. This shows in particular that a geomagnetic field with only two poles (south and north magnetic poles) can be recovered, except for a constant multiplier (positive, for the signed case) from directional data gathered at the Earth's surface. Finally, we note that our results are not restricted to the 3-D space and can readily be extended to two dimensions and higher dimensions.     

A Point-Based Intelligent Approach to Areal Interpolation

Areal interpolation is the data transfer from one zonal system to another. A survey of previous literature on this subject points out that the most effective methods for areal interpolation are the intelligent approaches, which often take two-dimensional (2-D) land use or one-dimensional (1-D) road network information as ancillary data to give insight on the underlying distribution of a variable. However, the 2-D or 1-D ancillary information is not always applicable for the variable of interest in a specific study area. This article introduces a point-based intelligent approach to the areal interpolation problem by using zero-dimensional (0-D) points as ancillary data that are locationally associated with the variable of interest. The connection between zonal variables and point locations can be modeled with a linear or a nonlinear exponential function, which incorporates the distribution of the variables in the transferring of the information from the source zone to the target zone. An experimental study interpolating the population data at a suburbanized area suggests that the proposed method is an attractive alternative to other areal interpolation solutions based on the evaluation of its resulting accuracy and efficiency.     

Travel From Home: An Economic Geography of Commuting Distances in Montreal

The question of how home and workplace are linked through commuting is at the heart of much recent work on metropolitan areas. However, the emphasis tends to be either on spatial-economic models or on the impact of empirically measured individual, household, neighborhood, and transport mode characteristics; relatively little work has focused on job characteristics and place of employment as they relate to travel to work. In this article, I investigate whether people travel different distances to access different types of job location, with particular attention to the different distances traveled by men and women. My points of reference are the major employment centers (poles) in the Montreal region. After controlling for a wide range of explanations that may account for different travel distances, I conclude that differences in commuting length between different places of work are, by and large, independent of possible explanatory factors such as residential location, economic sector, occupation, income, and participation in household earnings—some places of work generate longer commutes than others. Men and women behave differently in relation to these places: women will travel farther to access jobs in centers whereas men will not; and despite their shorter average overall commutes, women travel farther than men to reach jobs in the CBD. This suggests, at the metropolitan scale, that each job location may have its own local culture or "milieu," and that men and women react differently to them.