Crooked Line Research Articles

Towards more assertive advertising practices: An evolutionary, not revolutionary, step forward.

Abstract We presented arguments in favour of loosening self-imposed restrictions on advertising by psychologists (Shead & Dobson, 2004). Dr. Koocher's commentary on our paper suggested that these practices may, in fact, be viable. We view the implementation of these strategies as part of an evolution in advertising within the field of psychology, rather than a revolution that aims to encourage extreme business practices. A review of the historical changes in advertising practices by psychologists in North America indicates that progress has been slow (Shead & Dobson, 2004). Although regulatory bodies have tended to liberalize their guidelines concerning advertising practices, it appears that individual psychologists continue to favour a more traditional approach to announcing their services. Specifically, three types of advertising strategies that were once subject to disciplinary action are now typically permissible under current regulatory guidelines: 1) claims of unusual, unique, or one-of-a-kind abilities; 2) claims of the comparative desirability of one service over another; and 3) the use of statements appealing to a client's fear and anxiety if services are not obtained. Despite their official acceptability, the majority of advertisements abide by a time-honoured template that consists of very little distinguishing information about services offered. We presented arguments to suggest that each of the above three advertising approaches could be implemented in a manner that is consistent with ethical standards (Shead & Dobson, this issue). It is our contention that the movement towards more assertive advertising would be beneficial for both the psychologist, in terms of recruiting potential clients, and for the public, in terms of providing valuable information about available services. Dr. Koocher's response to our paper suggested that these practices may, in fact, be viable (Koocher, this issue). He also includes an opt-out clause, however, noting that if these recommendations do not end up benefiting both psychologists and public stakeholders, then the blame can be placed on Canada. His response suggests our recommendations were revolutionary in nature. It was not our intention to revolutionize the way psychologists advertise, however, but to present arguments in favour of practices that seem long overdue. As noted above, the current approach to advertising professional services has changed very little in recent decades. The arguments we present seem in line with practices that might currently be employed had the discipline followed a more natural evolution. We were careful, however, not to suggest the deployment of distasteful and unscrupulous business practices that potentially benefit the professional more than the potential consumer. Other professions have begun to approach, or in some cases may have already crossed, the crooked line between assertive advertising and unscrupulous business. Today's marketplace has many examples of avaricious practices that aim to prey on naive consumers. …

The Importance of Being Equivalent: Newton?s Two Models of One-Body Motion

As an undergraduate at Cambridge, Newton entered into his ‘Waste Book’ an assumption that we have named the Equivalence Assumption (The Younger): ‘‘ If a body move progressively in some crooked line [about a center of motion] ..., [then this] crooked line may bee conceived to consist of an infinite number of streight lines. Or else in any point of the croked line the motion may bee conceived to be on in the tangent.’’ In this assumption, Newton somewhat imprecisely describes two mathematical models, a ‘‘polygonal limit model’’ and a ‘‘tangent deflected model,’’ for ‘‘one-body motion,’’ that is, for the motion of a ‘‘body in orbit about a fixed center,’’ and then claims that these two models are equivalent. In the first part of this paper, we study the Principia to determine how the elder Newton would more carefully describe the polygonal limit and tangent deflected models. From these more careful descriptions, we then create Equivalence Assumption (The Elder), a precise interpretation of Equivalence Assumption (The Younger) as it might have been restated by Newton, after say 1687. We then review certain portions of the Waste Book and the Principia to make the case that, although Newton never restates nor even alludes to the Equivalence Assumption after his youthful Waste Book entry, still the polygonal limit and tangent deflected models, as well as an unspoken belief in their equivalence, infuse Newton’s work on orbital motion. In particular, we show that the persuasiveness of the argument for the Area Property in Proposition 1 of the Principia depends crucially on the validity of Equivalence Assumption (The Elder). After this case is made, we present the mathematical analysis required to establish the validity of the Equivalence Assumption (The Elder). Finally, to illustrate the fundamental nature of the resulting theorem, the Equivalence Theorem as we call it, we present three significant applications: we use the Equivalence Theorem first to clarify and resolve questions related to Leibniz’s ‘‘polygonal model’’ of one-body motion; then to repair Newton’s argument for the Area Property in Proposition 1; and finally to clarify and resolve questions related to the transition from impulsive to continuous forces in ‘‘De motu’’ and the Principia.

Shallow Three-Dimensional Structure from Two-Dimensional Crooked Line Seismic Reflection Data over the Sturgeon Lake Volcanic Complex

In principle, partial three-dimensional structural information can be obtained from two-dimensional crooked line seismic reflection data by processing the traces as swath three-dimensional data, but this potential has rarely, if ever, been fully exploited. Here, we apply procedures newly designed for this purpose to mining exploration data from a high-resolution, two-dimensional crooked line survey over a part of the Sturgeon Lake Archean greenstone belt in northwest Ontario, Canada. We then examine the results in the light of geologic data based on about 20 years of mining activity in the immediate area. The area appears highly reflective, even when using standard two-dimensional data-processing methods. But because geologic dips in the section are typically steep and the majority of viewable contact surfaces do not lie directly below the processing and acquisition lines, special data-processing procedures have been essential. Despite appreciable background noise in the constructed images owing to the limitations of the crooked line data set, a large variety of reflection events are quite clearly positioned in three dimensions. The acquisition and processing lines run northeast-southwest, and most of the observed reflection events strike approximately east-west and dip northward. In the upper 1.5 km, they correlate well with expected layering of the mafic-felsic volcanic rocks, and in the vicinity of the Cu-Zn volcanogenic massive sulfide deposit at Lyon Lake, they agree well with information from drilling. The three-dimensional processing has successfully imaged an ore-controlling thrust fault at the Lyon Lake deposit, contacts within the volcanic pile (including the top of the Beidelman Bay subvolcanic intrusive complex), and fold structures in the volcanic stratigraphy. The results suggest that simple three-dimensional seismic surveys of limited offset and azimuth range may be sufficient for imaging structures in this type of geologic environment.

Shallow Three-Dimensional Structure from Two-Dimensional Crooked Line Seismic Reflection Data over the Sturgeon Lake Volcanic Complex

Shallow Three-Dimensional Structure from Two-Dimensional Crooked Line Seismic Reflection Data over the Sturgeon Lake Volcanic Complex

3‐D tomographic static correction

A 3‐D tomographic inversion approach based on a surface‐consistent model for static corrections is presented in this paper. Direct, reflected, and refracted waves are used simultaneously to update the near‐surface model. We analyze the characteristics of the first‐break traveltime in complicated low‐velocity layers. To improve the accuracy for the velocity model, the various first‐break times from direct, reflected, and refracted waves are considered for model inversion. A fractal algorithm which overcomes the error caused by wavelet shape differences is applied to pick first breaks. It also overcomes the leg jump of refractions. The method can pick a large number of first breaks automatically. The raypaths and traveltimes are calculated with a 3‐D ray tracer that does not increase computation time for complicated geological models. Our method can determine the raypath associated with minimum traveltimes regardless of wave mode (direct, refracted, or reflected). We use a least‐squares approach in conjunction with a matrix decomposition to reconstruct a 3‐D velocity model from the actual first‐break times obtained from 3‐D data. Finally, long‐ and short‐wavelength static corrections are calculated concurrently, based on the reconstructed velocity profile. The method can be applied to wide‐line profiles, crooked lines, and 2‐D and 3‐D seismic survey geometries. The results applied to a real 3‐D data example indicate that the 3‐D tomographic static corrections are effective for field data.

Estimation of Near‐Surface Velocity for 3‐D Complicated Topography and Seismic Tomographic Static Corrections

AbstractA static correction approach to 3‐D tomographic inversion based on the surfaceconsistent model is presented in this paper. This method can be applied to wide‐line profiles, crooked lines, conventional 2‐D and 3‐D seismic survey geometries. The accurate estimation for the thickness and velocities of shallow low‐velocity zones is vital to proper static correction in rough topography and complicated low‐velocity geological structure zones. We use a leastsquares approach in conjunction with QR decomposition to reconstruct the 3‐D velocity model from the actual first‐break times that are obtained from 3‐D data, and then the long and short wavelength components of static correction are calculated concurrently based on the reconstructed velocity images. We analyze characteristics of the first‐break traveltime in complicated low‐velocity layers. To improve the inversion accuracy of the velocity model, the various first‐break times from direct , reflection and refraction waves are considered for determining observed traveltimes and theoretical model calculations. The fractal algorithm is applied to determining the first breaks, which overcomes the errors caused by the differences of wavelet shapes and the leg‐jump of refractions. The method is capable of selecting large volume of first breaks automatically. The ray paths and traveltimes are calculated with a 3‐D ray tracer which does not require more CPUs for complicated geological models. This method can determine the ray paths associated with minimum traveltimes regardless of wave modes. The results indicate that the 3‐D tomographic static correction method is very effective for field data processing.

Navigation and behaviour of four Collembola species migrating on the snow surface

In Norway, four species of Collembola, Hypogastrura socialis, Vertagopus westerlundi, Isotoma hiemalis and I. violacea, are regularly active on the snow surface during mild weather. In all species, each individual jumps in a rather straight line, using the sun as a “compass”. If the sun's position was turned 180° using a mirror, the animal also turned 180°. As the sun does not have to be directly visible, the animals probably can use polarized light as well. Different individuals often migrate in quite different directions. At least three of the four species live in patchy and temporary habitats, and sooner or later have to find new patches. Winter migration on the smooth and moist snow surface is their only possibility to move over great distances. Before each jump, the collembolan orientates its body relative to the sun either by rotating horizontally on the spot or by walking a little in a crooked line. H. socialis lands with extended anal sacks, which adhere the animal to the snow surface and enable it to position itself rapidly again. Even in overcast weather, collembolans sometimes show a more or less directional movement. An experiment indicated that navigation under such conditions was by means of light and dark elements in the surroundings.

Jagged-edge noise barriers

Experimental, numerical, and analytical investigations have shown that noise barrier performance can be improved by making the top edge randomly jagged. The incident noise is a spherical N wave (produced by a spark in our model experiments). See Ho et al. [J. Acoust. Soc. Am. 101, 2669–2676 (1997)], and oral papers by (i) Menounou et al., (ii) Ohm et al., and (iii) Rosenberg et al., all in J. Acoust. Soc. Am. 101, 3075(A) (1997). In many, but not all, cases the jagged edge improves insertion loss by up to 5 dB. The most promising theoretical approach is to model the edge as a directive, crooked line source [paper (i) above]. Besides yielding predictions that agree favorably with measurements [paper (iii) above], the line source model helps in understanding the following results: (1) the jagged edge smears out the diffracted signal and makes the tail ragged, (2) insertion loss varies significantly with receiver position, and (3) the portion of the edge on the most direct path between source and receiver plays a very important role. Because the model is easy to apply, it is a promising and powerful tool for further research on jagged barriers. [Work supported by Texas Advanced Technology Program.]

A unified method for 2-D and 3-D refraction statics

Most of the seismic data processing procedures are divided into 2-D, 2.5-D, crooked lines or 3-D versions dictated by the differences in the shot and receiver configurations. In this paper, we introduce a tomographic approach that overcomes these geometrical difficulties and provides stable statics solutions from picked first‐break times. We also show that the first‐break picks contain both the short and the long wavelength surface statics. The solutions are obtained by solving a set of generalized surface‐consistent delay‐time equations using the method of weighted least squares and conjugate gradient. While iterating, each first‐break pick is evaluated to ensure its consistency with the least‐squares solution. Based on consistency, we weight the traveltime picks and use them in the next iteration. These weights also serve as an indicator of anomalous picks to the user. We show that long wavelength solutions leave large residual errors in the least‐squares solutions. We also use the expected length of the Fresnel zone to differentiate between short and long wavelength static solutions. After removing the influence of long wavelength statics, we apply short wavelength statics to reduce the residual errors further. We demonstrate the validity of our unified method by applying it to actual data examples. The removal of both long and short wavelength statics improves the initial data set that produces a more consistent set of velocities and leaves only the short wavelength residual reflection statics, which are generally less than quarter wavelet period delays. This removes the most probable cause of the leg jump contamination and poor velocity estimates from the residual statics computations, especially from the 3-D data.

Theoretical study of diffraction by a jagged-edge noise barrier

An approximate analytical method for calculating the diffraction field behind a jagged-edge noise barrier, idealized as a thin rigid half-plane having an irregular edge, is presented. Experimental studies have shown that for apertures, disks, and plane barriers, making the edge irregular can significantly decrease the diffracted signal [Bailey et al., J. Acoust. Soc. Am. 92, 2359(A) (1992); Ho et al., J. Acoust. Soc. Am. 101, article in press (1997)]. Straight-edge diffraction from a rigid half-plane has a known exact solution for plane, cylindrical, and spherical incident waves. It is observed that in all three cases the shadow zone signal, in the far field, is equivalent to radiation from an infinite line source, but modified by a certain directivity function. In the present work the jagged edge is modeled as a crooked line source having the same directivity as a straight edge. The radiation is calculated by treating the crooked line as an infinite set of point sources, summing their contributions, and adding the appropriate directivity. The method is simple to apply. Results are compared with those found by other methods. [Work supported by Texas Advanced Technology Program.]

Noise reduction by a barrier having a random edge profile

Sound generally reaches the shadow zone behind a noise barrier by diffraction, or scattering, from the edge at the top of the barrier. By redirecting the incident sound into the shadow zone, the edge acts as a line source. For the traditional straight-edge barrier, the line source is coherent. Since a crooked line source is less coherent, we propose to improve barrier performance by making the edge randomly jagged. Laboratory model experiments to compare insertion loss of straight- and jagged-edge barriers are reported here. A spark was used as a point source, the barriers were thin (compared to a wavelength), and ground and meteorological effects were not important. After preliminary measurements showed that a jagged edge can produce significantly more insertion loss at high frequency, a three level full factorial experiment was done. The results led to an empirical equation for insertion loss of a jagged-edge barrier. Improvement over the straight barrier was found to increase with jaggedness. An unexplained result was the poorer performance of the jagged-edge barrier at low frequency.

The Crooked Line

The Crooked Line

Seeing straight with crooked lines

Seeing straight with crooked lines

Crooked lines and taboo places: What are the rules that govern good line layout?

Geophysicists are trained to think in terms of geology when it comes to laying out a seismic grid. For example: • We want to cross fault trends at right angle • We want to shoot in the dip direction • We want to avoid paralleling a major fault. These are good, geologically based rules which are not followed often enough.

Pseudo-3D study using crooked line processing from the Swiss Alpine western profile—Line 2 (Val d'Anniviers-Valais)

First results are presented of the processing of one of the Seismic lines of the Swiss National Program to study the deep geological structure of the Swiss Alps, located in the Anniviers valley (Val d'Anniviers-Valais).The rough topography of the study area gives rise to a crooked line geometry allowing analysis of lateral dips across the common mid-point (CMP) swath corresponding to a pseudo-3D study. The coherency of the Seismic reflections has been improved by accounting for the lateral dips and applying a correction before performing the CMP stack. The main E-W dip found by the Seismic pseudo-3D investigation confirms the surface geological survey.Preliminary geological interpretation suggests large-scale recumbent folding at depths between 10 and 20 km.

Seismic reflection survey by the crooked line method applied to a coalfield in a mountainous region

In the past, seismic reflection surveys on land in Japan have usually been carried out along straight lines irrespective of surface terrain. However in Japan, where most of the areas are covered by mountainous terrain, it may require considerable time and cost to carry out field operations by the straight line method.From August to October in 1988, a reflection seismic survey was carried out at the Sarufutsu area in Hokkaido, Japan. The area is in a mountainous region where the straight line method was very difficult to conduct. A trial of the crooked line method was introduced to the area by laying out seismic lines along roads and valleys.Four test borings with VSP and extensive field geological surveys were carried out in this area by NEDO (New Energy and Industrial Technology Development Organization) prior to 1987, and the results show that there is a north-south trending syncline in the area and that the maximum depth of the main coal seam is approximately 600 m below the surface.The data acquisition system adopted was a 48-trace IFP digital recording system with one-millisecond sample interval.The result of the survey gives a good correlation with existing geological information.It has been concluded that seismic reflection surveys by the crooked line method are applicable for coal exploration in such a mountainous terrain.

On: “Three‐dimensional imaging of steeply dipping structure near the San Andreas fault, Parkfield, California” by John N. Louie, Robert W. Clayton, and Ronan J. LeBras, (GEOPHYSICS, 53, 176–185, February 1988).

Louie et al. (1988) apply to COCORP survey data a prestack migration process, which they describe, to image better reflections associated with structure in the upper 5 km of the San Andreas fault zone near Parkfield, California. They demonstrate the usefulness of this approach in an area along the survey where, as they point out, the CMP-stacking process may be particularly troublesome. While the authors were sensitive to the extreme lateral heterogeneities in and about the fault zone, the crooked survey line, and the complex terrain in which the survey was mounted (McBride and Brown, 1986), I suspect they were nevertheless a little too zealous in discounting, in this case, the value of conventional stacking applied and interpreted judiciously. Moreover, Louie et al. imply that their approach yields previously unobtained results; however, this is not the case.

Three‐dimensional determination of structure and velocity by seismic tomography

A computerized seismic tomographic method was developed to obtain body‐wave velocities and three‐dimensional (3-D) structure of interfaces from reflection data simultaneously. The medium consists of layers with continuous arbitrary 3-D curved interfaces separating homogeneous material with different acoustic properties. The interface is defined by a polynomial surface. The elastic waves are assumed to be transmitted or reflected at curved interfaces in which the raypaths satisfy Snell's law. The ray tracing for each source‐receiver pair is determined by solving a system of nonlinear equations. This method of 3-D ray tracing is effective in computing many seismic rays, including converted phases and multiples. A damped least‐squares inversion scheme is formulated to reconstruct the interval velocity and 3-D structure of the interface by minimizing the difference between observed traveltimes and computed traveltimes. The results from a synthetic model indicate that the solutions converge quickly to the true model. The seismic tomographic method was applied to a Vibroseis seismic section obtained in 1984 on Vancouver Island as part of PROJECT LITHOPROBE. The method was found to be useful for imaging the 3-D subsurface of subducting plates by taking advantage of crooked lines in the nominally two‐dimensional seismic reflection survey.

Further suggestions for writing memorable geophysical papers

In an earlier article in Eos (December 21, 1982, p. 1219), I suggested that members of AGU had been seriously remiss in not forming proper author teams in order to write “memorable” geophysical research papers. A number of the original suggestions were rejected either on the grounds of good taste (see the “unabridged” preprint version of the paper, available from the author) or else because of political sensitivity (e.g., “Crooked magnetic field lines” by AGU members Agnew and Nixon). Nonetheless, several examples of what might be done survived censorship and appeared in the Eos article. In summary, it was concluded that geophysicists could be a lot more active in this area.

Between the Lines of Billy Budd

Melville thinks he does, though he cannot speak quite so confidently of the rest of us. The Navy of Billy Budd is a heterocosm, a separate, self-contained and self-regulating world. The tale of the doomed, angelic foretopman begins with a swaggering parade. Billy enjoys his local triumph, to be followed in due course by his tragedy and his partly victorious aftermath. Neither he nor his black counterpart in the opening pages belongs to the nautical tradition of “Billy-be-Damn” (no doubt a more decorous avatar of Bollicky Bill). Their twin asexual cocksureness receives apparently sexless worship from their fellows, for whom they are first among equals. Perhaps because we see no battle action in this story, a curious passivity seems to reign. Billy is a “cynosure”: a static magnet for admiration, and later a hapless target for malevolence. Although “to deal in double-meanings and insinuations of any sort was quite foreign to his nature” and though he is hardly conscious of the pun involved when he bids farewell to his first ship, the “Rights of Man,” his creator Melville stands in for him in this function. “Indirection” is Melville's preferred mode, He exploits his impeccable hero as the locus of double dealing, innuendo, lies, ambiguity, treachery, perverted history, and finally popular legend. Simple goodness, and complex evil, may be freaks of human nature, ultimately unfathomable alike, but Melville refuses the passivity of his sailors, and intervenes to make some sense of mystery. As Polonius said to Reynaldo: “With assays of bias, By indirections find directions out.” Like God in the Portuguese proverb dear to Claudel, Melville seeks to write straight in crooked lines. Since the pun, like irony and oxymoron, is an oblique mode, he appeals to its devious resources in his search.The naval world provides a firm basis for this weaving approach, since it is governed by clear lines of demarcation: hierarchical vetoes, territorial imperatives, disciplinary codes. “Life is not a game with the sailor, demanding the long head; no intricate game of chess where few moves are made in straight-forwardness, and ends are attained by indirection.”