Horizontal Components Of Motion Research Articles

Nonlinear effects in a driven vibrating wire

A horizontal wire is driven sinusoidally with a vertical magnetic force. Horizontal and vertical optical detectors follow the motion of a point on the wire. With a moderately large driving force, the usual predicted nonlinear effects are observed as the driving frequency is increased from below resonance. These include the onset of a horizontal component of motion, phase shifted 90° with respect to the vertical component, and ultimately resulting in circular motion of the wire. However, with a much weaker driving force, the phase relation between the horizontal and vertical components is no longer fixed at 90° and becomes very frequency sensitive in a certain range. It appears to vary from 180°, producing inclined straight‐line motion, to 90°, to 0°, again producing straight‐line motion but with a positive slope. Further increase of the driving frequency causes the vertical excursion of the straight‐line motion to increase while the horizontal excursion changes little. A second harmonic in the horizontal component becomes pronounced and leads to figure‐eight motion. These effects appear not to have been predicted and will be illustrated on videotape.

Studies of the seismic coda using an earthquake cluster as a deeply buried seismograph array

Loosely speaking, the principle of Green's function reciprocity means that the source and receiver positions in a seismic experiment can be exchanged without affecting the observed seismograms. Consequently, the seismograms observed at a single observation location o and caused by a cluster of microearthquakes at locations {ei} are identical to the time series that would be measured by an array of stress meters emplaced at positions {ei}, recording waves generated by a source acting at o. By applying array analysis techniques like slant stacking and frequency‐wave number analysis to these seismograms, we can determine the directions and velocities of the component waves as they travel in the earthquake focal region rather than at the surface. We have developed a computationally rapid plane‐wave decomposition which we have applied to single‐station recordings of aftershocks of the 1984 Morgan Hill, California, earthquake. The analysis is applied to data from three seismic stations having considerably different site geologies. One is a relatively hard rock station situated on Franciscan metamorphics, one is within the Calaveras fault zone, and one is on semiconsolidated sand and gravels. We define the early coda to be the part of the coda initiating immediately after the direct S wave and ending at twice the S wave lapse time. The character of the S wave and early coda varies from being impulsive at the first station to highly reverberative at the last. We examine waves in sequential time windows starting at the S wave and continuing through the early part of the coda. At all seismic stations the early coda is dominated by a persistent signal that must be caused by multiple scattering, probably within 2 km of each seismic station. Despite clear station‐to‐station differences in the character of the early coda, coda Q values measured in the late coda (greater than twice the S lapse time) agree well among stations, implying that the mechanisms causing the varying behavior of the early coda do not control the coda decay rate at the stations we have considered. Coda Q values measured on horizontal components of motion agree within a factor of 2 with those measured on vertical components. We have not been able to determine the composition of the late coda because of a low signal‐to‐noise ratio. Our analysis technique, however, is quite appropriate for such a task.

Reply by the author to B. J. Evans

I wish to thank Dr. Evans for his comments. In the data of the subject paper, hodograms differ from particle motion for frequency components below the resonant frequency of the geophone (8 Hz) or above the corner frequency of the anti‐aliasing filter (125 Hz). The necessity of compensation for phase response depends upon the nature of the signal and purpose of the study. The method of multicomponent complex trace analysis is largely concerned with phase differences between vertical and horizontal components of motion.

Colour-coded stereo images from the tandem scanning reflected light microscope (TSRLM).

A method is described for the production of stereo-pair images in the tandem scanning reflected light microscope in which depths within the field imaged are coded in colour. The two images are recorded photographically whilst focusing vertically through the layer which is to be imaged. A horizontal component of motion is applied at the same time, but in opposing senses for the two images. Colour coding for depth is obtained by changing colour filters so that reflective features lying within different depth bands are imaged in corresponding colours.

Attenuation of ground motion in the Eastern United States

Abstract Frequency-dependent attenuation of ground motion in the Eastern United States is investigated for both vertical and horizontal components of motion. This is accomplished by digitizing and analyzing three-component, short-period Long Range Seismic Measurements data from over 200 earthquake-station pairs with epicentral distances less than about 1000 km. Pseudo-relative velocity as well as velocity response spectra, for 5 per cent damping, are obtained for the frequency range of 0.5 to 7 Hz. A multi-variate least-squares inversion is used to derive the station and source terms as well as the mean Q. Analysis of data for the entire Eastern United States indicates Q values for the vertical and horizontal components to be indistinguishable, substantial increase in Q with frequency (a factor of about 2 from 1 to 7 Hz), large (as much as a factor of 20 in amplitude) site terms for both the vertical and horizontal components, and the mean ratio of the peak horizontal to peak vertical component to be a stable characteristic of the site. Large regional variations in Q are also indicated by subsets of data such as for the Central United States and the Appalachian Mountains region.

Structural expressions of rifting: lessons from Lake Tanganyika, Africa

Summary The fundamental building blocks of Lake Tanganyika are half-graben that tend to be arcuate or crescent-shaped in plan view. When combined with the asymmetric subsidence of the half-graben, this geometry creates horizontal components of motion which are expressed as shearing and rotation along the ends of the units. The key to understanding rift-basin morphology is recognizing the various ways in which these fundamental units can be linked together in time and space. Although many modes of linking occur, the basic theme is one of alternating half-graben polarities along the strike of the rift. Where adjacent half-graben face in opposite directions and do not overlap with each other, they are usually separated by interbasinal ridges trending oblique to the rift axis. In cases where facing half-graben overlap, the apparent morphology can be that of a full-graben with a central high or a half-graben abutting a structural platform, depending upon the orientation of the observation line relative to the overlap geometry. Mechanically, such full-graben should be viewed as opposing half-graben which hinge away from the central high. Examination of the linking models in Tanganyika has enabled us to derive an empirical model of rifting. The model is extremely useful in understanding the stratigraphy of Tanganyika, and it seems to explain many of the styles and patterns of deposition which are peculiar to rift basins. If the model has general applicability to continental rifts, it can also be useful to those who deal with the mechanics of rifting and the deep structure of passive margins.

Riding toy with sound effects

A model horse is resiliently mounted to permit a child rider to cause motion of the horse having vertical and/or horizontal motion components. A trotting gait sound is generated in response to detected vertical motion, and a walk and/or gallop gait sound is generated in response to detected horizontal motion. The selection as between the walk and gallop gait is preferably based upon the amplitude or horizontal motion. The different gait sounds are obtained by generating a basic "clop" (hoofbeat) sound, and, repeating the clop sound in a different time sequence for each gait. In the preferred embodiment of the invention, the sounds of a horse's "snort" and "whinny" are also generated during riding. The sounds produced in accordance with the invention are obtained by digitally forming audio frequency signals and controlling the envelope of the audio frequency signals.

Seismic Ground Motion Parameter Relations

The relationships among spectral velocity for 0.5 hz and 1.0 hz frequencies, peak ground acceleration, and peak ground velocity of earthquake-induced ground motion are investigated using the horizontal components of motion from 70 California strong-motion records and accounting for event size, source-to-site distance, and geologic conditions at the recording site. These strong motion records indicate that the estimation of intermediate-frequency spectral response using ground acceleration and typical design spectra is unconservative for a large, distant event (magnitude-8+, 120-km epicentral distance) by a factor of about 2 to 6, depending on the site geology. Ground velocity can be used to estimate intermediate frequency spectral response; however, expected spectral response will exceed these estimates during the motion from large, distant events by a factor of about 1.4 to 2.5. Because of the large variabilities associated with strong motion data, these results are tentative.

Effect of Multidirectional Shaking on Pore Pressure Development in Sands

The effect of multidirectional shaking on the liquefaction of saturated sands is estimated using the results of multidirectional shaking table tests that measured the settlement of dry sand and a model of the mechanism of liquefaction of saturated sands that uses data obtained in cyclic simple shear tests on dry sand. It is shown that excess pore pressures may develop twice as fast under two equal horizontal components of motion than is the case under a single component, but that a reduction of only 10% in the shear stresses causing liquefaction is normally adequate to account for the effect of multidirectional shaking in analyses of liquefaction potential.

Near-field source parameters by finite-source theoretical seismograms

abstract Near-field seismograms due to finite faulting in a half-space were calculated. An attempt is made to evaluate near-field fault parameters by using two criteria: (1) agreement of observed and theoretical pulse width; and (2) agreement of observed and calculated amplitude ratios of the horizontal components of motion. Using this method we have investigated possible fault parameters of an earthquake along the San Andreas fault (source depth 12.5 km), recorded at two stations (epicentral distance 2.3, 5.5 km). It is found that computed seismograms are strongly dependent on the point in which a unilateral fracture begins. Assuming different initial failure points within the uncertainty region of the hypocentral location may effect fault parameter solutions. Thus, fault parameters obtained in this study should not be viewed as unique. However, we have shown, that for an assumed point and dynamics model, it is possible to determine rupture direction and source parameters. The seismic moment found in this study is weakly dependent on the dynamics model assumed.

Analysis of seismograms from a downhole array in sediments near San Francisco Bay

abstract A four-level downhole array of three-component instruments was established on the southwest shore of San Francisco Bay to monitor the effect of the sediments on low-amplitude seismic ground motion. The deepest instrument is at a depth of 186 m—2 m below the top of the Franciscan bedrock. Earthquake data from regional distances (29 km ≦ Δ ≦ 485 km) over a wide range of azimuths are compared with the predictions of a simple plane-layered model with material properties independently determined. Spectral ratios between the surface and bedrock, computed for the one horizontal component of motion that was analyzed, agree rather well with the model predictions; the model predicts the frequencies of the first three peaks within 10 per cent in most cases and the height of the peaks within 50 per cent in most cases. Surface time histories computed from the theoretical model predict the time variations of amplitude and frequency content reasonably well, but correlations of individual cycles cannot be made between observed and predicted traces.

Driven Nonlinear Oscillations of a String

Because of nonlinearities, the forced oscillations of a string, moving in a single plane, become unstable when the string is driven with sufficient amplitude near resonance. This paper describes the experimental conditions under which forced string oscillations in a vertical plane become unstable. It is found that planar oscillations become unstable in two different ways. One instability is triggered by a spontaneous growth or decrease in the amplitude of the driven vertical motion. The other instability is triggered by a spontaneous growth of a horizontal component of motion, thus leading to a whirling or nonplanar motion of the string. The conditions under which each instability occurs are distinct. These experimental observations agree with the conclusions by Anand [J. Acoust. Soc. Amer. 46, 667–677 (1969)], based on a theoretical analysis. This paper also describes the response of the nonplanar mode of oscillation. It is found for certain conditions that the vertical amplitude of oscillation decreases as the driving signal is increased.

LINEAR PHASE FILTERING OF MULTICOMPONENT SEISMIC DATA

The phase relationships between the vertical and horizontal components of motion at a free surface differ between the various modes of propagation. These differences in phase between the components of motion may be made the basis for a linear filtering technique to separate P, S, and Rayleigh waves when the components of motion at the free surface are recorded in reproducible form. In this paper, a set of linear filters is derived and applied to some three‐component reflection seismograph field data that separate P and Rayleigh wave motion on the basis of their phase relations between horizontal and vertical components of motion at the free surface. A comparison is made between the linear phase filtering technique, and the “Polarization Filtering” technique of Shimshoni and Smith, and a multichannel Wiener deconvolution using the vertical and horizontal components of motion as input channels.

MOTION PRODUCT SEISMOGRAMS

This paper describes a means of combining the voltages from a three‐component seismometer so as to suppress noise waves arriving randomly from all directions and to indicate the direction of arrival of any particular wave‐train, such as might be caused by an earthquake, explosion, or moving vehicle. Each of the horizontal components of motion is electronically multiplied by the vertical component, with or without phase shift, and the two resulting products are displayed as a vector pointing to the source of seismic waves. The equipment assembled to perform these operations is referred to as the Motion Product Detector. Mathematical analysis and small‐scale tests of the Motion Product Detector on the Research Center grounds look promising.

Some observations relating to the effect of the crust on long-period P-wave motion

abstract Long-period P waves recorded in the central United States at distances of 20 to 110 degrees for earthquakes of magnitude 6 and greater indicate that the amplitude of the ground motion is very similar at all stations in the area. The crust is uniform in this region, but the sedimentary section varies both in thickness and in character. Direction of approach, as determined by the ratio of the amplitudes of the horizontal components of motion, does not differ significantly from the great-circle path in the majority of cases studied. Apparent angles of incidence cannot be satisfactorily explained by a half-space model, because calculations based on such a model require a larger value of the P-wave velocity for the shorter period waves. However, calculations based upon Haskell's model of a crustal layer over a half-space give a satisfactory fit to the observed data.

Movement of mineralizing solutions in the Picher field, Oklahoma-Kansas

Evidence regarding the horizontal component of motion of the solutions which deposited the ore minerals in the Picher Field of northeastern Oklahoma and southeastern Kansas has been obtained from 159 localities in the mines in the area. Position of minerals and a symmetry of growth were interpreted according to the criteria of Newhouse. It appears that the direction of the horizontal component of solution flow can be determined within plus or minus 10 degrees. The difficulties involved in the interpretation of the vertical component of motion are discussed. These chiefly relate to the importance of gravity settling during precipitation of the minerals from solution. Conclusions from this study, therefore, are largely confined to those concerning the horizontal component of solution motion. The general similarity of direction of flow indicated by several different ore minerals suggests that the solutions had a similar horizontal component of direction throughout the period of ore deposition. The flow directions found are those which would be shown by solutions which spread laterally from the Miami shear trough, the major structure in the field. To the east of the trough, solution movement directions recorded are mostly southeasterly or southwesterly. To the west of the trough, the directions recorded are mostly northeasterly and northwesterly. It is postulated that the north-south tension fractures found in the region of the trough were the paths followed by solutions as they left the trough, and that the solutions spread from these channelways into a northeast-northwest system of fractures. In these fractures the solutions flowed southeasterly and southwesterly in the area east of the trough and north-easterly and northwesterly in the area west of the trough to reach the minor folds, domes, basins and fracture zones which have been shown by other investigators to be loci of ore deposition in this field.

Movements of Human Diaphragm During Cardiac Cycle in Respiratory Pause

SummaryIn man during respiratory pause there are changes in the position of the diaphragm during the cardiac cycle so that in ventricular systole the total thoracic volume is smaller than in diastole. Calculation of the net thoracic changes involved integration of measurements of both vertical and horizontal components of motion in posterior-anterior and lateral projections. The reduction in thoracic volume amounts to a large and apparently rather constant fraction of the cardiac stroke output.