Elastic displacements in the near-field of a propagating fault

1969 ◽  
Vol 59 (2) ◽  
pp. 865-908
Author(s):  
N. A. Haskell
Keyword(s):  
Fault Plane ◽  
Near Field ◽  
Strong Motion ◽  
Dislocation Motion ◽  
Displacement Discontinuity ◽  
Wave Form ◽  
Strong Motion Station ◽  
Ramp Function ◽  
Wave Forms ◽  
Parkfield Earthquake

abstract Displacement, particle velocity, and acceleration wave forms in the near field of a propagating fault have been computed by numerical integration of the Green's function integrals for an infinite medium. The displacement discontinuity (dislocation) on the fault plane is assumed to have the form of a unilaterally propagating finite ramp function in time. The calculated wave forms in the vicinity of the fault plane are quite similar to those observed at the strong motion station nearest the fault plane at the Parkfield earthquake. The comparison suggests that the propagating ramp time function is roughly representative of the main features of the dislocation motion on the fault plane, but that the actual motion has somewhat more high frequency complexity. Calculated amplitudes indicate that the average final dislocation on the fault at the Parkfield earthquake was more than an order of magnitude greater than the offsets observed on the visible surface trace. Computer generated wave form plots are presented for a variety of locations with respect to the fault plane and for two different assumptions on the relation between fault length and ramp function duration.

Very-Long-Period (VLP) Seismic Artifacts during the 2018 Caldera Collapse at Kīlauea, Hawai‘i

2020 ◽  
Vol 91 (6) ◽  
pp. 3417-3432
Author(s):  
Ashton F. Flinders ◽  
Ingrid A. Johanson ◽  
Phillip B. Dawson ◽  
Kyle R. Anderson ◽  
Matthew M. Haney ◽  
...  
Keyword(s):  
Amplitude Spectrum ◽  
Low Frequency ◽  
Seismic Signal ◽  
Sinc Function ◽  
Caldera Collapse ◽  
Velocity Amplitude ◽  
Long Period ◽  
Ramp Function ◽  
Instrument Response ◽  
Summit Caldera

Abstract Throughout the 2018 eruption of Kīlauea volcano (Hawai‘i), episodic collapses of a portion of the volcano’s summit caldera produced repeated Mw 4.9–5.3 earthquakes. Each of these 62 events was characterized by a very-long-period (VLP) seismic signal (>40  s). Although collapses in the later stage of the eruption produced earthquakes with significant amplitude clipping on near-summit broadband seismometers, the first 12 were accurately recorded. For these initial collapse events, we compare average VLP seismograms at six near-summit locations to synthetic seismograms derived from displacements at collocated Global Positioning System stations. We show that the VLP seismic signal was generated by a radially outward and upward ramp function in displacement. We propose that at local distances the period of the VLP seismic signal is solely dependent on the duration of this ramp function and the instrument transfer function, that is, the seismic VLP is an artifact of the bandlimited instrument response and not representative of real ground motion. The displacement ramp function imposes a sinc-function velocity amplitude spectrum that cannot be fully recovered through standard seismic instrument deconvolution. Any near-summit VLP signals in instrument-response-corrected velocity or displacement seismograms from these collapse events are subject to severe band limitation. Similarly, the seismic amplitude response is not flat through the low-frequency corner, for example, instrument-response-uncorrected seismograms scaled by instrument sensitivity are equally prone to band limitation. This observation is crucial when attempting to clarify the different contributions to the VLP source signature. Not accounting for this effect could lead to misunderstanding of the magmatic processes involved.

scholarly journals Implications of Dipole Moment Secular Variation from 50,000–10,000 Years for the Radiocarbon Record

Radiocarbon ◽  
1992 ◽  
Vol 34 (2) ◽  
pp. 189-198 ◽  
Author(s):  
R. S. Sternberg ◽  
P. E. Damon
Keyword(s):  
Dipole Moment ◽  
Production Function ◽  
Secular Variation ◽  
Good Match ◽  
Average Value ◽  
The Past ◽  
Dc Gain ◽  
Ramp Function ◽  
Holocene Record ◽  
Linear Ramp

Sparse paleointensity data from 10–50 ka suggest that the average dipole moment (DM) was 50–75% of the average of 8.67 μ 1022 A m2 for the past 5 Ma, and 8.75 μ 1022 for the past 12 ka. A linear ramp function, increasing the DM from 4 to 8.75 μ 1022 A m2 between 50–10 ka BP, generates a total 14C inventory of 126 dpm/cme2, agreeing very well with an inventory assay of 128 dpm/cme2, which includes 14C in sediments. With the Lingenfelter and Ramaty (1970) production function and a model DC gain of about 100, this DM function would give a Δ14C of 500‰ at 20 ka BP, consistent with the Barbados coral record, and also gives a good match to the Holocene record. A Laschamp geomagnetic event at about 45 ka BP, with a DM of 25% of its average value and lasting 5 ka, would only increase the present inventory by 0.3–1.2 dpm/cme2, and would probably have only a small effect on Δ14C at 20 ka BP, but could produce a short-lived 14C spike of over 500‰.

Ramp-function work test suitable for automatic computation

1986 ◽  
Vol 6 (1) ◽  
pp. 53-62
Author(s):  
P. J. Samuelsson ◽  
H. Gill ◽  
C. Lassvik ◽  
D. Linnarsson ◽  
O. Wigertz
Keyword(s):  
Automatic Computation ◽  
Ramp Function

Discussions and Communications: Propagation of Transient Electromagnetic Waves in a Conducting Medium

Geophysics ◽  
1955 ◽  
Vol 20 (4) ◽  
pp. 959-961 ◽  
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Electromagnetic Waves ◽  
Step Function ◽  
Conducting Medium ◽  
Initial Value ◽  
Transient Electromagnetic ◽  
Ramp Function

Wait (1951) has calculated the transient electric fields for several types of step-function current sources placed inside a conducting medium. Now any generated pulse will require a finite build-up time to reach its final magnitude from its initial value of zero. In most cases, this type of pulse may be very well approximated by a ramp-function pulse (Figure 1). Expressions for the electric field of this type of pulse will be deduced in the following analysis.

scholarly journals THE FRACTAL DIMENSION-BASED DESCRIPTOR OF THE MICROVASCULAR PATTERN ON THE HISTOLOGICAL SECTION

2020 ◽  
Vol 49 (3) ◽  
pp. 83-86
Author(s):  
Jaromír Šrámek ◽  
Aneta Pierzynová ◽  
Tomáš Kučera
Keyword(s):  
Fractal Dimension ◽  
Three Dimensional ◽  
Histological Section ◽  
Relevant Information ◽  
Dimensional Structure ◽  
Point Pattern ◽  
Independent Analysis ◽  
Ramp Function ◽  
Histological Processing ◽  
Microvascular Pattern

The microvascular pattern in the histological section, i.e. the point-pattern composed of capillaries perpendicular to the plane of section, contains information about the three-dimensional structure of the capillary network. Histological processing is followed by the shrinkage of tissue of uncertain magnitude. In order to obtain relevant information, the scale-independent analysis is necessary. We used an approach based on the Minkowski cover of measured set. The true fractal dimension of the point pattern is obviously of zero, but the artificial result of the algorithm can be related to the complexity of shape. We fitted the log-log plot by the modified rounded ramp function and the slope of the oblique part was used as the fractal based descriptor. We demonstrated on histological samples of the heart that this fractal-based parameter has the property of scale and rotation invariance.

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