Amplitude Decay Rate Research Articles

Teleseismic P coda analyzed by three-component and array techniques: Deterministic location of topographic P-to-Rg scattering near the NORESS array

Abstract P -wave coda of 75 sec duration from eight teleseismic events recorded by the NORESS array, Norway, were examined using both array and three-component analysis techniques. The array data have been analyzed using the semblance technique that allows us to determine accurately the time of arrival, apparent velocity, and azimuth of the scattered waves. Coda coherency was found to vary considerably, probably reflecting extended source duration for some events. Slow beam amplitude decay rates support significant coda generation within the source region although source-end scattering could not be separated from the source pulse per se . At the receiver end of the path, we resolved locally scattered wavelets even within highly coherent teleseismic P coda by subtracting the teleseismic array beam from the records. The majority of receiver-end scattering contributions appear to be P -to- Rg conversions occurring in both forward and backward directions from two nearby areas with pronounced topographic relief, namely Bronkeberget (distance ∼ 10 km, azimuth ∼ 80°) and Skreikampen (distance ∼ 30 km, azimuth ∼ 225°). The scattering is multiple in the sense that both primary and secondary phases from the source region contribute to the scattered Rg waves. P -to- S scattering constitutes a significant part of the receiver-end scattering observed later in the P coda, although it is more diffuse than Rg and forward scattering is more dominant. P -to- P scattering is weak and mostly confined to the immediate vicinity of the array. The analysis of individual three-component records shows high sensitivity to interference from locally scattered waves. This interference is probably responsible for a marked decrease in apparent velocity observed for some events 3 to 4 sec after P onset.

Acoustic pulse propagation above grassland and snow: Comparison of theoretical and experimental waveforms

Theoretical predictions are made of the effect of an absorbing ground surface on acoustic impulsive waveforms propagating in a homogeneous atmosphere for frequencies below 500 Hz. The lower frequencies of the pulse are enhanced as the effective flow resistivity of the ground surface decreases and as the propagation distance increases. The pulse waveforms and peak amplitude decay observed for propagation distances of 40 to 274 m over grassland were satisfactorily matched by calculations using an assumed effective flow resistivity of 200 kN s m−4. Measurements over snow gave much greater amplitude decay rates, and the waveforms were radically changed in appearance, being dominated by the lower frequencies. These waveforms were satisfactorily matched only when a layered ground was incorporated into the calculations; then, an assumed surface effective flow resistivity of 20 kN s m−4 gave good agreement with the observed waveforms and peak amplitude decay.

AUTOMATIC EDITING OF NOISY SEISMIC DATA1

ABSTRACTSeismic data often contain traces that are dominated by noise; these traces should be removed (edited) before multichannel filtering or stacking. Noise bursts and spikes should be edited before single channel filtering. Spikes can be edited using a running median filter with a threshold; noise bursts can be edited by comparing the amplitudes of each trace to those of traces that are nearby in offset‐common midpoint space. Relative amplitude decay rates of traces are diagnostic of their signal‐to‐noise (S/N) ratios and can be used to define trace editing criteria. The relative amplitude decay rate is calculated by comparing the time‐gated trace amplitudes to a control function that is the median trace amplitude as a function of time, offset, and common midpoint. The editing threshold is set using a data‐adaptive procedure that analyses a histogram of the amplitude decay rates.A performance evaluation shows that the algorithm makes slightly fewer incorrect trace editing decisions than human editors. The procedure for threshold setting achieves a good balance between preserving the fold of the data and removing the noisiest traces. Tests using a synthetic seismic line show that the relative amplitude decay rates are diagnostic of the traces’S/N ratios. However, the S/N ratios cannot be accurately usefully estimated at the start of processing, where noisy‐trace editing is most needed; this is the fundamental limit to the accuracy of noisy trace editing.When trace equalization is omitted from the processing flow (as in amplitude‐versus‐offset analysis), precise noisy‐trace editing is critical. The S/N ratio of the stack is more sensitive to type 2 errors (failing to reject noisy traces) than it is to type 1 errors (rejecting good traces). However, as the fold of the data decreases, the S/N ratio of the stack becomes increasingly sensitive to type 1 errors.

CodaQbefore the 1983 Hawaii (MS= 6.6) earthquake

AbstractCoda Q values were derived for more than 300 microearthquakes that occurred in a 6-yr period before the 16 November 1983 Kaoiki, Hawaii, earthquake (MS = 6.6). The sources were located within a 14 × 16 km rectangular region surrounding the main shock epicenter, and most of them occurred at depths between 5 and 10 km. Digital recordings from three stations at epicentral distances ranging from 0 to 18 km were used. Coda Q was calculated from the amplitude decay rate of the S-wave coda in nine frequency bands from 4.5 to 27 Hz. The average Q of the NW part of the studied area is about 15 per cent higher than that of the SE part. These two subregions also showed differences in seismicity, b value, and microearthquake source mechanisms. In the high-Q volume, the b value was 1.0, and the rate of earthquakes per unit volume was about 50 per cent of the rate in the low-Q volume where b = 1.3. One interpretation of these observations is that more extensive faulting in the SE Kaoiki fault zone leads to lower Q, higher b value, and a higher seismicity rate. During the 5 to 6 yr before the mainshock, the 1-yr average Q values were stable. No significant Q change could be identified as a precursor to the main shock.

Comparison of amplitude decay rates in reflection, refraction, and local earthquake records

Three types of seismic data recorded near Coalinga, California were analyzed to study the behavior of scattered waves: 1) aftershocks of the May 2, 1983 earthquake, recorded on verticalcomponent seismometers deployed by the Usgs; 2) regional refraction profiles using large explosive sources recorded on essentially the same arrays above; 3) three common-midpoint (CMP) reflection surveys recorded with vibrator sources over the same area. Records from each data set were bandpassed filtered into 5 Hz wide passbands (over the range of 1-25 Hz), corrected for geometric spreading, and fit with an exponential model of amplitude decay. Decay rates were expressed in terms of inverse coda (Q c -1 ). Q c -1 values for earthquake and refraction data are generally comparable and show a slight decrease with increasing frequency. Decay rates for different source types recorded on proximate receivers show similar results, with one notable exception. One set of aftershocks shows an increase of Q c -1 with frequency.

Frequency dependent characteristics of coda wave quality factor in central and southcentral Alaska

Coda wave quality factor (Q c ) was investigated by using digital data (100 sample sec-1) recorded by a vertical component short-period station installed for this study. The station was located in the greater Fairbanks area in central Alaska. From several hundred earthquakes recorded by this station in about a year, 27 earthquakes were selected for the above study; 7 of these selected earthquakes were located along the Alaska Wadati-Benioffzone (Pacific plate). The other 20 earthquakes were located in the area of intraplate seismicity (North American plate). The data was filtered using 9 pass-bands with center frequency varying from 1.5 Hz to 16 Hz with octave bandwidth. The values of Q c obtained from the coda amplitude decay rates measured on the filtered data after corrections due to the recording instrument and source-receiver separation show appreciable frequency dependence. The value of Q c varies in the range of 253 and 1190 corresponding to the frequency interval from 1.5 Hz to 16 Hz for the study area. This variation is close to that reported by others for the Kanto region of Japan. Moreover, the characteristics of Q c obtained in the present case seem to be independent of epicentral distance and hypocentral depth.

Electrical coupling effects on the temporal evolution of F layer plasma structure

A time dependent model of F region structure decay by “classical” cross field diffusion and electrical coupling along magnetic field lines to the E region is examined. The temporal behavior of the ion concentration fluctuations is determined by the electric field in the coupled system as well as by the initial perturbation spectra and the E region recombination rate. The formation of image structure in the E region ion concentration affects the lifetime of F layer structure in a scale size dependent way. Once an image is formed, the image amplitude and the driving F region structure amplitude decay at the same rate. At large scale sizes, λ(λ=2π/k), this rate is proportional to k² and the ratio of the temperatures in each region. At small scale sizes it depends on the E region recombination rate and the temperatures of the two regions but is only very weakly dependent on k. The background E region concentration determines the wave number beyond which the structure amplitude decay rate is almost independent of its scale size.

Characteristics of coda waves: Central and southcentral Alaska

Abstract Code amplitude decay rates as a function of lapse time (time measured from the origin time) for two moderate size Alaskan earthquakes are related to their known values of seismic moments. This relation is then used to compute seismic moments from coda-wave data for a selected group of small earthquakes located in the greater Fairbanks, Alaska, seismic zone. The computed values of moment appear to be consistent with the local magnitudes. Next, with the moment and magnitude data, an empirical moment-magnitude relation is obtained for central and southcentral Alaska. This relation is similar to those for central and northern California proposed by others. Computation for Q values in the frequency ( f ) band 1.03 to 1.5 Hz for central and southcentral Alaska with local coda-wave data yielded values in the range from about 160 to 290. The minimum of Q(f) appears to be in the frequency interval from 0.5 to 1.5 Hz. Moreover, Q values ( f = 1 Hz) in the above range have been recently reported by others for areas in western United States having similar tectonic history as the Alaskan study area.

Comment on "Spontaneous radiative coupling of atomic energy levels"

Recently Cardimona and Stroud emphasized that, when the energy levels of an atom are degenerate or nearly so, there can exist a strong radiative interaction between different spontaneous transitions of the atom. This interaction is described by the generalized damping terms and generalized frequency-shift terms in the equation of motion for the atomic density matrix. We here point out that the generalized damping terms can play an important role in the absence of degeneracy for systems other than atoms, and cite the harmonic oscillator as an example. Specifically, we show that these terms are needed for a proper classical limit of radiation damping, and that a small anharmonicity can have a very large effect on the radiative decay rate of the oscillator's amplitude.

Further study of spectral composition ofPcodas of earthquakes and explosions

abstractThe spectral compositions (bandwidth 0.4 to 4.5 Hz) of the P codas of 108 explosions and 225 earthquakes recorded at LASA are the basis of a technique by which all earthquakes studied are discriminated successfully from all Semipalatinsk explosions. Such complete separation is not achieved, however, for the full set of presumed Russian explosions. The lack of detectable change in frequency content of P signals in the distance range 30° to 90° suggests a very high Qp value for the central mantle. This result, together with the observed rate of amplitude decay for long-period S waves, implies Qs for the central mantle is high while Qs values for the crust-upper mantle and lower mantle are very low.

On the Evolution of Isolated, Nonlinear Vortices

The evolution of an isolated, axially symmetric vortex is calculated with a quasi-geostrophic, adiabatic, hydrostatic. β-plane, two vertical mode model. The circumstances of greatest interest are those of weak friction and large vortex amplitude (strong nonlinearity). Systematic studies are made of the consequences of varying the frictional coefficient, the vortex amplitude, the vortex radius (relative to the deformation radius), the degree of nonlinear coupling between the two vertical modes and the initial vertical structure of the vortex. Results of note include the following. Within the approximation of a single vertical mode model (i.e., in the absence of modal coupling), a baroclinic vortex has an increased westward and a finite meridional propagation speed when its amplitude is greater than infinitesimal. Both of these speeds, however, are limited by the wave speeds (as determined from infinitesimal amplitude theory) of the weak dispersion field outside the vortex. The vortex amplitude decay rate, in the limit of strong nonlinearity, is governed by the frictional coefficient rather than dispersion. When vertical modal coupling is included, the vortex propagation and decay rate can be altered. Asymptotically in time, the vortex approaches a state of deep compensation (i.e., beneath a shallow thermocline, there is no flow in phase with the upper ocean vortex), with a propagation velocity less rapid in the westward direction and more rapid in the meridional direction (compared to a single mode vortex), and with a decay rate again controlled by the friction coefficient. At earlier times, however, more bizarre behavior can occur; for example, a vortex with initially pure baroclinic mode vertical structure can behave as an eastward-propagating vortical modon for a brief interval. This study focuses on vortices whose baroclinic component is of only one sign (a positive temperature extremum in the thermocline); however, because of a symmetry of the model chosen (in particular due to its quasi-geostrophic assumption), these solutions can be simply reinterpreted to apply to vortices of both signs.

Physical properties of treble recorder tones suitable for baroque music

Using real and synthesized tones, we have investigated how the quality of treble recorder tones depends on their physical properties, such as harmonic structure, nonperiodic amplitude and frequency fluctuations of overtones, and noise content. By the use of a paired comparison method, the quality of the tones was judged by professional recorder players and by amateurs with some musical training. As the result, psychological interval scales of quality were constructed against (1) two parameters of harmonic structure, (2) magnitude and frequency structure of harmonic's amplitude fluctuation and (3) those of harmonic's frequency fluctuations. The best quantities are as follows: (1) Decay rate of harmonic amplitude is 4 dB/harmonic. (2) The second, fourth and sixth harmonics are some 10 dB weaker than the values calculated from this decay rate. (3) Frequency fluctuation magnitude of the second and third harmonics is about 1.7% expressed in effective value. Frequency fluctuation of the higher harmonics is rather harmful for quality.

Observation of the frequency-dependent amplitude variation with distance ofP waves from 87� to 119�

The variation of log amplitude with distance and the log amplitude decay rate for four short period frequency bands have been studied over the distance range 87° to 119° for earthquakes in the Indonesian region recorded at the Swedish and Finnish seismographic stations. For these ray paths, which are in the vicinity of the core-mantle interface under. Central Asia, it appears that the log amplitude variation is consistent withP velocity models which are nearly constant or have only a slight velocity decrease in the bottom of the mantle. Some anomalous log amplitude behaviour is ascribed to inhomogeneous structure near the core-mantle interface.

Some characteristics of surface gravity waves in the sea produced by nuclear explosions

Low-frequency dispersive gravity waves produced by nuclear explosions at Bikini, Marshall lslands, were recorded at four distant island stations. The results of these wave measurements are compared with those predicted by linear theory, and good agreement is observed in the nature of the dispersion and the rate of amplitude decay with distance. The wave system associated with the large tsunami of March 9, 1957 is also considered. The dispersion for both types of disturbances was virtually identical, in agreement with the theoretical argument that the dispersion of a centered wave system is independent of the nature of the source disturbance. In analyzing the rate of amplitude decay, it was found necessary to correct the observations for enhancement due to scattering by the islands upon which the recording stations were located, showing that even relatively small islands are effective as scatterers. These experiments show rather conclusively that tide-gage records of tsunami-like disturbances are grossly misleading insofar as the characteristics of the wave systems in the open sea are concerned.

Propagation of a Pressure Transient in a Two‐Layer, Liquid Model

The propagation of a pressure transient in a model consisting of a surface layer of liquid overlying a thick (essentially semi‐infinite) bottom layer of liquid has been investigated experimentally. Attention is restricted to the behavior in and near the surface layer at a range large compared with the depth of the surface layer. The results have been analyzed to determine the group velocity curve, variation of pressure amplitude with source and receiver depth, and the rate of amplitude decay with range for the maximum envelope amplitude. The results are found to be in general agreement with the “Theory of Propagation of Explosive Sound in Shallow Water,” by C. L. Pekeris. In addition, the rate of decay with range for the first peak amplitude was measured and found to be r−2 within experimental error.