Wave Attenuation Rate Research Articles

Waves over Soft Muds: A Two-Layer Fluid Model

Abstract The problem of water waves propagating over a mud bottom, characterized as a laminar viscous fluid, is treated in several ways. First, two complete models are present, each valid for different lower (mud) layer depths, and second, a boundary layer model is presented as an appendix for the case where the lower layer is thick with respect to the boundary layer. These models are compared to the shallow water model and experimental results of Gade (1957, 1958) and agree well. The results show that extremely high wave attenuation rates are possible when the thickness of the lower layer is the same order as the internal boundary layer thickness and when the lower layer is thick.

Variations in shock deformation at the Slate Islands Impact Structure, Lake Superior, Canada

A progressive change in the level of shock deformation is documented in autochthonous rocks from the central uplift of the Slate Islands impact structure, Lake Superior. Correlation of these observations, which are based mainly on the relative frequency of planar features of specific crystallographic orientation in quartz, with experimental data is used to estimate the average shock pressures recorded in the samples studied. Recorded pressures range from 5.8 to 15.3 GPa and generally increase towards the proposed shock centre. Variations in the shock response of quartz of different grain size and texture are observed within and between samples. It is apparent that large interlocking quartz grains in “eyes” record approximately 15–20% higher levels of shock deformation than small grains in mosaics or large isolated phenocrysts. These variations in shock deformation are attributed to the effect of shock wave reverberations between grains and length of shock pulse duration within grains. Comparison of the Slate Islands data with similar observations at the larger Charlevoix impact structure indicates that the rate of change of recorded shock pressure with distance is greater at the Slate Islands structure. This is interpreted as due to variations in the strain rates and/or the rate of shock wave attenuation with radial distance between impact structures of different size.

Variation of radiation intensity behind an attenuating shock wave

An analysis is presented relating the radiation intensity time gradient behind shock waves in air to the shock−wave attenuation rate in a shock tube and boundary−layer effects on particle flow time. The analytical results are compared with the experimental data. It is shown that the very large variation of radiation gradient with shock−wave velocity is related to the strong dependency of shocked temperature with shock velocity within the range of 0.6−1.6 cm/μsec.

Propagation of extremely low-frequency (ELF) atmospherics over a mixed day-night path

An experiment was conducted to evaluate the averaging of propagation parameters of extremely low-frequency (ELF) radio waves propagating over a path in which the ionospheric environment changed within one wavelength. The Fourier spectral components of ‘slow-tail’ atmospherics recorded simultaneously at California and Hawaii were used to determine wave attenuation rates and phase velocities for the frequency band 48–290 Hz when the propagation path was either full-day or full-night. A third receiving station in Oklahoma, located near the great circle common to the two remote stations, aided in locating the lightning sources. From measured changes as the night-day transition region traversed the propagation path the averaging of phase velocity and propagation loss was evaluated with respect to percentage of day and night paths from the sources to the receiving stations. Results indicate that a simple weighted average of the day and night phase velocities is a valid description of measured phase velocities across the day-night transition. Less agreement was obtained between the measured propagation loss across the transition region and that predicted from a simple day-night weighted average of wave attenuation rates.

Attenuation of elastic surface waves by anharmonic interactions at low temperatures

Based on the theory of surfons, we present a formalism to calculate the attenuation rate of elastic surface waves at low temperatures in the high-frequency region. A general formula for the attenuation rate due to the cubic anharmonic terms in the elastic energy of an isotropic elastic continuum is given by means of a temperature-dependent Green's function. In a frequency region between 20 and 40 GHz at T=1°K, our result shows quite different frequency and temperature dependence ω1+n T4−n (1.9 ≲ n ≲ 2.2) from that obtained in the low-frequency region.

Attenuation of swell by sea ice

A mechanism of steady state creep is proposed to describe the attenuation rate of long-period ocean waves in fields of sea ice. It is shown that this mechanism fits the existing wave observations of Robin [1963] and Wadhams [1973] provided a Glen-type flow law is employed with an exponent n = 3 and a flow law parameter 〈B〉 similar to the value for polycrystalline ice near the melting point.

Acoustic Amplitude Ratio Logging

Abstract A calibration system is obtained that permits correlation of amplitude data from borehole to borehole regardless of composition of hole fluid, hole diameter, or other both-derived parameters. Two-receiver attenuation logging provides better interpretation of acoustic cement bond logs because of this calibration system. Recent advances in acoustic amplitude logging have left undone the requisite of all physical measurements, that is, calibration to a known acceptable and consistently repeatable standard unit. In our study of two-receiver amplitude ratios we show that the ratio scale may be precisely stated in a common term of attenuation rate-decibels per foot. Results of amplitude ratio logging in various representative areas including both eased and open holes are given. Curves are presented showing ratio relations for various spacings. A nomograph for determining hole factor kh from the ratio and one single-receiver amplitude (recorded simultaneously) has been developed. This indicates the possibility that new information concerning acoustic energy translation at the wellbore-formation interfaces may be obtained. Shear wave and compressive wave attenuation rates are discussed as a means to assess fluid mobility. Introduction The objective of a logging service company should be to provide accurate measurement of any and all physicochemical characteristics of rock formations in situ. Historically it has been shown that any bonafide physical parameter will be found useful in providing primary or supplemental information regarding the economic evaluation of formations. An excellent example is found in the extensive use of acoustic wave amplitude recording. From the inceptions of acoustic logging, researchers in this field have studied amplitude response of the various wave types existent in the acoustic wave train. In the work of Vogel, Wylie and others, numerous speculative references to the value of amplitudes of the various waveforms have kept alive our interest in making available an accurate amplitude measurement in the borehole. More recently Pickett and Morlet have reported on the qualitative value of attenuation measurements. The qualitative use of acoustic amplitudes is now well established in estimating the effectiveness of cement bond to pipe and to formation in cased holes, as well as interpretation of amplitude anomalies in terms of numbers of acoustic interfaces intersecting the signal path of uncased holes. The following analysis of hole and formation factors which lie in the signal path, and which must be taken into account, provides a basis for calibration to a known and acceptable unit. A scale can be derived for the amplitude ratio between any two receivers, and can be stated in terms of attenuation rate, decibels per foot (db/ft).Although the user benefits from the information derived from single-receiver amplitude logs, it is apparent that a number of corrections need be applied. These are quantities which vary from well to well and include type of fluid in the hole, fluid path length and degree of acoustic coupling from fluid to formation. By use of the two-receiver amplitude ratio logging technique described here, these parameters fall by the way and the user has available a record of the effective attenuation rate of signal in the formation opposite two receivers. Present Acoustic Amplitude Log Forms A typical acoustic tool for amplitude logging contains an acoustic pulse transmitter and receivers at several distances from the transmitter. The main signal paths and typical resulting wave trains are shown in Fig. 1. Recording the amplitude of the first-arriving compressional wave has been most useful in bond logging. Logs of the later arriving shear wave have been used extensively for fracture location in open hole. The amplitude information in any one receiver may be recorded in several forms:1. A curve showing electronically-measured amplitude of a particular portion of the waveform, such as the shear wave;2. A sequence of photographs of the full wave train where the receiver signal is available at the surface equipment-information from this full "character" log, although considered quantitative, does not allow rapid comparison on location with other logs run at the same time; and3. A variable-density presentation photographed from an oscilloscope as a function of depth-the microseismogram type of log of the signal allows rapid qualitative analysis of the acoustic wave from one receiver (Fig. 2). JPT P. 1243ˆ

Extremely Low-frequency Radio Propagation in an Inhomogeneous Ionosphere

EXPERIMENTAL results1 show that the attenuation rate of extremely-low frequency radio waves decreases with decreasing-frequency in the range from a few kc/s to about 70 c/s, below which it appears to increase again. The experimental results, however, are not yet fully confirmed. Moreover, theoretical work to date has given no indication that this behaviour would be expected. It has been suggested1, however, that it might be possible to explain the observations by considering a stratified ionosphere consisting of three homogeneous layers having different conductivities. Although a two-layer model was considered, no calculations have so far been given for the more complicated case.

Observed attenuation rate of ELF radio waves

Observed attenuation rate of ELF radio waves

Shipboard Hydraulic Breakwater

Model hydraulic breakwater was constructed on 1:86.5 scale model Liberty Ship; ship was moored in model basin in 7 in, of water and subjected to series of different wave conditions; mooring forces and wave attenuation were measured; graphs showing relationship between wave attenuation and jet-flow rate and dependence of mooring force on wave height are included.

The Attenuation of Repeated Shock Waves

The sound waves generated by the siren described in an earlier paper on this program by the same authors develop shock fronts in a short distance of travel and their shape finally approximates the characteristic sawtooth form. The spatial attenuation rates of such waves have been measured as a function of the siren frequency in the range 30–100 cps. A typical datum shows that a 100-cps wave with a pressure ratio across the shock of 1.5 is reduced by a factor of 2 in a travel distance of 55 feet. A first-order theory using the Rankine Hugoniot shock conditions is developed for a sawtooth wave. This gives attenuation rates which are higher than those observed experimentally. For the datum given the ratio of theoretical to observed attenuation rate is 1.5. This discrepancy will be discussed.