Numerical computation of individual far‐field arrivals excited by an acoustic source in a borehole

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 852-866 ◽  
Author(s):  
Andrew L. Kurkjian
Keyword(s):  
Numerical Computation ◽  
The Body ◽  
Body Waves ◽  
Head Wave ◽  
Far Field ◽  
Trapped Mode ◽  
Full Waveform ◽  
Full Wave ◽  
Head Waves ◽  
Strong Shear

In this paper, I model the acoustic logging problem and numerically compute individual arrivals at far‐field receivers. The ability to compute individual arrivals is useful for examining the sensitivities of each arrival to various factors of interest, as opposed to examining the full waveform as a whole. While the numerical computation of the mode arrivals (Peterson, 1974) and the numerical computation of the first head waves (Tsang and Rader, 1979) have been previously reported, the numerical computation of the entire set of head‐wave arrivals is new and is the major contribution of this paper. Following Roever et al. (1974) and others, the full wave field is represented as a sum of contributions from both poles and branchcuts in the complex wavenumber plane. The pole contributions correspond to mode arrivals while the branch cuts are associated with the body waves (i.e., head waves). Both the pole and branch cut contributions are computed numerically and results are presented for the cases of a slow and a fast formation. The shear event in the slow formation is found to be relatively small, consistent with observations in measured data. Contrary to existing knowledge, the shear event in the fast formation is also relatively small. The apparent strong shear arrival in the full waveforms is due primarily to the trapped mode pole in the vicinity of cutoff.

A dynamic model for far-field acceleration

1982 ◽  
Vol 72 (4) ◽  
pp. 1049-1068
Author(s):  
John Boatwright
Keyword(s):  
Stress Drop ◽  
High Frequency ◽  
Dynamic Stress ◽  
The Body ◽  
Body Waves ◽  
Far Field ◽  
Rupture Velocity ◽  
Frequency Level ◽  
Average Change ◽  
Dynamic Stress Drop

abstract A model for the far-field acceleration radiated by an incoherent rupture is constructed by combining Madariaga's (1977) theory for the high-frequency radiation from crack models of faulting with a simple statistical source model. By extending Madariaga's results to acceleration pulses with finite durations, the peak acceleration of a pulse radiated by a single stop or start of a crack tip is shown to depend on the dynamic stress drop of the subevent, the total change in rupture velocity, and the ratio of the subevent radius to the acceleration pulse width. An incoherent rupture is approximated by a sample from a self-similar distribution of coherent subevents. Assuming the subevents fit together without overlapping, the high-frequency level of the acceleration spectra depends linearly on the rms dynamic stress drop, the average change in rupture velocity, and the square root of the overall rupture area. The high-frequency level is independent, to first order, of the rupture complexity. Following Hanks (1979), simple approximations are derived for the relation between the rms dynamic stress drop and the rms acceleration, averaged over the pulse duration. This relation necessarily depends on the shape of the body-wave spectra. The body waves radiated by 10 small earthquakes near Monticello Dam, South Carolina, are analyzed to test these results. The average change of rupture velocity of Δv = 0.8β associated with the radiation of the acceleration pulses is estimated by comparing the rms acceleration contained in the P waves to that in the S waves. The rms dynamic stress drops of the 10 events, estimated from the rms accelerations, range from 0.4 to 1.9 bars and are strongly correlated with estimates of the apparent stress.

scholarly journals Finite‐difference synthetic acoustic logs

Geophysics ◽  
1985 ◽  
Vol 50 (10) ◽  
pp. 1588-1609 ◽  
Author(s):  
R. A. Stephen ◽  
F. Cardo‐Casas ◽  
C. H. Cheng
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Two Dimensions ◽  
Body Waves ◽  
Head Wave ◽  
Stoneley Wave ◽  
Sharp Interface Model ◽  
Head Waves ◽  
The Finite Difference Method

The finite‐difference method is a powerful technique for studying the propagation of elastic waves in boreholes. Even for the simple case of an open borehole with vertical homogeneity, the snapshot format of the method displays clearly the interaction between the borehole and the rock, and the origin and evolution of phases. We present an outline of the finite‐difference method applied to the acoustic logging problem, including a boundary condition formulation for liquid‐solid cylindrical interfaces which is correct to second order in the space increments. Absorbing boundaries based on the formulations of Reynolds (1978) and Clayton and Engquist (1977) were used to reduce reflections from the grid boundaries. Results for a vertically homogeneous sharp interface model are compared with the discrete‐wavenumber method and excellent agreement is obtained. The technique is also demonstrated by considering sharp and continuous transitions (damaged zones) at the borehole wall and by considering the effects of washouts and horizontal fissures on acoustic logs. The latter two cases are examples of wave propagation in media with properties which vary in two dimensions. For the models considered, amplitudes of head waves and head wave multiples (leaky PL modes) are frequently enhanced by washouts. The compressional body waves are less affected by the washouts and horizontal fissures than the guided Stoneley waves which are reflected and only partially transmitted at changes in borehole radius. Amplitude changes of up to 6 dB are observed in the compressional wave due to the borehole deformation. For the Stoneley wave, borehole deformations can cause changes in amplitude of 20 dB and dramatic changes in waveform.

A borehole-model-derived algorithm for estimating QP logs from full-waveform sonic logs

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. E107-E117 ◽  
Author(s):  
Jorge O. Parra ◽  
Pei-cheng Xu ◽  
Chris L. Hackert
Keyword(s):  
Spectral Ratio ◽  
Exact Formula ◽  
Seismic Attenuation ◽  
Absolute Difference ◽  
Head Wave ◽  
Full Waveform ◽  
Lower Accuracy ◽  
Head Waves ◽  
Geometric Spreading ◽  
Sonic Logs

We develop a processing algorithm to estimate the intrinsic seismic attenuation [Formula: see text] from P head waves of full-waveform sonic logs. The algorithm, based on an extended version of the amplitude spectral ratio (ASR) method, corrects the apparent attenuation for the effects of multiple raypaths within the borehole, geometric spreading of head waves, and formation inhomogeneity. The algorithm is derived from two ray models. The first model simulates the interaction among rays reflected within the borehole and rays reflected from layer interfaces. This model removes these reflections and extracts the leading borehole wavelet. The second model uses a single-ray model for the borehole head wave in layered formations. This model provides the transmission coefficients across the layer interfaces between the source depth and the receiver depth with sectional geometric spreading within these layers. We use these two models to simultaneously separate, correct for, and normalize the effects of the borehole, geometric spreading, and layering. Then we test the accuracy and limits of the models using the finite-difference solution of a point source in a fluid-filled borehole surrounded by uniform and layered formations. In 255 tested cases, the absolute difference between the estimated and exact divided by the exact [Formula: see text] is within 3% for more than half of the cases and 5% for more than two-thirds of the cases. The lower accuracy in the remaining cases is associated mainly with certain receiver locations with regard to the layer interfaces and is caused by the limitations of the ray models.

Estimating slowness dispersion from arrays of sonic logging waveforms

Geophysics ◽  
1987 ◽  
Vol 52 (4) ◽  
pp. 530-544 ◽  
Author(s):  
S. W. Lang ◽  
A. L. Kurkjian ◽  
J. H. McClellan ◽  
C. F. Morris ◽  
T. W. Parks
Keyword(s):  
Prediction Models ◽  
Temporal Frequency ◽  
Exponential Model ◽  
Dispersion Relations ◽  
The Body ◽  
Body Waves ◽  
Rock Properties ◽  
Scale Model ◽  
Receiver Array ◽  
Head Waves

Acoustic wave propagation in a fluid‐filled borehole is affected by the type of rock which surrounds the hole. More specifically, the slowness dispersion of the various body‐wave and borehole modes depends to some extent on the properties of the rock. We have developed a technique for estimating the dispersion relations from data acquired by full‐waveform digital sonic array well‐logging tools. The technique is an extension of earlier work and is based on a variation of the well‐known Prony method of exponential modeling to estimate the spatial wavenumbers at each temporal frequency. This variation, known as the forward‐backward method of linear prediction, models the spatial propagation by purely real‐valued wavenumbers. The Prony exponential model is derived from the physics of borehole acoustics under the assumption that the formation does not vary in the axial or azimuthal dimensions across the aperture of the receiver array, but can vary arbitrarily in the radial dimension. The exponential model fits the arrivals of body waves (i.e., head waves) well, because the body waves are dominated by a pole rather than a branch point. Examples of this processing applied to synthetic waveforms, laboratory scale‐model data, and field data illustrate the power of the technique and verify its ability to recover dispersion relations from sonic array data. The interpretation of the estimated dispersion in terms of rock properties is not discussed.

scholarly journals Slithering CSF: Cerebrospinal Fluid Dynamics in the Stationary and Moving Viper Boa, Candoia aspera

Biology ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 672
Author(s):  
Bruce A. Young ◽  
Skye Greer ◽  
Michael Cramberg
Keyword(s):  
Cerebrospinal Fluid ◽  
Cardiac Cycle ◽  
Low Frequency ◽  
Mean Amplitude ◽  
The Body ◽  
Body Waves ◽  
Lower Amplitude ◽  
Lateral Undulation ◽  
Recovery From Anesthesia ◽  
The Relationship

In the viper boa (Candoia aspera), the cerebrospinal fluid (CSF) shows two stable overlapping patterns of pulsations: low-frequency (0.08 Hz) pulses with a mean amplitude of 4.1 mmHg that correspond to the ventilatory cycle, and higher-frequency (0.66 Hz) pulses with a mean amplitude of 1.2 mmHg that correspond to the cardiac cycle. Manual oscillations of anesthetized C. aspera induced propagating sinusoidal body waves. These waves resulted in a different pattern of CSF pulsations with frequencies corresponding to the displacement frequency of the body and with amplitudes greater than those of the cardiac or ventilatory cycles. After recovery from anesthesia, the snakes moved independently using lateral undulation and concertina locomotion. The episodes of lateral undulation produced similar influences on the CSF pressure as were observed during the manual oscillations, though the induced CSF pulsations were of lower amplitude during lateral undulation. No impact on the CSF was found while C. aspera was performing concertina locomotion. The relationship between the propagation of the body and the CSF pulsations suggests that the body movements produce an impulse on the spinal CSF.

scholarly journals Investigation on Wireless Link for Medical Telemetry Including Impedance Matching of Implanted Antennas

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1431
Author(s):  
Ilkyu Kim ◽  
Sun-Gyu Lee ◽  
Yong-Hyun Nam ◽  
Jeong-Hae Lee
Keyword(s):  
Real Time ◽  
Human Body ◽  
Near Field ◽  
Impedance Matching ◽  
The Body ◽  
Field Pattern ◽  
Communication Link ◽  
Far Field ◽  
Antenna Coupling ◽  
Medical Telemetry

The development of biomedical devices benefits patients by offering real-time healthcare. In particular, pacemakers have gained a great deal of attention because they offer opportunities for monitoring the patient’s vitals and biological statics in real time. One of the important factors in realizing real-time body-centric sensing is to establish a robust wireless communication link among the medical devices. In this paper, radio transmission and the optimal characteristics for impedance matching the medical telemetry of an implant are investigated. For radio transmission, an integral coupling formula based on 3D vector far-field patterns was firstly applied to compute the antenna coupling between two antennas placed inside and outside of the body. The formula provides the capability for computing the antenna coupling in the near-field and far-field region. In order to include the effects of human implantation, the far-field pattern was characterized taking into account a sphere enclosing an antenna made of human tissue. Furthermore, the characteristics of impedance matching inside the human body were studied by means of inherent wave impedances of electrical and magnetic dipoles. Here, we demonstrate that the implantation of a magnetic dipole is advantageous because it provides similar impedance characteristics to those of the human body.

A STUDY OF TWO‐DIMENSIONAL HEAD WAVES IN FLUID AND SOLID SYSTEMS

Geophysics ◽  
1963 ◽  
Vol 28 (4) ◽  
pp. 563-581 ◽  
Author(s):  
John W. Dunkin
Keyword(s):  
Half Space ◽  
Vertical Displacement ◽  
Point Of View ◽  
Head Wave ◽  
Apparent Velocity ◽  
Two Dimensional ◽  
Multiple Reflections ◽  
Transient Wave ◽  
Line Load ◽  
Head Waves

The problem of transient wave propagation in a three‐layered, fluid or solid half‐plane is investigated with the point of view of determining the effect of refracting bed thickness on the character of the two‐dimensional head wave. The “ray‐theory” technique is used to obtain exact expressions for the vertical displacement at the surface caused by an impulsive line load. The impulsive solutions are convolved with a time function having the shape of one cycle of a sinusoid. The multiple reflections in the refracting bed are found to affect the head wave significantly. For thin refracting beds in the fluid half‐space the character of the head wave can be completely altered by the strong multiple reflections. In the solid half‐space the weaker multiple reflections affect both the rate of decay of the amplitude of the head wave with distance and the apparent velocity of the head wave by changing its shape. A comparison is made of the results for the solid half‐space with previously published results of model experiments.

Seismic cone penetration test and seismic tomography in permafrost

2004 ◽  
Vol 41 (5) ◽  
pp. 796-813 ◽  
Author(s):  
Anne-Marie LeBlanc ◽  
Richard Fortier ◽  
Michel Allard ◽  
Calin Cosma ◽  
Sylvie Buteau
Keyword(s):  
Seismic Tomography ◽  
Dynamic Properties ◽  
Cone Penetration Test ◽  
The Body ◽  
Body Waves ◽  
Reconstruction Technique ◽  
Seismic Velocities ◽  
Penetration Test ◽  
Cone Penetration ◽  
Seismic Cone Penetration Test

Two high-resolution multi-offset vertical seismic profile (VSP) surveys were carried out in a permafrost mound near Umiujaq in northern Quebec, Canada, while performing seismic cone penetration tests (SCPT) to study the cryostratigraphy and assess the body waves velocities and the dynamic properties of warm permafrost. Penetrometer-mounted triaxial accelerometers were used as the VSP receivers, and a swept impact seismic technique (SIST) source generating both compressional and shear waves was moved near the surface following a cross configuration of 40 seismic shot-point locations surrounding each of the two SCPTs. The inversion of travel times based on a simultaneous iterative reconstruction technique (SIRT) provided tomographic images of the distribution of seismic velocities in permafrost. The Young's and shear moduli at low strains were then calculated from the seismic velocities and the permafrost density measured on core samples. The combination of multi-offset VSP survey, SCPT, SIST, and SIRT for tomographic imaging led to new insights in the dynamic properties of permafrost at temperatures close to 0 °C. The P- and S-wave velocities in permafrost vary from 2400 to 3200 m/s and from 900 to 1750 m/s, respectively, for a temperature range between –0.2 and –2.0 °C. The Young's modulus varies from 2.15 to 13.65 GPa, and the shear modulus varies from 1.00 to 4.75 GPa over the same range of temperature.Key words: permafrost, seismic cone penetration test, vertical seismic profiling, seismic tomography, dynamic properties.

Dynamic properties of reflected and head waves near the critical point

1979 ◽  
Vol 16 (7) ◽  
pp. 1388-1401 ◽  
Author(s):  
Larry W. Marks ◽  
F. Hron
Keyword(s):  
Exact Solution ◽  
High Frequency ◽  
Classical Problem ◽  
Plane Boundary ◽  
Head Wave ◽  
Disk File ◽  
Ray Theory ◽  
Computational Point ◽  
Spherical Waves ◽  
Head Waves

The classical problem of the incidence of spherical waves on a plane boundary has been reformulated from the computational point of view by providing a high frequency approximation to the exact solution applicable to any seismic body wave, regardless of the number of conversions or reflections from the bottoming interface. In our final expressions the ray amplitude of the interference reflected-head wave is cast in terms of a Weber function, the numerical values of which can be conveniently stored on a computer disk file and retrieved via direct access during an actual run. Our formulation also accounts for the increase of energy carried by multiple head waves arising during multiple reflections of the reflected wave from the bottoming interface. In this form our high frequency expression for the ray amplitude of the interference reflected-head wave can represent a complementary technique to asymptotic ray theory in the vicinity of critical regions where the latter cannot be used. Since numerical tests indicate that our method produces results very close to those obtained by the numerical integration of the exact solution, its combination with asymptotic ray theory yields a powerful technique for the speedy computation of synthetic seismograms for plane homogeneous layers.

An experimental study of source motion synthesis from first arrivals

1963 ◽  
Vol 53 (5) ◽  
pp. 955-963
Author(s):  
Henry N. Pollack
Keyword(s):  
Experimental Study ◽  
Source Function ◽  
Seismic Source ◽  
The Body ◽  
Body Waves ◽  
Fixed Position ◽  
Explosive Source ◽  
Simple Medium ◽  
Surface Ice ◽  
Source Motion

Abstract The motion near a seismic source is synthesized from experimentally obtained seismograms of non-dispersed body waves. The body waves were emitted from an explosive source submerged in a lake with a frozen surface. The seismograms were recorded at several distances by moving the source to a greater depth for each record, while the seismometer remained in a fixed position on the surface ice sheet. All syntheses of the waveform one meter from the source yield the impulsive nature of the source. Deviations between the synthesized one-meter record and the observed one-meter motion are thought to reflect primarily the changing character of the shot medium with depth from the ice. These results indicate that over the short propagation distances (about three wavelengths for the higher frequencies recorded) through the simple medium of this experiment, the observed waveforms and their associated spectra retain characteristics of the source function. The records also yield some information regarding the nature and structure of the elastic medium about the source.

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