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.

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.

Acoustic modes of propagation in the borehole and their relationship to rock properties

Geophysics ◽  
1982 ◽  
Vol 47 (8) ◽  
pp. 1215-1228 ◽  
Author(s):  
F. L. Paillet ◽  
J. E. White
Keyword(s):  
Elastic Solid ◽  
Body Waves ◽  
Radioactive Waste Disposal ◽  
Plane Geometry ◽  
Rock Properties ◽  
Geometry Model ◽  
Head Waves ◽  
Time Domain Response ◽  
Tube Wave ◽  
The Time Domain

Acoustic waveform measurements in boreholes have important applications in fracture hydrology and radioactive waste disposal, but ambiguities in existing interpretation techniques remain a problem. We have addressed the problem by using residue theory to predict the relative excitation of various modes contained in experimental waveforms. A plane‐geometry model involving a layer of fluid between two elastic half‐spaces is shown to provide velocity dispersion curves for propagating modes that are very similar to those for the fluid‐filled borehole. We use the plane‐geometry model to illustrate the effects of the confined borehole fluid on surface and body waves traveling along the borehole in the elastic solid. We also computed excitation functions for some of the lowest‐order symmetric modes, calculated the time‐domain response of the trapped modes following the shear head waves, and compared them to waveforms recorded in boreholes through several homogeneous formations. The insight into the mode composition of the experimental waveforms obtained in these formations is used to construct amplitude logs that should be especially sensitive to variations in the presence of fluid‐filled fractures in the borehole wall. Initial tests show the technique is most successful when the waveform is dominated by the fundamental tube wave, and yet frequencies remain relatively high. The model analysis indicates these conditions can only be obtained when the borehole diameter is not much larger than that of the logging tool.

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.

P- and S-wave attenuation logs from monopole sonic data

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 755-765 ◽  
Author(s):  
Xinhua Sun ◽  
Xiaoming Tang ◽  
C. H. (Arthur) Cheng ◽  
L. Neil Frazer
Keyword(s):  
Wave Attenuation ◽  
Fluid Velocity ◽  
P Wave ◽  
Reservoir Rock ◽  
Rock Properties ◽  
S Wave ◽  
Intrinsic Attenuation ◽  
Modified Method ◽  
Receiver Array ◽  
Attenuation Profiles

In this paper, a modification of an existing method for estimating relative P-wave attenuation is proposed. By generating synthetic waveforms without attenuation, the variation of geometrical spreading related to changes in formation properties with depth can be accounted for. With the modified method, reliable P- and S-wave attenuation logs can be extracted from monopole array acoustic waveform log data. Synthetic tests show that the P- and S-wave attenuation values estimated from synthetic waveforms agree well with their respective model values. In‐situ P- and S-wave attenuation profiles provide valuable information about reservoir rock properties. Field data processing results show that this method gives robust estimates of intrinsic attenuation. The attenuation profiles calculated independently from each waveform of an eight‐receiver array are consistent with one another. In fast formations where S-wave velocity exceeds the borehole fluid velocity, both P-wave attenuation ([Formula: see text]) and S-wave attenuation ([Formula: see text]) profiles can be obtained. P- and S-wave attenuation profiles and their comparisons are presented for three reservoirs. Their correlations with formation lithology, permeability, and fractures are also presented.

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.

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.

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.

scholarly journals Asymptotic analysis for dispersion relations and travel times in noise cross-correlations: spherically symmetric case

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180382
Author(s):  
Tianshi Liu ◽  
Haiming Zhang
Keyword(s):  
Asymptotic Analysis ◽  
Surface Waves ◽  
Green's Functions ◽  
Green’S Functions ◽  
Dispersion Relations ◽  
Body Waves ◽  
Spherically Symmetric ◽  
Travel Times ◽  
Cross Correlations ◽  
The Cross

The cross-correlations of ambient noise or earthquake codas are massively used in seismic tomography to measure the dispersion curves of surface waves and the travel times of body waves. Such measurements are based on the assumption that these kinematic parameters in the cross-correlations of noise coincide with those in Green's functions. However, the relation between the cross-correlations of noise and Green's functions deserves to be studied more precisely. In this paper, we use the asymptotic analysis to study the dispersion relations of surface waves and the travel times of body waves, and come to the conclusion that for the spherically symmetric Earth model, when the distribution of noise sources is laterally uniform, the dispersion relations of surface waves and the travel times of SH body-wave phases in noise correlations should be exactly the same as those in Green's functions.

scholarly journals Long-period mechanism of the 8 November 1980 Eureka, California, earthquake

1982 ◽  
Vol 72 (2) ◽  
pp. 439-456
Author(s):  
Thorne Lay ◽  
Jeffrey W. Given ◽  
Hiroo Kanamori
Keyword(s):  
Point Source ◽  
Seismic Moment ◽  
Moment Tensor ◽  
Strike Slip ◽  
The Body ◽  
Body Waves ◽  
Long Period ◽  
Amplitude Data ◽  
The Moment ◽  
Scalar Moment

Abstract The seismic moment and source orientation of the 8 November 1980 Eureka, California, earthquake (Ms = 7.2) are determined using long-period surface and body wave data obtained from the SRO, ASRO, and IDA networks. The favorable azimuthal distribution of the recording stations allows a well-constrained mechanism to be determined by a simultaneous moment tensor inversion of the Love and Rayleigh wave observations. The shallow depth of the event precludes determination of the full moment tensor, but constraining Mzx = Mzy = 0 and using a point source at 16-km depth gives a major double couple for period T = 256 sec with scalar moment M0 = 1.1 · 1027 dyne-cm and a left-lateral vertical strike-slip orientation trending N48.2°E. The choice of fault planes is made on the basis of the aftershock distribution. This solution is insensitive to the depth of the point source for depths less than 33 km. Using the moment tensor solution as a starting model, the Rayleigh and Love wave amplitude data alone are inverted in order to fine-tune the solution. This results in a slightly larger scalar moment of 1.28 · 1027 dyne-cm, but insignificant (<5°) changes in strike and dip. The rake is not well enough resolved to indicate significant variation from the pure strike-slip solution. Additional amplitude inversions of the surface waves at periods ranging from 75 to 512 sec yield a moment estimate of 1.3 ± 0.2 · 1027 dyne-cm, and a similar strike-slip fault orientation. The long-period P and SH waves recorded at SRO and ASRO stations are utilized to determine the seismic moment for 15- to 30-sec periods. A deconvolution algorithm developed by Kikuchi and Kanamori (1982) is used to determine the time function for the first 180 sec of the P and SH signals. The SH data are more stable and indicate a complex bilateral rupture with at least four subevents. The dominant first subevent has a moment of 6.4 · 1026 dyne-cm. Summing the moment of this and the next three subevents, all of which occur in the first 80 sec of rupture, yields a moment of 1.3 · 1027 dyne-cm. Thus, when the multiple source character of the body waves is taken into account, the seismic moment for the Eureka event throughout the period range 15 to 500 sec is 1.3 ± 0.2 · 1027 dyne-cm.

Evaluation of a Small and Fast Planing Boat’s Seakeeping Performance at the Design Stage

2015 ◽  
Author(s):  
Dong Jin Kim ◽  
Sun Young Kim
Keyword(s):  
Model Tests ◽  
Full Scale ◽  
Scale Model ◽  
Design Stage ◽  
Small Scale ◽  
Irregular Wave ◽  
Seakeeping Performance ◽  
Head Waves ◽  
Scale Ratio ◽  
Free Running

Seakeeping performance of a planing boat should be sufficiently considered and evaluated at the design stage for its safe running in rough seas. Model tests in seakeeping model basins are often performed to predict the performance of full-scale planing boats. But, there are many limitations of tank size and wave maker capacity, in particular, for fast small planing boats due to small scale ratio and high Froude numbers of their scale models. In this research, scale model tests are tried in various test conditions, and results are summarized and analyzed to predict a 3 ton-class fast small planing boats designed. In a long and narrow tank, towing tests for a bare hull model are performed with regular head waves and long crested irregular head waves. Motion RAOs are derived from irregular wave tests, and they are in good agreements with RAOs in regular waves. Next, model ships with one water-jet propulsion system are built, and free running model tests are performed in ocean basins. Wave conditions such as significant heights, modal periods, and directions are varied for the free running tests. Motion RMS values, and RAOs are obtained through statistical approaches. They are compared with the results in captive tests for the bare hull model, and are used to predict the full-scale boat performances.

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