Stoneley-wave speed modeling in general anisotropic formations

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. F67-F77 ◽  
Author(s):  
Shihong Chi ◽  
Xiaoming Tang

For determining anisotropy using acoustic logging data, Stoneley waves are the only wave modes that are sensitive to formation properties transverse to the borehole axis. We derive Stoneley-wave speeds in deviated and horizontal wells penetrating anisotropic formations. We first apply the elastic theory of an anisotropic body to find the radial displacement of a borehole cross section under uniform pressure. We then derive the effective formation modulus based on quasistatic analysis. Finally, we derive a two-dimensional analytical solution for low-frequency Stoneley-wave speed in a horizontal well penetrating a transversely isotropic formation with a vertical symmetry axis. For deviated wells, we derive a 3D analytical solution that is also valid for general anisotropic formations. Our analytic solutions agree with the finite-difference modeling results and are particularly suited for strongly anisotropic formations. With increasing well deviation the sensitivity of Stoneley-wave speed to horizontal shear-wave velocity decreases and the sensitivity to vertical shear-wave velocity increases.

2008 ◽  
Vol 9 (11) ◽  
pp. 1490-1496 ◽  
Author(s):  
Yan-guo Zhou ◽  
Yun-min Chen ◽  
Yoshiharu Asaka ◽  
Tohru Abe

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 437-443 ◽  
Author(s):  
Ningya Cheng ◽  
Chuen Hon Cheng

Field data sets collected by an array monopole acoustic logging tool and a shear wave logging tool are processed and interpreted. The P‐ and S‐wave velocities of the formation are determined by threshold detection with cross‐correlation correction from the full waveform and the shear‐wave log, respectively. The array monopole acoustic logging data are also processed using the extended Prony’s method to estimate the borehole Stoneley wave phase velocity and attenuation as a function of frequency. The well formation between depths of 2950 and 3150 ft (899 and 960 m) can be described as an isotropic elastic medium. The inverted [Formula: see text] from the Stoneley wave phase velocity is in excellent agreement with the shear‐wave log results in this section. The well formation between the depths of 3715 and 3780 ft (1132 and 1152 m) can be described as a porous medium with shear‐wave velocity anisotropy about 10% to 20% and with the symmetry axis perpendicular to the borehole axis. The disagreement between the shear‐wave velocity from the Stoneley wave inversion and the direct shear‐wave log velocity in this section is beyond the errors in the measurements. Estimated permeabilities from low‐frequency Stoneley wave velocity and attenuation data are in good agreement with the core measurements. Also it is proven that the formation permeability is not the cause of the discrepancy. From the estimated “shear/pseudo‐Rayleigh” phase velocities in the array monopole log and the 3-D finite‐difference synthetics in the anisotropic formation, the discrepancy can best be explained as shear‐wave anisotropy.


2011 ◽  
Vol 368-373 ◽  
pp. 2586-2590
Author(s):  
Zhao Bo Meng ◽  
Shi Cai Cui ◽  
Teng Fei Zhao ◽  
Liu Qin Jin

According to measured shear wave velocity of Xi’an Bell Tower area (Loess Area), the dynamic parameters of site soil are determined by using the relationship between shear wave velocity and compression wave velocity. Using Matlab program, the finite element size for low frequency subway vibration is obtained by analyzing soil dispersion phenomenon. On this basis, two-dimensional model with viscous - elastic boundaries is established by using the ANSYS program. The load-time history of the train is applied to the right tunnel, and the effects of the depth and breadth of the different models on the ground vibration velocity are discussed. Finally, the dimensions and element sizes of finite element model are obtained for the Xi'an No. 2 Metro Line with 15m depth in the loess regions.


2021 ◽  
Author(s):  
François Lavoué ◽  
Sergei Lebedev ◽  
Nicolas Celli ◽  
Andrew Schaeffer

<p>We present new models of shear-wave velocity and of its radial and azimuthal anisotropy in the crust and upper mantle at global scale. Seismic anisotropy is the consequence of the preferential orientation of minerals due to deformation. The reconstruction of both its radial and azimuthal components provides insights into past and present deformation and flow in the lithosphere and asthenosphere. The full consideration of anisotropy also makes possible to accurately determine the isotropic shear-velocity average, and therefore to isolate the effects of thermal or compositional variations from those of anisotropic fabric. </p><p>Our model is constrained by a large compilation of waveform fits for more than 750,000 vertical-component and 250,000 transverse-component seismograms. We follow a two-step procedure that comprises the Automated Multimode Inversion of surface, S, and multiple-S waveforms in a period range from 10 to 450 s, followed by a 3D tomographic inversion that reconstructs <em>dV<sub>SH</sub></em> and <em>dV<sub>SV</sub></em> velocity perturbations and their 4-ψ and 2-ψ azimuthal dependencies. The joint inversion of vertical and transverse components is regularised in terms of linear isotropic average perturbations <em>dV<sub>S0</sub> = (dV<sub>SH</sub></em> + <em>dV<sub>SV</sub></em>)/2 and of radial anisotropy δ <em>= dV<sub>SH</sub></em> - <em>dV<sub>SV</sub></em>.</p><p>We compare our model with other published anisotropic models. The different models show good agreement on major isotropic structures but relatively poor agreement on anisotropic features. We identify different patterns of anisotropy for different tectonic regions. At shallow depths (< 60 km), there is a clear difference between oceanic and continental regions of different ages. While radial anisotropy is consistently negative (<em>V<sub>SH</sub></em> < <em>V<sub>SV</sub></em>) in the top 50 km of oceanic lithosphere, it is positive (<em>V<sub>SH</sub></em> > <em>V<sub>SH</sub></em>) under continents, with a thick layer of slightly positive anisotropy under cratons and a shallower layer of stronger anisotropy under phanerozoic crust, subject to more recent deformation. The largest anisotropy —positive and exceeding 2% in our and most other models— occurs between 70 and 150 km depth. This pattern is observed in both continents and oceans, and depends on their age and lithospheric thickness, which is indicative of the anisotropic fabric developed in the asthenosphere and frozen in the lithosphere. Finally, we observe a remarkable reversal from positive to negative anisotropy between 200 and 330 km depth over the entire globe. Again, the depth at which this reversal occurs depends on the tectonic settings: it is deeper under cratons and old oceans than under young continents and oceans. Synthetic tests demonstrate the robustness of this observation. While it could be interpreted as a transition from dominantly horizontal to dominantly vertical deformation in the mantle, this anisotropy reversal is also consistent with mineralogic experiments that suggest a transition in olivine slip mechanism which causes horizontal shear to induce negative seismic anisotropy below a certain depth. In lack of a satisfying scenario that could explain a global trend to vertical mantle flow between 260 and 410 km depth, we favour the second interpretation. If this interpretation is correct, our anisotropic model provides global-scale evidence for the transition in the olivine slip mechanism documented in the mineralogic literature.</p>


2020 ◽  
Vol 39 (9) ◽  
pp. 646-653 ◽  
Author(s):  
Siyuan Yuan ◽  
Ariel Lellouch ◽  
Robert G. Clapp ◽  
Biondo Biondi

Due to the broadband nature of distributed acoustic sensing (DAS) measurement, a roadside section of the Stanford DAS-2 array can record seismic signals from various sources. For example, it measures the earth's quasistatic deformation caused by the weight of cars (less than 0.8 Hz) as well as Rayleigh waves induced by earthquakes (less than 3 Hz) and by dynamic car-road interactions (3–20 Hz). We directly utilize the excited surface waves for shallow shear-wave velocity inversion. Rayleigh waves induced by passing cars have a consistent fundamental mode and a noisier first mode. By stacking dispersion images of 33 passing cars, we obtain stable dispersion images. The frequency range of the fundamental mode can be extended by adding the low-frequency earthquake-induced Rayleigh waves. Due to the extended frequency range, we can achieve better depth coverage and resolution for shear-wave velocity inversion. To assure clear separation from Love waves and to align apparent and true phase velocities, we choose an earthquake that is approximately in line with the array. The inverted models match those obtained by a conventional geophone survey, performed using active sources by a geotechnical service company contracted by Stanford University, from the surface to about 50 m. To automate the VS inversion process, we introduce a new objective function that avoids manual dispersion curve picking. We construct a 2D VS profile by performing independent 1D inversions at multiple locations along the fiber. From the low-frequency quasistatic deformation recordings, we also invert for a single Poisson's ratio at each location along the fiber. We observe spatial heterogeneity of both VS and Poisson's ratio profiles. Our approach is less expensive than ambient field interferometry, and reliable estimates can be obtained more frequently because no lengthy crosscorrelations are required.


2014 ◽  
Vol 51 (11) ◽  
pp. 1284-1302 ◽  
Author(s):  
Fawad S. Niazi ◽  
Paul W. Mayne

The Osterberg cell (O-cell) type of bidirectional pile load testing is a modern full-scale proofing method in the realm of performance-based pile design. It is done at considerable cost, not possible on small- to medium-size projects. An economical approach of utilizing the flexible and approximate analytical solution proposed by Randolph has frequently been adopted in the past for evaluating pile settlements under static, unidirectional, top-down axial compression loading. To extend this solution for O-cell loadings, the following adaptations are warranted: (i) appropriate modifications to handle the loadings in two directions and (ii) development of a nonlinear stiffness reduction model, derived from the back-analysis of O-cell pile load tests. Accordingly, a modified analytical solution is presented for the two common cases of O-cell loading arrangements. Using these modified sets of solutions and a well-documented database of O-cell load tests on drilled shaft foundations from different sites, two stiffness reduction models have been developed. The shear wave velocity readings obtained from the hybrid geophysical–geotechnical seismic piezocone tests afford the evaluation of fundamental shear stiffness modulus (Gmax) profiles. These profiles together with the re-arranged modified solution were applied to the axial loads versus displacements (Q–w) from the database of load tests to back-calculate the applicable operational shear stiffness (G) values. Additional sensitivity analyses indicate that pile geometry and soil stiffness profile are the two most significant factors affecting the outcome of this solution. A comprehensive set of step-by-step example calculations is included to explain the procedure for implementing the solution.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Joanna Sichitiu ◽  
Jean-Yves Meuwly ◽  
David Baud ◽  
David Desseauve

AbstractThis study aims to evaluate the feasibility and clinical interest of shear wave elastography, by quantitatively estimating the baseline stiffness of the myometrium before and after placental expulsion. We conducted a prospective cohort study of women at term, without known risk factors for postpartum hemorrhage, who gave birth via spontaneous labor in our tertiary center. Myometrium tonicity was evaluated based on measurements of shear wave speed (SWS) in the anterior uterine corpus. All data points were collected by a single operator. Measurements were carried out at three different time points: after fetal delivery (T1), after placental delivery (T2) and 30 min after placental delivery (T3). Our primary objective was to assess the feasibility of this new imaging technique. Ten valid SWS measurements obtained at each of the three different time points were considered as a positive primary outcome. Our secondary objectives were to evaluate the difference in median myometrial shear wave velocity between each time point, as well as to determine the correlation between myometrial shear wave velocity and patients’ characteristics. 38 women were recruited during the study period, of whom 34 met the study criteria. 1017 SWS measurements were obtained. The median time to perform measurements was 16 s for one value, and 2 min 56 s for ten. For 11 women (32%) it was not possible to achieve ten SWS at T1 as placental expulsion immediately followed the birth of the newborn. One patient experienced placental retention and only measurements at T1 were performed. For all other patients, we were successfully able to obtain all measures as intended. There was no difference in the mean shear wave speed between the three time points. After adjustments for confounders, we observed a significant correlation for total blood loss (correlation coefficient = − 0.26, p < 0.001, units of oxytocin (correlation coefficient = − 0.34, p = 0.03), and newborn weight (correlation coefficient = − 0.08, p = 0.001). It is feasible to assess uterine tonicity by shear wave imaging, after placental expulsion. We did not observe a variance in uterine tonicity between the three time points. Women who had higher blood loss, received more units of oxytocin and/or those with newborns of a higher weight exhibited lower shear wave speed measures.


2021 ◽  
Vol 11 (3) ◽  
pp. 1036
Author(s):  
Yinqiu Zhou ◽  
Xiuming Wang ◽  
Yuyu Dai

In this article, a novel design of a piezoelectric dipole transducer is proposed for formation acoustic velocity measurement in the vicinity of a borehole with a frequency range of 0.4–6 kHz. The transducer which actuates a cylindrical shell to generate a pure dipole mode wave by using multiple piezoelectric bender bars is analyzed theoretically and simulated numerically by using the finite element method (FEM). Moreover, the transducer is fabricated and tested to compare with the numerical simulation results, which shows that the test and simulation results are in good agreement. Finally, compared with numerical simulation results of the traditional dipole transducer, it is shown that the proposed dipole transducer has higher transmitting sensitivities than commonly used ones, especially in low frequency responses. This work lays a foundation for the new development of the transducer in borehole dipole acoustic shear wave measurements. Especially, in a slow formation where the shear wave velocity is lower than that of compressional wave in the borehole fluid, the transducer could be used for highly efficient shear wave velocity measurements.


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