Elastic stiffness coefficients of a skirted spudcan foundation in clay

2022 ◽  
Vol 120 ◽  
pp. 103054
Author(s):  
Shuai Yin ◽  
YuZhou Xiang ◽  
Jun Xu ◽  
Hui Cheng ◽  
YueWen Jiang ◽  
...  
Geophysics ◽  
2003 ◽  
Vol 68 (3) ◽  
pp. 1022-1031 ◽  
Author(s):  
Pawan Dewangan ◽  
Vladimir Grechka

Vertical seismic profiling (VSP), an established technique, can be used for estimating in‐situ anisotropy that might provide valuable information for characterization of reservoir lithology, fractures, and fluids. The P‐wave slowness components, conventionally measured in multiazimuth, walkaway VSP surveys, allow one to reconstruct some portion of the corresponding slowness surface. A major limitation of this technique is that the P‐wave slowness surface alone does not constrain a number of stiffness coefficients that may be crucial for inferring certain rock properties. Those stiffnesses can be obtained only by combining the measurements of P‐waves with those of S (or PS) modes. Here, we extend the idea of Horne and Leaney, who proved the feasibility of joint inversion of the slowness and polarization vectors of P‐ and SV‐waves for parameters of transversely isotropic media with a vertical symmetry axis (VTI symmetry). We show that there is no need to assume a priori VTI symmetry or any other specific type of anisotropy. Given a sufficient polar and azimuthal coverage of the data, the polarizations and slownesses of P and two split shear (S1 and S2) waves are sufficient for estimating all 21 elastic stiffness coefficients cij that characterize the most general triclinic anisotropy. The inverted stiffnesses themselves indicate whether or not the data can be described by a higher‐symmetry model. We discuss three different scenarios of inverting noise‐contaminated data. First, we assume that the layers are horizontal and laterally homogeneous so that the horizontal slownesses measured at the surface are preserved at the receiver locations. This leads to a linear inversion scheme for the elastic stiffness tensor c. Second, if the S‐wave horizontal slowness at the receiver location is unknown, the elastic tensor c can be estimated in a nonlinear fashion simultaneously with obtaining the horizontal slowness components of S‐waves. The third scenario includes the nonlinear inversion for c using only the vertical slowness components and the polarization vectors of P‐ and S‐waves. We find the inversion to be stable and robust for the first and second scenarios. In contrast, errors in the estimated stiffnesses increase substantially when the horizontal slowness components of both P‐ and S‐waves are unknown. We apply our methodology to a multiazimuth, multicomponent VSP data set acquired in Vacuum field, New Mexico, and show that the medium at the receiver level can be approximated by an azimuthally rotated orthorhombic model.


2006 ◽  
Vol 115 ◽  
pp. 63-66
Author(s):  
U. Straube ◽  
Giovanni Mazzolai ◽  
A. Biscarini ◽  
B. Coluzzi ◽  
Fabio M. Mazzolai ◽  
...  

The ultrasound pulse echo overlap method has been used to determine the elastic stiffness coefficients and the corresponding ultrasonic attenuation for a single crystal of the Ni40Ti50Cu10 alloy as a function of temperature. The elastic stiffness coefficients exhibit anomalies near the martensitic phase transition. In the shear stiffness coefficient, corresponding to C44 propagation mode in austenite, a large jump occurs from 36 GPa, above the transition, down to 15 GPa, below the transition. This jump is accompanied by a strong increase in the ultrasonic attenuation. The stiffness coefficients corresponding to C11 and C' = (C11 – C12)/2 modes in austenite show an anomaly at the phase transition, however, these are small effects compared to the one associated with C44 mode. The elastic behavior of this crystal has been characterised down to a temperature of 100 K.


Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. R27-R39 ◽  
Author(s):  
Faranak Mahmoudian ◽  
G. F. Margrave ◽  
P. F. Daley ◽  
J. Wong ◽  
D. C. Henley

We acquired 3C ultrasonic transmission seismograms, measured group velocities associated with the three quasi-body wave types, and determined density-normalized stiffness coefficients ([Formula: see text]) over an orthorhombic physical (laboratory) model. The estimation of [Formula: see text] is based on an approximate relationship between the nine orthorhombic [Formula: see text] and group velocities. Estimation of the anisotropic [Formula: see text] is usually done using phase velocities with well-known formulas expressing their theoretical dependence on [Formula: see text]. However, on time-domain seismograms, arrivals are observed traveling with group velocities. Group velocity measurements are found to be straightforward, reasonably accurate, and independent of the size of the transducers used. In contrast, the accuracy of phase velocities derived from the [Formula: see text] transform analysis was found to be very sensitive to small differences in picked arrival times and to transducer size. Theoretical phase and group velocities, calculated in a forward manner from the [Formula: see text] estimates, agreed with the originally measured phase and group velocities, respectively. This agreement confirms that it is valid to use easily measured group velocities with their approximate theoretical relationship to the [Formula: see text] to determine the full stiffness matrix. Compared to the phase-velocity procedure, the technique involving group velocities is much less prone to error due to time-picking uncertainties, and therefore is more suitable for analyzing physical model seismic data.


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