I would like to have your kind opinions on the issue that concerns rock mechanics and geophysics in relation to it, for a very specific problem I have.
I have attempted to find a range in the Barton’s graph (Barton 1995), for Qc vs Vp, which applies to the rock masses which I study (those of Doha, Qatar). However, I only have data from MASW geophysical surveys, which yield only Vs.
Hence, I looked for a way to convert Vs values range into a Vp range. I came to discover that there is a very active Nigerian scientific community which deals with geophysical research at their home turf. So I came across the below expression
ni(poisson) = [(Vp/Vs)^2 - 2]/[2(Vp/Vs)^2 - 2]
from which Vp can be obtained from Vs, with a known Poisson’s ratio. The formula is from a paper by Atat et al. (2012).
Qatari rock masses are sedimentary limestone and dolomite soft to medium hard rock masses situated in a very flat terrain (so there is no need for obtaining Vp, I suppose), and in the above paper, the Authors have used the formula on sedimentary shale layers of Niger delta.
Would you use this formula without reservation, for Vs to Vp conversion, regardless of rock (mass) type?
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Dear Hrvoje and colleagues:
To give a couple of ideas and answers to your questions, allow me to share some points of view regarding some phrases or statements, trying to be as simple as possible from the point of view of my own experience such as Geophysicist for oil and gas E&D (Exploration and Development).
First, I want to say the Poisson's ratio for common materials ranges from 0 to 0.5. Incompressible materials, such as liquids, have a Poisson's ratio of 0.5. Gas sands theoretically have a Poisson's ratio below 0.2; porous wet sands and shales have much higher Poisson's ratio (0.25 to 0.4), and the value of carbonates is approximately 0.3.
But, one important issue is that Poisson's ratio varies as a nonlinear of Vp/Vs!!! the rocks that exhibit high values of Vp/Vs also exhibit high Poisson's ratios. Further, Vp/Vs as a function of Poisson´s ratio, for sedimentary rocks, sandstones and limestones, could be higher for well-lithified, otherwise. Shales are in other world, literally.
On the other hand, the formula from a paper by Atat et al. (2012) is only for an isotropic elastic material, and if you graph of Vp/Vs against Poisson's ratio, the plotted show you a nonlinear relationship, where clearly high values of Vp/Vs correspond to high Poisson's ratio.
From a geological point of view, when you say that “…Qatari rock masses are sedimentary limestone and dolomite soft to medium hard rock masses situated in a very flat terrain (so there is no need for obtaining Vp, I suppose) …” it is a very important issue, because the poorly consolidated and / or brine – saturated rocks or “soft” rocks have a high Poisson's ratio, whereas highly lithified or “hard” rocks (carbonates, granite, basalt, quartzite) have low values of Poisson's ratio. For example, unconsolidated shales near the water bottom can have Poisson's ratio approaching 0.5, corresponding to a Vp/Vs value approaching infinity. However, as the depth of burial increases, the rocks become harder and the Poisson's ratio decreases. Most consolidated rocks have Poisson's ratios below 0.33 (Vp/Vs value of 2). You are talking about dolomites, it has a Poisson´s ratio near 0.3 and high density (2.85 – 2.88 g/cm3) and Vp, Vs, 7.7 and 4, respectively, km/s.
Also, please, the sentence “…in a very flat terrain …so there is no need for obtaining Vp, I suppose…” it is not a valid reason. Furthermore, in E&D for oil and gas, the most common scenario, I work only with P-wave and density logs from wells, and compressional-wave-reflectivity seismic surveys (P-wave). Precisely, one of the purposes of my work as a Reservoir Geophysicist is to estimate the P – to - S-wave mode conversion / contribution, both, logs and seismic, for example, by empirical equations and approximations to the exact Zoeppritz equations, e.g., by elastic - simultaneous (refers to performing the AVO extraction and computing the seismic impedance together) prestack (seismic gathers from PSTM) inversion.
From the point of view of geomechanics, Poisson's ratio is routinely used in stress analysis, and in seismic inversion, but “there is not a single seismological equation where Poisson's ratio enters in a natural way” as Thomsen stated.
Poisson's ratio for a rock depends on the solid-rock material (in turn depends on mineral composition), the shape of the pore space, and the fluid saturating it.
Therefore, when you ask: Would you use this formula without reservation, for Vs to Vp conversion, regardless of rock (mass) type?
The answer is no use for Vs to Vp conversion, the Poisson's ratio of shale Niger delta. Reasons:
1- The geological´s scenario (You do not give us any idea about the depth range of your data (top and bottom meters) and the Niger´s shales) is dramatically different: Qatari rock masses are sedimentary limestone and dolomite soft to medium hard rock and the Atat et al., are shales, therefore the Poisson's ratio could be very different in one case than in another.
2- Shales are in another world. Because of the strongly anisotropic nature of mudrocks, P and S-waves velocities can vary with direction – azimuth propagation, and sonic velocities measured in vertical wells values, elastic, geomechanics of unconventional shales such as brittleness, horizontal stress, is not the equivalent to limestones and dolomites.
3- If you check the bibliography (Lekhnitsky´s notations) there are two independent Young´s modulii and there are three different Poisson's ratios for shales, and it is a misleading to refer to the Poisson´s ratios measured in vertical (VTI) rocks as being vertical and / or horizontal, because there is only one that is purely horizontal.
4- From the seismic point of view, 3D seismic to characterize unconventional shale reservoirs remains a challenge.
Therefore, I suggest to you, if you have only S-wave data from logs, is trying to use statistical relationships between compressional-wave-velocity (Vp) and shear-wave-velocity (Vs), e.g., from linear regression analysis, Castagna´s mud-rock line equation for example. A good practice, anyway, is trying to calibrate Vp / Vs by the flexural-dipole logs in your work area / near it, or an analogous scenario.
If you are interested, I can send you bibliographical papers, to illustrate what I am trying to explain.
Best regards Hrvoje, Mario E. Sigismondi
@ Mario Emilio Sigismondi
Dear Mario. Thanks for a very elaborate answer.
The poisson's ration I intended to use is an average value from over 600 lab UCS (unconfined compressive strength) tests on intact rock samples. The average value is 0.25.
The depth considered is down to 30-40 m only. The paper from Niger delta shales also deals with small depths, not deeper than those of my problem. They had no lab results for poisson's, unlike myself, and were also obtaining negative values for it.
I am not sure I have detailed records which you describe, for a regression analysis, but nonetheless please send everything you got. Much obliged.
Dear Hrvoje, in your scenario of rock samples in lab , in your depth's range 30 - 40 m, I DO NOT HAVE EXPERIENCE, my answer is thinking about E&D well-logs + seismic.
Best regards Sir, Mario