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Comparison of an Estimated Shear Wave Log
with a Measured Shear Wave
Log
*
Felix Oghenekohwo1 and George Smith1
Search and Discovery Article #40687 (2011)
Posted February 15, 2011
*Adapted from oral presentation at AAPG International Conference and Exhibition, Calgary, Alberta, Canada, September 12-15, 2010
1University of Cape Town, South Africa ([email protected])
This study presents a work flow for quantitative interpretation of sonic and seismic data. Measured data collected at the point of logging can be fraught with errors that can lead to wrong interpretation. Examples of such data are the shear wave velocity, and the compressional wave velocity.
The measured shear wave and compressional wave velocity log
may contain errors that are due to drilling conditions, mud invasion, etc. They may also contain cycle skips and might have a lot of missing data and information. It is the poor quality of this type of
log
that has often made
well
log
analysis
companies and
log
interpreters neglect the measured shear wave
log
and subsequently generate or create an estimated shear wave
log
which they use for interpretation and modeling to check how the amplitudes vary with increasing offsets, among other uses.
The work flow presented in this study considers the effect of working with the measured data, a reprocessed shear wave log
and a locally estimated shear wave
log
. Specific correction procedures for invasion of the logs was done and synthetic seismograms were created for each type after correction for comparison to 3D seismic data.
The results of this study suggest that oil-based mud invasion can cause significant problems to sonic logs. It also suggests that, if a shear wave log
is of low or bad quality, a reprocessed shear wave
log
would be better for interpretation and modeling rather than a locally calibrated shear wave
log
or an estimated shear wave
log
using global predictions. The conclusion is evident from the synthetics generated using the measured shear wave data and the estimated shear wave data.
Figure 1 shows the origin of the problem to be solved. It is evident that the shear wave velocity (Vs) is of a poor quality while the compressional wave velocity (Vp) is of a good quality. However, the above shear wave velocity log
was reprocessed to obtain a better Vs and this “better Vs”, hereafter refered to as the “Measured Vs”, is compared with another Vs which is generated from the Vp, after correction of the Vp for invasion. The Vs generated in the latter case is hereafter refered to as the “Estimated Vs”. Answers to the following questions would enable us to distinguish between two kinds of shear waves that are used in industry.
Questions:
● Why are there gaps in the measured Vs?
● Should we discard it even if it appears to be good over the reservoir zone?
● Have the logs been invaded, and if so, what is the extent of invasion?
● What is the difference between the original Vs and the reprocessed Vs?
● How can we estimate a Vs from the Vp and what constants must be used?
● Which is better and which would give a true representation of the subsurface? Is it the
Measured (Reprocessed) or Estimated Vs ?
Copyright � AAPG. Serial rights given by author. For all other rights contact author directly.
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The density, gamma and sonic logs cannot indicate whether or not there was invasion of the sandstones by the oil-based mud which was used for drilling. Hence, the resistivity
Figure 2 shows how the invading fluid sweeps away the reservoir fluid during drilling. This invasion is caused by relative pressure difference between the borehole pressure and formation pressure. The effect is to change resistivity, density, electric potentials, sonic velocities, and other logs which may be reading the invaded zone. Oil based mud (OBM) filtrate invasion correction is more difficult than water based mud (WBM) filtrate invasion correction due to the fact that one cannot easily determine the type of invasion profile. Also one needs to consider the type of saturation in the water sands because we have a case of OBM filtrate with brine, unlike brine filtrate with brine in WBM. The oil based mud filtrate does not completely mix with the formation brine, so one may assume a kind of “patchy saturation” for which treatment is different from the “effective fluid behavior” (Mavko et al., 2003). In a recent study by Carr et al. (2004) on oil based mud invasion, they showed the possible kinds of invasion profiles (see Figure 3) which may be present in both hydrocarbon saturated sandstones and water or brine saturated sandstones. Rxo and Rt are the resistivities measured in the shallow and deep zones respectively. Sw is computed from Rt, and Sxo is computed from Rxo; Swirr is the irreducible water saturation, which is always present in the pores of the sandstones.
From the resistivity
Two main models were considered namely the “Measured Shear Wave Model” and the “Estimated Shear Wave Model”. For both models, the extent of invasion of the density and sonic partially invaded.
Before correcting the velocities, the density
1) Calculation of porosity - from the measured density 2) Fluid substitution, i.e. obtaining the density of the in situ state, hereby referred to as the “Corrected Density”.
Measured Shear Wave Model ● Import Measured Shear Wave Velocity ● Perform fluid substitution using Gassmann's relations to obtain the saturated bulk moduli of the new fluid saturated states, i.e. oil in Oil-saturated sandstones and brine in Brine-saturated sandstones. ● Calculate the corrected Vp from the new bulk modulus. ● Calculate the new Vs (corrected Vs) from the new shear modulus. ● Using the corrected density, Vp and Vs, create synthetics for the “Measured Model” for comparison with the real seismic data.
Estimated Shear Wave Model ● Import the Measured Compressional Wave Velocity (Vp) ● Use the modified form of Gassmann's relations to obtain the P-wave moduli of the initial fluid saturated sandstones. ● Perform fluid substitution in order to get the corrected Vp of the respective fluid saturated states, i.e. oil or brine. ● A crossplot of the original Vp and Vs is used to generate “fitting” constants. ● Use the “fitting” constants to estimate a Vs using the Greenberg-Castagna algorithm. ● Using the Corrected Density, corrected Vp and estimated Vs, create synthetics for the Estimated Model for comparison with the real seismic data. Finally compare the synthetics from both models to choose the best fit.
Simmons and Backus (1994) showed that primaries-only Zoeppritz modeling of thin layers can be very misleading and that synthetic seismograms obtained by use of a linearized approximation (Aki and Richards, 1980) to the Zoeppritz equations to describe the reflection coefficients are more accurate than those obtained by use of the exact Zoeppritz reflection coefficients.
Using the Aki and Richards algorithm, still in the same reservoir zone on the Measured Shear Wave Model, we obtain what is shown in Figure 5. The long offset reflection events on the Aki-Richards gather look more like the in situ gather than do those on the Zoeppritz gather.
The conclusion can be drawn that the measured S-wave
Aki, K., and P. Richards, 1980, Quantitative seismology: Theory and Methods, v. I, 557 p.; v. II, 373 p. W.H. Freeman and Co., San Francisco. Web accessed 11 January 2011, http://journals.cambridge.org/action/displayAbstract;jsessionid=230614E94C835C30AAE86E9FC5A897BF. tomcat1?fromPage=online&aid=4522584
Carr, M.B., M. Ascanio, M. Smith, and J. Walls, 2004, The use of fluid substitution modelling for correction of oil based mud filtrate invasion in sandstone reservoirs: 74th Annual SEG International Meeting, Expanded Abstracts, Biographies, v. 1, p. 306-309.
Gassmann, F., 1951, Uber die elastizitat poroser medien: Veirteljahrsschrift der naturforschenden gesellschaft in Zurich, v. 96, p. 1-23.
Mavko, G., C. Chan, and T. Mukerji, 1995, Fluid substitution: Estimating changes in Vp without knowing Vs, Geophysics, v. 60, no. 6, p. 1750-1755.
Mavko, G., T. Mukerji, and J. Dvorkin, 2003, The rock Physics Handbook, Tools for seismic http://www.amazon.ca/Rock-Physics-Handbook-Seismic-
Simmons, J., and M.M. Backus, 1994, AVO modeling and the locally converted shear wave, Geophysics, v. 59, no. 9, p. 1237-1248.
Walls, J., and M.B. Carr, 2001, The use of fluid substitution modeling for correction of mud filtrate invasion in sandstone reservoirs, 71st Annual International Meeting, SEG, Expanded Abstracts, p. 385-387.
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