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acquired on all sensors at each receiver station to yield four waveforms corresponding to the inline and offline responses at every depth to the two orthogonal dipole transmitters. Next, these waveforms are mathematically rotated to put them in a coordinate system consistent with the directions of maximum and minimum offline waveform energy.1 7


Then, the waveforms corre-


sponding to fast- and slow-shear orientations undergo semblance processing to obtain the fast and slow shear-wave slownesses.1 8


Z ones with


equal fast and slow shear-wave slownesses are isotropic, while zones with large differences between fast and slow shear-wave slownesses are highly anisotropic.


The slownesses of the fast and slow S-waves


and the P- and Stoneley waves— the four slow- nesses that can be measured by sonic logging in an anisotropic medium— are transformed into four anisotropic moduli. These four moduli can almost characterize the simplest of anisotropic media. TIV and TIH media require five moduli to


Inhomogeneity


Formation properties may vary not only with measurement direction, as in anisotropic forma- tions, but also from place to place, in what are called inhomogeneous, or equivalently, hetero- geneous, formations. As with anisotropy, detecting and quantifying inhomogeneity using acoustic waves will depend on the type of formation variation and its geometry relative to the borehole axis. Standard sonic logging can characterize formation properties that vary along the borehole. Early sonic-logging tools run in vertical


be fully characterized. For more complex types of anisotropy, more measurements are required, such as P-waves propagating in different azimuths or inclinations, or S-waves traveling vertically and horizontally. Surface seismic and borehole seismic surveys often can provide this information.


boreholes identified inhomogeneities in the form of boundaries between horizontal layers (see


“ History of Wireline Sonic Logging,” page 32). Other heterogeneities, such as high-permeability zones or open fractures that intersect the borehole, can be detected using Stoneley waves, as described earlier.


Formation properties that vary away from the borehole, or along the radial axis, are evidence of the drilling process and are more difficult to assess. The drilling process removes rock and causes the in-situ stresses to redistribute, or concentrate, around the borehole in a well-known elastic manner.1 9


breaks the rock that


borehole, but also may mechanically damage a volume of rock surrounding the hole.2 0


In addition, drilling not only is removed to form the


This type of


F ast Shear Differential


0 %


Distance from B orehole Center


2 ft 0 1 0 2 5 0 %


G amma R ay


gAP I 1 1 0 0


Distance from B orehole Center


ft 2 0


Slow Shear Differential


2 5 0 %


Distance from B orehole Center


ft 2


Compressional Differential


2 5


damage is called plastic deformation, in contrast to elastic, or reversible, deformation. In addition to plastic deformation, drilling fluid may react with clays, causing swelling and altering near- wellbore velocities. Mud that invades pore space displaces formation fluids that probably have different properties, also altering sonic velocities. Drilling-induced variations may be more gradual than variations across layer interfaces.


17 . Alford RM: “ Shear Data in the Presence of Azim uthal Anisotropy : Dilley , Tex as, ” Ex panded Ab stracts, 5 6th SEG Annual International Meeting, Houston ( Novem b er 2– 6, 19 86) :


4 7 6– 4 7 9 .


Brie A, Endo T, Hoy le D, Codazzi D, Esm ersoy C, Hsu K , Denoo S, Mueller MC, Plona T, Shenoy R and Sinha B:


“ New Directions in Sonic Logging, ” Oil eld Review 10, no. 1 ( Spring 19 9 8) : 4 0– 5 5 .


18. Esm ersoy C, K oster K , William s M, Boy d A and K ane M: X ,4 8 0


“ Dipole Shear Anisotropy Logging, ” Ex panded Ab stracts, 64 th SEG Annual International Meeting, Los Angeles ( Octob er 23 – 28, 19 9 4 ) : 113 9 – 114 2.


K im b all and Marzetta, reference 10.


19 . Wink ler K W, Sinha BK and Plona TJ : “ Effects of Borehole Stress Concentrations on Dipole Anisotropy Measurem ents, ” Geophy sics63 , no. 1 ( J anuary – Feb ruary 19 9 8) : 11– 17 .


X ,4 9 0


20. Wink ler K W: “ Acoustic Evidence of Mechanical Dam age Surrounding Stressed Borehole, ” Geophy sics62, no. 1 ( J anuary – Feb ruary 19 9 7 ) : 16-22.


21. Z eroug S, Valero H-P and Bose S: “ Monopole Radial Pro ling of Com pressional Slow ness, ” prepared for presentation at the 7 6th SEG Annual International Meeting, New Orleans, Octob er 1– 3 , 2006.


> Com pressional and shear radial pro les in an anisotropic inhom ogeneous form ation. The pro le of variation in com pressional slow ness ( Track 4 ) is created b y tom ographic reconstruction b ased on tracing ray s through a m odeled form ation


w ith properties that vary gradually aw ay from the b orehole. The percentage difference b etw een ob served slow ness and slow ness of the unaltered form ation is plotted on color and distance scales to indicate the ex tent of difference aw ay from the b orehole. In these sandstones, identi ab le from the gam m a ray log in Track 2, com pressional slow ness near the b orehole varies b y up to 15 % from far- eld slow ness, and the variation ex tends to m ore than 12 in. [ 3 0 cm ] from the b orehole center. The b orehole is show n as a gray zone. Shear radial pro les show the difference b etw een fast shear-w ave slow ness and far- eld slow ness ( Track 1) and the difference b etw een slow shear-w ave slow ness and far- eld slow ness ( Track 3 ) . Large differences in shear slow ness ex tend out to alm ost 10 in. [ 25 cm ] from the


b orehole center. The radial variation in com pressional and shear velocities is drilling-induced.


22. Sinha B, Vissapragada B, K isra S, Sunaga S, Y am am oto H, Endo T, Valero HP, Renlie L and Bang J :


“ Optim al Well Com pletions Using Radial Pro ling of Form ation Shear Slow nesses, ” paper SPE 9 5 83 7 , presented at the SPE Annual Technical Conference and Ex hib ition, Dallas, Octob er 9 – 12, 2005 .


Sinha BK : “ Near-Wellb ore Characterization Using Radial Pro les of Shear Slow nesses, ” Ex panded Ab stracts, 7 4 th SEG Annual International Meeting, Denver ( Octob er 10– 15 , 2004 ) : 3 26– 3 29 .


23 . Chang C, Hoy le D, Watanab e S, Coates R, K ane R, Dodds K , Esm ersoy C and Forem an J : “ Localized Maps of the Sub surface, ” Oil eld Review 10, no. 1 ( Spring 19 9 8) : 5 6– 66.


24 . Hornb y BE: “ Im aging of Near-Borehole Structure Using Full-Waveform Sonic Data, ” Geophy sics5 4 , no. 6 ( J une 19 89 ) : 7 4 7 – 7 5 7 .


42


Oilfield Review


M easured depth, ft


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