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STC Coherence W a v e f orm s f rom 3 , 7 6 4 . 8 9 f t


Compressional wave


1 3 1 2 1 1 1 0


9 8 7 6 5 4 3 2 1 1 ,0 0 0 2 ,0 0 0 3 ,0 0 0 Time, µs 3 ,7 6 0 3 0 0 4 ,0 0 0 5 ,0 0 0


Shear wave


Stoneley wave


4 0


Slowness µs/ ft


3 4 0


2 0 0


1 0 0 1 ,0 0 0 2 ,0 0 0 3 ,0 0 0 Time, µs 3 ,7 7 0


> Slow ness-tim e-coherence ( STC) processing for m onopole arrivals. Waveform s at a given depth ( top left) are scanned over tim e w indow s and over a range of angles— called m oveouts, w hich are related to slow ness. When the signals on the w aveform s w ithin the w indow are b est correlated, coherence is m ax im um . An STC plot for that depth ( b ottom left) display s color-coded coherence in the slow ness-tim e plane, w ith m ax im um coherence in red. The coherence values are proj ected onto a vertical strip along the slow ness ax is and then display ed as a thin horizontal strip at the appropriate depth on the STC proj ection log ( right) . A slow ness log for each w ave is generated b y j oining the coherence m ax im a at all depths.


4 ,0 0 0 5 ,0 0 0


Dipole Sources So far, the discussion has focused on waves generated by monopole sources, but for some applications, a different type of source is required. For example, in slow formations, where monopole sources cannot excite shear waves, a dipole source can be effective. The dipole source primarily excites flexural waves, along with compressional and shear head waves. The motion of a flexural wave along the borehole can be thought of as similar to the disturbance that travels up a tree when someone standing on the ground shakes the tree trunk. The analogy works better if the tree trunk is fixed at the top and has constant diameter. Typically, a tool designed to generate flexural waves will contain two dipole sources oriented orthogonally along the tool X- and Y-axes. The dipole transmitters are fired separately. First, the X-dipole is fired, and a flexural waveform is recorded. Then, the Y-dipole is fired, and a separate measurement is taken. The flexural wave travels along the borehole in the plane of the dipole source that generated it. The particle motion of the flexural wave is perpendicular to the direction of wave propagation, similar to S-waves, and flexural-wave slowness is related to S-wave slowness. Extracting S-wave slowness from flexural-wave data is a multistep process. Flexural waves are dispersive, meaning their slowness varies with frequency (below). In many sets of flexural waveforms, it is possible to see the wave shape change across the receiver array as different frequency components propagate at different speeds. Because the wave shape


1 3 1 1


The method starts with an assumed arrival time and slowness for each wave type and searches the set of waveforms for the time and slowness that maximize coherence. The graph of coherence for different values of slowness and time is called a slowness-time-coherence (STC) plot, from which local maxima of the coherence contours can be identified (above). Maxima


Slownesses can be estimated in a robust way with minimal human intervention using a signal- processing technique that looks for similarity— known mathematically as semblance, or coherence— in waveforms across the receiver array.1 0


corresponding to compressional, shear and Stoneley slownesses plotted for each depth create a slowness log. The two dimensions of an STC plot are compressed into a single dimension by projecting the coherence peaks onto the slowness axis. This vertical strip of color-coded coherences, when plotted horizontally at the appropriate depth, forms an element of an STC- projection log, a standard sonic-logging output. The slowness of each mode is plotted on top of the STC projection.


9 7 5 3 1 1 ,0 0 0 3 ,5 0 0 Time,  s


> Flex ural-m ode w aveform s, show ing a change in w ave shape across the receiver array . In this case, the w ave shape stretches out in tim e from near receiver ( b ottom ) to far receiver ( top) . The change in w ave shape is caused b y dispersion.


6 ,0 0 0


38


Oilfield Review


Slowness, µs/ ft


W aveform number


W aveform number


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