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same effect at a much smaller scale leads to


“ ground roll” noise in surface seismic surveys. In 1924, Stoneley looked at waves propa- gating at the interface between two solids and found a similar type of surface wave.5


The


R eceiver array


The waves traveling at the fluid- borehole interface are nonetheless known as Stoneley waves. In other areas of geophysics, such as marine seismic surveys, waves traveling at a fluid-solid interface are called Scholte or Scholte-Stoneley waves.7


particular case corresponding to a fluid-filled borehole, that is, the interface between a solid and a liquid, was described not by Stoneley, but by Scholte.6


A Stoneley wave appears in nearly every monopole sonic log. Its speed is slower than the shear- and mud-wave speeds, and it is slightly dispersive, so different frequencies propagate at different speeds.


Transmitter


The decay of Stoneley-wave amplitude with distance from the interface is also frequency- dependent; at high frequencies, the amplitude decays rapidly with distance from the borehole wall. However, at low frequencies— or at wave-


Z one of alteration


U naltered formation


> Ray tracing using Snell’ s law to m odel ray paths. Here, ray s are traced through a form ation that has radially vary ing velocity in a zone of alteration. Velocity is low er near the b orehole and grow s larger w ith distance, a situation that arises w hen drilling induces near-w ellb ore dam age. Ray s traveling to the receivers nearest the transm itter travel only through the altered zone ( dark


b row n) , and ray s traveling to distant receivers sense the velocity of the unaltered form ation ( light b row n) .


spacing and near-wellbore altered-zone thick- ness and velocity contrast (above). In addition, ray tracing is used in inversion techniques such as tomographic reconstruction, which solves for slowness models given arrival-time information. After the P and S head waves, the next waves to arrive at the receivers from a monopole source are the direct and reflected mud waves. These are followed by trapped modes and interface waves that owe their existence to the cylindrical nature of the borehole. Trapped modes arise from multiple internal reflections inside the borehole. Wavefronts of particular wavelengths bouncing between the walls of the borehole interfere with each other constructively and produce a series of resonances, or normal modes. Trapped modes are not always seen on logs and may be affected by borehole condition. In slow formations, trapped modes lose part of their energy to the formation in the form of waves that


radiate into the formation. These are called leaky modes, and propagate at speeds between P and S velocities. Leaky modes are dispersive, meaning their different frequency components travel at different speeds.


Stoneley Waves


The last arrivals from a monopole source are interface, or surface, waves. Surface waves were first suggested by Lord Rayleigh in 1885 .4


He


investigated the response at the planar surface of an elastic material in contact with a vacuum and found that a wave propagated along the surface with particle motion that decreased in amplitude with distance from the surface— a property called evanescence. Rayleigh’s findings predicted the existence of waves that propagate along the Earth’s surface and give rise to the devastating shaking caused by earthquakes. The


Transmitter


> The Stoneley w ave, traveling at the interface bet w een the bor ehole and the form ation. The Stoneley w ave is dispersive and its particle


m otion is sy m m etric ab out the b orehole ax is. At low freq uencies, the Stoneley w ave is sensitive to form ation perm eab ility . Waves traveling past perm eab le fractures and form ations lose  uid, and viscous dissipation causes attenuation of


w ave am plitude and an increase in w ave slow ness. At open fractures, Stoneley w aves are b oth re ected and attenuated. Red arrow s in the center of the b orehole sy m b olize Stoneley -w ave am plitude.


P ermeable formation


Attenuated and slowed down


Cond ition R eceiver E f f e c t


Attenuated R eflected


Stoneley wave


36


Oilfield Review


F racture


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