Due to the analogy of wave propagation mechanism between the traditional surface seismic refraction and borehole sonic logging the solutions of the former can be well used to understand better the response of the latter in the near well bore space, which in general is not homogeneous from the geomechanical and hydraulic point of view due to mud invasion and existence of discontinuities. In this paper two-time-distance equations of seismic refraction for the general case of multiple dipping interfaces were revisited. Some examples of applications for correction and analysis of sonic logging data with reference to effects due to borehole deviation, tool tilting, mud invasion and weathering/fracturing etc. are discussed. As an illustration of their applications, a chart was constructed for correction of sonic data regarding the effects of borehole deviation and sonic tilting.


Time-distance equation of seismic refraction is one of the most classical geophysical problems, which is ever-present in any geophysics textbook. The multi-layered time-distance equation has been studied and derived by many researchers. In this study, two solutions are revisited, i.e., by Adachi (1954) and Giao (2003), respectively.

Some of the factors that can affect sonic log measurement are, but not limited to, overbalance drilling, borehole stress concentrations, shale swelling, near wellbore damage and supercharging of permeable formations etc., all of these can alter near-wellbore formation wave velocity. In addition, the wellbore conditions such as borehole fluid, well geometry, well size and verticality of the sonic logging probe can also cause significant effects on sonic measurements.

One can imagine sonic logging as a seismic refraction profile rotated by 900(see Fig. 1). The analogy between a traditional land seismic refraction survey and sonic logging allows the use of the time-distance equation for the former in solving many problems related to the latter, e.g., to quantify the effects of mud type, mud salinity, borehole deviation, tool tilting, and presence of fractures in the near-wellbore zones etc on sonic log data.

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