Modeling of Low Frequency Stoneley Wave Propagation in an Irregular Borehole

This paper describes a propagator matrix formulation for the problem of the Stoneley wave propagation in an irregular borehole. This is based on a simple one-dimensional theory that is possible for the low frequency Stoneley wave, because it is a guided wave with no geometrical spreading in the borehole. The borehole and the surrounding formation are modeled by multi-layers discretized along the borehole axis, then the propagator matrices at each boundary are calculated. The mass balance boundary condition is introduced to express an interaction of the Stoneley wave at the interfaces which include radius changes. We have used the method to investigate the reflection and the transmission characteristics of the Stoneley wave with several models. The results are consistent with the results obtained by other existing modeling methods such as the finite difference method and the boundary integral method. The calculation speed is much faster than those of the other methods. We have applied the method to the field data to simulate the synthetic iso-offset records and have compared them with the actual field records. The results show a good agreement in the major reflections due to the washout zones and an important disagreement in the reflections related to the fractures. This result suggests the possibility of distinguishing the fracture induced reflections from others.