Full-waveform inversion (FWI) is a technique having the potential for building high-resolution elastic velocity models. We proposed to apply this technique to wireline monopole acoustic logging data to obtain the near wellbore formation velocity structures, which can be used in wellbore damage or fluid intrusion evaluation. A 2D FWI using monopole acoustic logging data is presented. The FWI is established in cylindrical coordinates instead of Cartesian coordinates in order to adapt to the borehole geometry. A preconditioner is designed for suppressing the influence of the strong borehole guided waves in the inversion. Synthetic tests demonstrate that high-resoultion elastic velocity profile around borehole can be inverted from monopole acoustic logging data by using the proposed method.

The conventional energy flux density vector indicates the propagation direction of mixed P- and S-wave wavefields, which means when a wavefront of P-wave encounters a wavefront of S-wave with different propagation directions, the vectors cannot indicate both directions accurately. To avoid inaccuracies caused by superposition of P- and S-waves in a conventional energy flux density vector, P- and S-wave energy flux density vectors should be calculated separately. Because the conventional energy flux density vector is obtained by multiplying the stress tensor by the particle-velocity vector, the common way to calculate P- and S-wave energy flux density vectors is to decompose the stress tensor and particle-velocity vector into the P- and S-wave parts before multiplication. However, we have found that the P-wave still interfere with the S-wave energy flux density vector calculated by this method. Therefore, we have developed a new method to calculate P- and S-wave energy flux density vectors based on a set of new equations but not velocity-stress equations. First, we decompose elastic wavefield by the set of equations to obtain the P- and S-wave particle-velocity vectors, dilatation scalar, and rotation vector. Then, we calculate the P-wave energy flux density vector by multiplying the P-wave particle-velocity vector by dilatation scalar, and we calculate the S-wave energy flux density vector as a cross product of the S-wave particle-velocity vector and rotation vector. The vectors can indicate accurate propagation directions of P- and S-waves, respectively, without being interfered by the superposition of the two wave modes.

Full-waveform inversion (FWI) is a technique that has the potential for building high-resolution elastic velocity models. We apply this technique to wireline monopole acoustic logging data to image the near-wellbore formation velocity structures, which can be used in fluid intrusion evaluation. Our FWI workflow is established in cylindrical coordinates instead of Cartesian coordinates to adapt to the borehole geometry. Assuming the acoustic logging tool is centralized and formation properties are azimuthally invariant, we can simplify the problem to 2D in the inversion. Synthetic tests show that the high-resolution P- and S-wave velocity model around the borehole could be successfully inverted using FWI once a reasonable starting velocity model is given. However, borehole FWI differs from seismic FWI in that strong borehole guided waves exist near the borehole wall due to the elastic effects. The borehole guided waves have little sensitivity to velocity away from the borehole wall. In addition, it is difficult to match the waveform of both body waves and guided waves in synthetic data and field data. Therefore, for field data applications, we propose to obtain the formation velocity structures around the borehole by FWI using only the first arrived P waves. Field data tests show that the proposed method is applicable for inverting the P-wave velocity structure around the borehole with a similar resolution compared to ray-tracing tomography. FWI may achieve higher resolution in field applications in the future with better assumptions made in the forward modeling and using more information in the field data.

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