An effective scheme of joint migration inversion in the pseudo-time domain

Traditional full-waveform inversion is a non-linear and ill-posed inversion problem. To reduce the non-linearity of it, joint migration inversion (joint migration inversion) was proposed as an alternative. Joint migration inversion tries to minimize the mismatch between measured and modelled reflection data. One key feature of joint migration inversion is its parameterization: two separate parameters, reflectivity (for the amplitudes of reflected events) and propagation velocity (for the phase effects). This separation helps to reduce the non-linearity of the inversion. During joint migration inversion, with the velocity being updated, the reflectors in the updated image are also shifting in depth accordingly, this phenomenon is called depth–velocity ambiguity. This interaction between the two parameters during inversion is desired to keep the image time consistent with the measured data but may lead to non-robustness of joint migration inversion due to the presence of local minima. Therefore, we propose a more robust joint migration inversion scheme, which parameterizes the models with vertical time, termed pseudo-time joint migration inversion. In pseudo-time, the updates of velocity will not result in the associated vertical location changes of reflectors in the estimated image. Instead, the reflectors are mainly getting more focused. One limitation is that the depth-pseudo-time conversion process assumes a simple linear relationship between depth and pseudo-time, which might cause some artefacts in the converted models when there exist strong lateral velocity variations. One subsequent round of depth joint migration inversion is recommended to resolve this issue. We demonstrate the effectiveness of our proposed method with a two-dimensional synthetic example in an extreme scenario, where the initial velocity model is homogeneous, a realistic offshore two-dimensional synthetic example, a two-dimensional field example from the Vøring basin in Norway and a simple three-dimensional synthetic example. In all examples, pseudo-time joint migration inversion manages to recover more reasonable updates in the inverted velocity and invert more focused reflectors in the inverted image, compared to depth joint migration inversion.