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Vertical seismic profiling data can provide a high‐resolution reservoir image because the receivers are located close to the reservoir and, hence, the wavefield encounters less distortion in the overburden compared to surface seismic data. However, conventional migration of vertical seismic profiling data using only upgoing primary wavefields often suffers from poor illumination, imaging artefacts and low image reliability, especially at image locations away from the well. We propose full‐wavefield migration to image vertical seismic profiling data using the primaries and all orders of surface multiples and internal multiples. The downgoing internal or surface multiples are treated as an additional source of illumination. In full‐wavefield migration, we aim to estimate a high‐resolution reflectivity image of the subsurface with this extended illumination. The algorithm is recursive in depth like conventional wavefield extrapolation‐based migration, however, it incorporates the non‐linear transmission and scattering effects at each depth level. Further, full‐wavefield migration is posed as a constrained least‐squares inversion problem that could be solved using a conjugate gradient method. We propose an iterative full‐wavefield forward modelling engine as the backbone of this inversion scheme. The parameter used in the modelling is subsurface reflectivity. Full‐wavefield modelling iteratively incorporates the non‐linearity of the wavefield due to multiple scattering, where every iteration utilizes one higher order of scattered wavefields to estimate the subsurface reflectivity. In addition, the constrained inversion helps in reducing the extrapolation artefacts and provides a high‐resolution image of the reservoir. In this paper, we discuss the concept of full‐wavefield migration and demonstrate its potential as an imaging tool for vertical seismic profiling data using synthetic examples.

Nowadays, full‐waveform inversion, based on fitting the measured surface data with modelled data, has become the preferred approach to recover detailed physical parameters from the subsurface. However, its application is computationally expensive for large inversion domains. Furthermore, when the subsurface has a complex geological setting, the inversion process requires an appropriate pre‐conditioning scheme to retrieve the medium parameters for the desired target area in a reliable manner. One way of dealing with both aspects is by waveform inversion schemes in a target‐oriented fashion. Therefore, we propose a prospective application of the convolution‐type representation for the acoustic wavefield in the frequency–space domain formulated as a target‐oriented waveform inversion method. Our approach aims at matching the observed and modelled upgoing wavefields at a target depth level in the subsurface, where the seismic wavefields, generated by sources distributed above this level, are available. The forward modelling is performed by combining the convolution‐type representation for the acoustic wavefield with solving the two‐way acoustic wave‐equation in the frequency–space domain for the target area. We evaluate the effectiveness of our inversion method by comparing it with the full‐domain full‐waveform inversion process through some numerical examples using synthetic data from a horizontal well acquisition geometry, where the sources are located at the surface and the receivers are located along a horizontal well at the target level. Our proposed inversion method requires less computational effort and, for this particular acquisition, it has proven to provide more accurate estimates of the target zone below a complex overburden compared to both full‐domain full‐waveform inversion process and local full‐waveform inversion after applying interferometry by multidimensional deconvolution to get local‐impulse responses.

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