The first step towards FWI is to have an initial velocity model that can predict the waveforms within half the dominant period for the data (Virieux and Operto, 2009). Usually, the starting velocity model for FWI is built by reflection tomography, but due to the deficiency of coherent signals in hardrock seismic data, the method is certainly out of question. FAT has proven to be successful in few past case studies done in the hardrock environment; therefore we decided to use FAT for building the starting velocity model (Singh et al., 2019; Bräunig et al., 2020). Approximately 1.1 million traces were semi-automatically picked and manually corrected. We performed FAT using the inversion framework of Zhang and Toksöz (1998) implemented in the Geotomo TomoPlus software. We used all the shots and receivers from the 3D survey to build the starting velocity model. The grid spacing for forward modelling was kept at 10×10×5 m while the inversion was performed with a grid spacing of 20×20×5 m. A root-mean-squared (rms) value of approximately 5 m s-1 was obtained in 10 iterations. The FAT velocity model was resampled to a 10 m grid size as final output (411×231×151 cells). The upper boundary of the velocity model is 250 m a.s.l. All the velocity models and subsequent depth images shown later in this article have the same configuration. Figure 2 shows horizontal slices through the FAT velocity model masked by the ray coverage. A highly variable near-surface velocities are observed in the NE part of the model due to the presence of an old tailing dam (Fig. 2b). Overall high velocities can be observed in the shallower part of the model with velocity details restricted to only first few tens of metres below the Earth's surface (compare Fig. 2b, c). However, some degree of velocity variation is observed at the basement level too (Fig. 2d). The velocities obtained towards the end of profile P1 (see Fig. 2a for location) are poorly constrained due to the one-sided ray propagation (no sources), although we still used this section of data to complement the illumination in the main survey area. We checked the quality of our FAT model by inspecting calculated first-arrival travel times with the picked first arrivals for different shot gathers, assuring that majority of the traces are not cycle-skipped. We used a smoothed version of the model for forward modelling, to avoid any strong heterogeneities produced by travel-time inversion and thus allowing a smooth energy propagation in depth. The smoothing was done by splitting the velocity model in two parts: top part with depth range between 0–250 m and bottom part between 250–1500 m. A Gaussian smoothing was applied with a shorter operator length on the top part to preserve the overall velocity variations. A larger operator length was used on the bottom part as the velocity model was not exhibiting detailed structures.

If we consider Earth as a non-attenuating homogenous medium, we can start FWI from the raw data without any significant signal preprocessing. However, in real conditions, some signal processing is required to improve the SNR, especially at low frequencies, or to balance the frequency content. For acoustic FWI, it is also important to eliminate elastic effects, such as the surface waves and normalise the amplitudes such that the original amplitude vs. offset (AVO) is discarded. Our preprocessing is mainly focused on preserving the early arrival energy and improved signal coherency (compare Fig. 3a and b). A minimum-phase conversion was performed first. We did not apply any static corrections which are usually applied during reflection processing of land data in order to account for the weathered layer (refraction statics). We did not want to introduce any bias in the recovered velocity model related to prior statics application, even though our vertical grid size (10 m) is of the order of the thickness of the low-velocity weathered layer (10–20 m), so this layer is highly unlikely to be recovered properly during the FWI. In order to reduce the effect of the weathered layer on the source estimation, surface-consistent trace amplitude scaling was used to average shot and receiver amplitudes due to variable near-surface conditions (Table 1). Then, a predictive deconvolution was applied to enhance the first arrivals, followed by FX deconvolution for improved coherency and band-pass filtering (2–6–25–40 Hz) based on different frequency-band testing. A mute function was designed to remove the shear and surface waves. Finally, a trace normalisation was applied to provide equal representation to all offsets, effectively removing any viscoelastic responses. A comparison of raw data and data after pre-processing is shown in Fig. 3. One can note that the first arrivals are much better preserved with higher SNR, and improved coherency is achieved.

Inversion parameters such as choice of optimisation algorithm, type of gradient preconditioning and regularisation, data weighting and source wavelet estimation were thoroughly tested and fine-tuned accordingly. We inverted for the P-wave velocity keeping a constant density during the inversion (2850 kg m-3). Based on different frequency tests on the highly energetic early arrivals and their SNR response, we observed that these arrivals are becoming prominent only around 16–18 Hz. In order to relax the condition imposed on the starting model accuracy to prevent cycle-skipping, the actual frequency band being inverted started at 6 Hz and continued to 25 Hz. We used the SD optimisation algorithm with an approximate Hessian. L-BFGS optimisation has also been tested, but due to its higher rate of convergence, we encountered several artefacts yielding instability of the inversion. Also due to the presence of a lot of noise in the data, we decided to use SD optimisation as its convergence rate is much slower and it is less likely to be trapped in the local minima. Both the forward modelling and inversion were carried out on a uniform grid spacing of 10 m in each direction – the same as for the resampled starting velocity model. We used a smoothed model topography obtained from the lidar survey in the area. We modelled a vertical single force source and vertical single force receivers (vertical geophones) without a free surface. Data weighting and muting is implemented implicitly in the code.

As FWI is computationally very intensive, we need to find a good balance between processing power and memory bandwidth. In this study, we manually chose a subset of 216 good-quality shots out of more than 1000 shots available in the survey due to computational limitations (this was the amount fitting to 36 cluster nodes with 24 cores each, such that 4 cores were dedicated to one shot point). The criteria for the selection of shots were good SNR, clear first arrivals and uniform distribution within the survey area (red stars marked in Fig. 2a). Although we manually picked the preferred 216 shots, at a later stage we also performed the tests with random shot selections to quantify the effect of the shot grouping.

Since we aimed at using early arrivals only to build our velocity model, we designed an external mute function to restrict the direct and shear waves. This is required to remove the part of data that contains the elastic effects; otherwise, the acoustic approximation will fail. Since trace normalisation is already applied to the data, we do not preserve amplitude variation with offset information anymore. To drive the model updates in the deeper section, we used data weighting of the misfit function equivalent to the absolute offset value of the trace.

The final part to start with the inversion was the estimation of the source wavelet following the linearised method of Pratt (1999). During FWI of land data several factors like source coupling, receiver coupling, local ground condition, statics, etc. significantly affect the characteristic of the source wavelet, making it difficult to derive the correct source signature for the modelling. Here we essentially tested two strategies: (i) a single average source wavelet estimated using all the shots (216) (see estimated source wavelet in the lower-right side of Fig. 7) and (ii) individual source wavelets for each shot point (Fig. 8). In both cases, source wavelets resembled the minimum-phase equivalent of the Vibroseis sweep signature. Before being used in FWI, source wavelets were bandpass filtered and scaled to match the amplitude of the observed data. However, after several tests with individually estimated source wavelets, we concluded that scaling and handling each wavelet separately to match the amplitudes of the observed data was difficult and was producing artefacts in the velocity model. Therefore, we decided to use the average source wavelet which was also additionally scaled to match the observed data. We also tested the scenario where the average source wavelet is re-estimated after every 10 FWI iterations. However, there were no significant changes in the estimated source wavelet signature from one cycle to another. In the end, we observed that this exercise did not contribute to a significant change in the final velocity model as well compared to the approach where the wavelet is kept the same for the whole inversion. Therefore, we decided to follow the latter approach. All the results presented afterwards in this article are produced using this approach.

Due to computational limitations, we were unable to process all the 1000 shots from the survey at the same time. The baseline dataset is comprised of the 216 manually selected best-quality (and relatively uniformly distributed) shots. In the next stage, three different subsets of 216 randomly selected shots with a uniform distribution within the survey area were used in FWI (Fig. 4). In this section, we present the results obtained from both approaches. We started with the general approach of FWI. As FWI is a local optimisation technique, we used the velocity model produced from FAT as a starting model (Fig. 5a). We used a single source wavelet, the constant density of 2850 kg m-3, SD optimisation algorithm and smoothed Hessian to build a P-wave velocity model. We checked the quality of the velocity models based on data fitting, wavelet estimation, drop in the cost function, comparison with other results obtained from direct measurement in boreholes and visualisation.

Smoothing is applied in each iteration to the gradient before it is scaled to obtain model perturbations which are then added to the current velocity model. An approximately ∼18 % reduction in the cost function is observed in the first 40 iterations after which the drop was still monotonously decreasing but negligible (light blue line, Fig. 4). From Fig. 5, we can infer that the velocity details in FAT (Fig. 5a) are restricted to the first few tens of metres from the surface; otherwise, it is almost a 1D velocity model in depth. On the other hand, the velocity model from FWI (Fig. 5b) is characterised by velocity details to ∼1000 m in depth.

Further, in order to validate our inversion strategy, we randomly selected three different subsets each containing 216 shots with uniform distribution in the survey area as previously done. The idea here was to see the effect of a random selection of shots compared to the manual selection of best quality shots on the inversion strategy. A large difference in the velocity model produced from both approaches would suggest that more emphasis on data selection has to be given, and a more detailed investigation on inversion strategy is required. Here, we kept the same configuration as followed in the previous section to produce our preferred model. The velocity model is produced for all the three subsets with a similar drop in cost function and convergence (see comparison in Fig. 4). The velocity model obtained from a subset of randomly selected shots (subset-2, Fig. 4) is shown in Fig. 6a (compare with Fig. 5b). Both the velocity models show similar characteristics in terms of different features that can be observed (compare marked arrows, Figs. 5b and 6a). Figure 6b and c show velocity perturbation for two different subsets, i.e. subset-1 and subset-2 with respect to the model produced from a manual selection of shots (Fig. 5b). We observed an average velocity difference of around ±50 m s-1 (Fig. 6b and c, also for subset-3) in the area which is well illuminated, while a large difference is observed where sampling is poor or velocity model is less-constrained (i.e. on the edges of the survey). A histogram plot shown in Fig. 6d and e (for models shown in Fig. 6b and c, respectively) is also produced to understand the velocity perturbation quantitatively. One can note that the majority of the points are clustered within the displayed range (±50 m s-1), whereas the total number of points outside this range constitutes less than ∼6 % of the total points. These comparisons indicated that our inversion strategy is effective and stable, and it does not rely substantially on the shot selection as long as their uniform areal distribution is followed.

In order to check the accuracy of the velocity model, we assess the data fitting between observed and synthetic gathers, wavelet estimation and cost-function drop. We also confronted our velocity model with a priori information and other available results in the survey area. Here, we are presenting the result assessment for our preferred velocity model only (Fig. 5b).

Data fitting of common-shot and common-offset (CO) sections between observed data and synthetics produced from the FWI velocity model is shown in Fig. 7. A CO section is produced by selecting different source–receiver pairs within a fixed offset distance. In comparison to a common-shot gather where only a single shot can be evaluated at a time, CO sections enable displaying information from all the inverted shots at once. This way all the shots can be evaluated simultaneously for different offsets. We computed the CO section with a bin width of 50 m and bin-centred sections produced every 250 m. Final CO sections are produced for the data range used during the FWI after applying linear-moveout velocity of 5500 m s-1 and a bulk shift of 100 m s-1. A common-shot gather comparison between observed data and synthetics is shown in Fig. 7a. Based on different shot gather comparisons, we noted that the overall fitness of the data is good with some localised areas susceptible to cycle-skipping in short to mid-offset ranges. For far offset traces, the velocity model was only able to find a partial fit in some cases, such as shown by the yellow arrow in Fig. 7a. It is most likely inherited from the starting model where it was locally unable to provide a kinematically good fit to first arrivals. Three different CO sections for bin-centred at 250, 1000 and 1500 m are shown in Fig. 7b–d. Different CO sections at various ranges show overall good data fit for at least the first cycle of the waveforms for a majority of shot points. Local cycle-skipped positions are marked by yellow arrows in Fig. 7b–d for different shot points. It is likely to be inherited by the fact that statics correction had not been applied during the data preprocessing prior to FWI.

Another diagnostic of the robustness of the FWI-derived velocity model is the quality of the source estimation in the final model. In Fig. 8, we are showing wavelet estimation for all 216 shots for the initial model obtained from FAT (Fig. 5a) and FWI velocity model (Fig. 5b). It can be inferred that the estimated wavelets from the FWI velocity model produce more coherent signatures with better amplitude responses. Shot locations for which low-amplitude wavelets are estimated (marked by red arrows) belong to the area where the tailing dam is located (see Fig. 2b for location).

Another way of assessing the quality of the velocity model is to check the cost function convergence with each iteration. From Fig. 4, for all the cases, a drop-in cost function is observed until the 40th iteration by large, after which the convergence was minimal. To quantify the contribution of individual shot gathers to cost function, we calculated root-mean-squared error (RMSE) on a trace-by-trace basis. In Fig. 9, we present the RMSE plots for two shot gathers. We show the evolution of the data fit for the starting model (0th iteration), after the 10th iteration (up to which the most significant drop in the cost function is observed, Fig. 4) and at the 50th iteration. An initial observation of the RMSE maps shows that the drop in the cost function is mainly driven by the traces present in the near-to-intermediate offset ranges (compare traces marked by blue arrows for different iterations in Fig. 9). The traces present in the intermediate-to-far offset range have comparatively less contribution in the reduction of cost function. It might be due to the fact that the starting model was not able to produce the kinematic fit to first arrivals at far-offset ranges as well as because they are least-constrained due to their presence at the edge of the survey.

The data used for RTM were processed in a similar way as discussed in Hloušek et al. (2021). The processing was mainly aiming at the suppression of surface waves and improvement of reflected signals associated with the mineralisation (Table 2). Refraction static corrections were calculated and applied to the data in two different ways. In the case of migration using the constant velocity model, a generalised refraction travel-time inversion approach was used (GLI3D, Hampson and Russell, 1984). In the case of RTM with the FAT and FWI velocity models, a tomostatics approach was used with the same velocity model as used as starting model for FWI (Fig. 5a); however, only the residual part of the statics was actually applied to the data.

We used a RTM algorithm implemented in Shearwater Reveal software to run 3D RTM using our 3D dataset consisting of 1044 shots. We used a minimum-phase Ricker wavelet with a peak frequency of 70 Hz as a source wavelet based on an average medium velocity of 6000 m s-1. An isotropic wave propagation was modelled with fourth order in space and second order in time using finite-difference operators. A convolutional perfectly matched layer (CPML) boundary condition was used with 12 grid points in thickness and 8 grid points for padding at the boundaries. A standard zero-lag cross-correlation was used as the imaging condition. The inline and crossline aperture was fixed to 1 and 1.8 km, respectively. A 10 % aperture taper was used to suppress the migration noise on the edges. The time step and grid size were automatically adapted to the velocity model (see Table 3). However, migrated shot gathers were produced with a grid spacing of 10 m, the same as the input velocity model. The final RTM stack was produced by accumulative stacking of all migrated shot gathers. Only a low-cut filter was applied to the stack to remove the near-surface low-frequency noise typical for many RTM implementations. RTM was run in parallel mode at our local cluster. It took ca. 8.5 h to produce the final result for the constant velocity model using 7 nodes of Intel(R) Xeon(R) processor, each containing 24 cores. For the FAT and FWI case, it took ca. 20.8 and 28.5 h respectively.

RTM with a constant velocity model was able to highlight a dipping reflector in the SE direction, which follows a curved nature in the SW direction with a hint of cross-cutting fault dipping in opposite direction (see yellow arrows in Fig. 10a). On the other hand, RTM with the FAT velocity model further improves the reflectivity of mineralisation and clearly highlights the termination of the dipping reflector by a cross-cutting fault (Fig. 10b). The depth image otherwise is very noisy in the near-surface area. RTM with FWI velocity model produces a depth image with much better focussing of the dipping reflector and a clear representation of the cross-cutting fault, which appears much deeper in depth towards the west and to the surface in the east (Fig. 10c). The depth image with the FWI velocity model also highlights other reflectors, normal and cross-cutting faults in the near-surface section, which is significantly more noisy for the previous two results. The image also has less migration noise, which comprehends the fact that a detailed velocity model can be a great asset in producing accurate subsurface images.

To further understand the depth extent and geometrical nature of the dipping reflector associated with mineralisation, the 3D cube was investigated in more detail. Figure 11 shows successive slices in depth, crossline and inline direction. In the depth slices (Fig. 11a–e, left panels), the reflectivity related to the mineralisation can be tracked comfortably down to the depth of 1000 m. Similarly, depth images along the crossline direction (middle panels, from NW to SE direction) show the curved nature of the mineralisation clearly in the SW direction, which was earlier believed to be flat. After almost crossing the middle of the survey area from SW to NE, a second prominent reflector below the mineralisation appears to be in place until the end of the acquisition line in the NE direction (middle panels, Fig. 11d–e). The inline sections (right panels) confirm the progression of the mineralisation at depth until it breaks off at a major cross-cutting fault (Fig. 11c). The extent of the mineralisation can be easily followed from the NW to SE direction.

Offset-domain common-image gathers (CIGs) or surface offset gathers (SOGs) are commonly produced in ray-based migrations to check the quality or update the migration velocity model. In RTM, it is easier to produce angle-domain CIGs than the offset gathers. The implementation that we used to compute SOGs is as described in Yang et al. (2015). All the receiver data were grouped in 100 m wide offset bins. Each of these offset classes is injected and reverse-propagated separately, whereas the source wave field is propagated in its entirety. SOG image output is formed for all offset classes of each shot. Similar operation is performed for all the shot gathers. Supposedly, a good velocity model should result in reflection events being flat across the offset bins in the SOGs. We used same parameterisation to produce SOGs as discussed in Sect. 3.2.3 except that the crossline aperture was reduced to 1 km to save the computational and storage cost of producing SOGs. For example, SOGs for a subset of 20 shots for a constant velocity model and inline/crossline aperture equal to 1 and 2 km took ∼1.5 and ∼14 h of computation time using 40 processors taking storage space equivalent to 17 and 71 GB, respectively. Therefore, we were unable to produce the SOGs using all the shots (>1000); instead we calculated it for the same subset of shot points we used for FWI (Fig. 5b, shot points marked by red stars in Fig. 2a). Figure 12 shows SOGs produced using a subset of 20 shots (for illustration purposes) selected with uniform areal distribution for all the three velocity models: constant velocity model (Fig. 12a), FAT velocity model (Fig. 12b) and FWI velocity model (Fig. 12c). We can note a clear improvement in focusing and the flatness of the reflector marked by an arrow, which indicates that the FWI model is superior to the FAT model.