SUMMARY: Elastic full waveform inversion (EFWI) can, theoretically, give high-resolution estimates of the subsurface. However, in practice, the resolution and illumination of EFWI are limited by the bandwidth and aperture of seismic data. The often-present wells in developed fields as well as some exploratory regions can provide complementary information of the target area. We, thus, introduce a regularization technique, which combines the surface seismic and well log data, to help improve the resolution of EFWI. We use deep neural networks to learn the statistical relations between some selected features of the inverted model and the facies interpreted from well logs. The selected features are the means and variances of the inverted velocities defined within Gaussian windows. Using multiple fully connected layers, we train our neural networks to identify the relation between the means and variances at the well location and those from the inverted model. The network is used to map the means and variances extracted from the well to the whole model domain. We then perform another EFWI in which we fit the predicted data to the observed ones as well as fit the model over a Gaussian window to the predicted means and variances. The tests on synthetic and real seismic data demonstrate that the proposed method can effectively improve the resolution and illumination of deep-buried reservoirs, which often encounter poor illumination from seismic data.

Elastic full-waveform inversion (FWI) provides a better description of the subsurface information than those given by the acoustic assumption. However, it suffers from a more serious cycle-skipping problem compared with the latter. Reflection waveform inversion (RWI) is able to build a good background model, which can serve as an initial model for elastic FWI. Because, in RWI, we use the model perturbation to explicitly fit reflections, such perturbations should include density, which mainly affects the dynamics. We applied Born modeling to generate synthetic reflection data using optimized perturbations of the P- and S-wave velocities and density. The inversion for the perturbations of the P- and S-wave velocities and density is similar to elastic least-squares reverse time migration. An incorrect background model will lead to misfits mainly at the far offsets, which can be used to update the background P- and S-wave velocities along the reflection wavepath. We optimize the perturbations and background models in an alternate way. We use two synthetic examples and a field-data case to demonstrate our proposed elastic RWI algorithm. The results indicate that our elastic RWI with variable density is able to build reasonably good background models for elastic FWI with the absence of low frequencies, and it can deal with the variable density, which is required in real cases.

Conventional full-waveform inversion (FWI) based on the least-squares misfit function faces problems in converging to the global minimum when using gradient methods because of the cycle-skipping phenomena. An initial model producing data that are at most a half-cycle away from the observed data is needed for convergence to the global minimum. Low frequencies are helpful in updating low-wavenumber components of the velocity model to avoid cycle skipping. However, low enough frequencies are usually unavailable in field cases. The multiplication of wavefields of slightly different frequencies adds artificial low-frequency components in the data, which can be used for FWI to generate a convergent result and avoid cycle skipping. We generalize this process by multiplying the wavefield with itself and then applying a smoothing operator to the multiplied wavefield or its square to derive the nonlinearly smoothed wavefield, which is rich in low frequencies. The global correlation-norm-based objective function can mitigate the dependence on the amplitude information of the nonlinearly smoothed wavefield. Therefore, we have evaluated the use of this objective function when using the nonlinearly smoothed wavefield. The proposed objective function has much larger convexity than the conventional objective functions. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to that of the conventional FWI except for the adjoint source. We progressively reduce the smoothing width applied to the nonlinear wavefield to naturally adopt the multiscale strategy. Using examples on the Marmousi 2 model, we determine that the proposed FWI helps to generate convergent results without the need for low-frequency information.

Building subsurface models is a very important but challenging task in hydrocarbon exploration and development. The subsurface elastic properties are usually sourced from seismic data and well logs. Thus, we design a deep learning (DL) framework using Vision Transformer (ViT) as the backbone architecture to build the subsurface model using well log information as we apply full waveform inversion (FWI) on the seismic data. However, training a ViT network from scratch with limited well log data can be difficult to achieve good generalization. To overcome this, we implement an efficient self-supervised pre-training process using a masked autoencoder (MAE) architecture to learn important feature representations in seismic volumes. The seismic volumes required by the pre-training are randomly extracted from a seismic inversion, such as an FWI result. We can also incorporate reverse time migration (RTM) image into the seismic volumes to provide additional structure information. The pre-training task of MAE is to reconstruct the original image from the masked image with a masking ratio of 75%. This pre-training task enables the network to learn the high-level latent representations. After the pre-training process, we then fine-tune the ViT network to build the optimal mapping relationship between 2D seismic volumes and 1D well segments. Once the fine-tuning process is finished, we apply the trained ViT network to the whole seismic inversion domain to predict the subsurface model. At last, we use one synthetic data set and two field data sets to test the performance of the proposed method. The test results demonstrate that the proposed method effectively integrates seismic and well information to improve the resolution and accuracy of the velocity model.

Detection of the property changes in the reservoir during injection and production is important. However, the detection process is very challenging using surface seismic surveys because these property changes often induce subtle changes in the seismic signals. The quantitative evaluation of the subsurface property obtained by full-waveform inversion allows for better monitoring of these time-lapse changes. However, high-resolution inversion is usually accompanied with a large computational cost. Besides, the resolution of inversion is limited by the bandwidth and aperture of time-lapse seismic data. We have applied a target-oriented strategy through seismic redatuming to reduce the computational cost by focusing our high-resolution delineation on a relatively small zone of interest. The redatuming technique generates time-lapse virtual data for the target-oriented inversion. Considering that the injection and production wells are often present in the target zone, we can incorporate the well velocity information with the time-lapse inversion by using regularization to complement the resolution and illumination at the reservoir. We use a deep neural network to learn the statistical relationship between the inverted model and the facies interpreted from well logs. The trained network is used to map the property changes extracted from the wells to the target inversion domain. We then perform another time-lapse inversion, in which we fit the predicted data difference to the redatumed one from observation, as well as fit the model to the predicted velocity changes. The numerical results demonstrate that our method is capable of inverting for the time-lapse property changes effectively in the target zone by incorporating the learned model information from well logs.