Obtaining high-resolution models of the earth, especially around the reservoir, is crucial to properly image and interpret the subsurface. We have developed a regularized elastic full-waveform inversion (FWI) method that uses facies as the prior information. Deep neural networks (DNNs) are trained to estimate the distribution of facies in the subsurface. Here, we use facies extracted from wells as the prior information. Seismic data, well logs, and interpreted facies have different resolution and illumination to the subsurface. Besides, a physical process, such as anelasticity in the subsurface, is often too complicated to be fully considered. Therefore, there are often no explicit formulas to connect the data coming from different geophysical surveys. A deep-learning method can find the statistically correct connection without the need to know the complex physics. In our deep-learning scheme, we specifically use it to assist the inverse problem instead of the widely used labeling task. First, we conduct an adaptive data-selection elastic FWI using the observed seismic data and obtain estimates of the subsurface, which do not need to be perfect. Then, we use the extracted facies information from the wells and force the estimated model to fit the facies by training DNNs. In this way, a list of facies is mapped to a 2D or 3D inverted model guided mainly by the structure features of the model. The multidimensional distribution of facies is used either as a regularization term or as an initial model for the next waveform inversion. Our method has two main features: (1) It applies to any kind of distribution of data samples and (2) it interpolates facies between wells guided by the structure of the estimated models. Results with synthetic and field data illustrate the benefits and limitations of this method.

Recorded surface waves often provide reasonable estimates of the S-wave velocity in the near surface. However, existing algorithms are mainly based on the 1D layered-model assumption and require picking the dispersion curves either automatically or manually. We have developed a wave-equation-based inversion algorithm that inverts for S-wave velocities using fundamental and higher mode Rayleigh waves without picking an explicit dispersion curve. Our method aims to maximize the similarity of the phase velocity spectrum ([Formula: see text]) of the observed and predicted surface waves with all Rayleigh-wave modes (if they exist) included in the inversion. The [Formula: see text] spectrum is calculated using the linear Radon transform applied to a local similarity-based objective function; thus, we do not need to pick velocities in spectrum plots. As a result, the best match between the predicted and observed [Formula: see text] spectrum provides the optimal estimation of the S-wave velocity. We derive S-wave velocity updates using the adjoint-state method and solve the optimization problem using a limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Our method excels in cases in which the S-wave velocity has vertical reversals and lateral variations because we used all-modes dispersion, and it can suppress the local minimum problem often associated with full-waveform inversion applications. Synthetic and field examples are used to verify the effectiveness of our method.

Full waveform inversion (FWI) incorporates all the data characteristics to estimate the parameters described by the assumed physics of the subsurface. However, current efforts to utilize full waveform inversion beyond improved acoustic imaging, like in reservoir delineation, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Some anisotropic parameters are insufficiently updated because of their minor contributions to the surface collected data. Adding rock physics constraints to the inversion helps mitigate such limited sensitivity, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a global constraint for the whole area. Since similar rock formations inside the Earth admit consistent elastic properties and relative values of elasticity and anisotropy parameters (this enables us to define them as a seismic facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel approach to use facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such facies using Bayesian theory and update them at each iteration of the inversion using both the inverted models and a prior information. We take the uncertainties of the estimated parameters (approximated by radiation patterns) into consideration and improve the quality of estimated facies maps. Four numerical examples corresponding to different acquisition, physical assumptions and model circumstances are used to verify the effectiveness of the proposed method.

Many full-waveform inversion schemes are based on the iterative perturbation theory to fit the observed waveforms. When the observed waveforms lack low frequencies, those schemes may encounter convergence problems due to cycle skipping when the initial velocity model is far from the true model. To mitigate this difficulty, we have developed a new objective function that fits the seismic-waveform intensity, so the dependence of the starting model can be reduced. The waveform intensity is proportional to the square of its amplitude. Forming the intensity using the waveform is a nonlinear operation, which separates the original waveform spectrum into an ultra-low-frequency part and a higher frequency part, even for data that originally do not have low-frequency contents. Therefore, conducting multiscale inversions starting from ultra-low-frequency intensity data can largely avoid the cycle-skipping problem. We formulate the intensity objective function, the minimization process, and the gradient. Using numerical examples, we determine that the proposed method was very promising and could invert for the model using data lacking low-frequency information.

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He B, et al. (2018) Normalized nonzero-lag crosscorrelation elastic full-waveform inversion.ABSTRACT Full-waveform inversion (FWI) is an attractive technique due to its ability to build high-resolution velocity models. Conventional amplitude-matching FWI approaches remain challenging because the simplified computational physics used does not fully represent all wave phenomena in the earth. Because the earth is attenuating, a sample-by-sample fitting of the amplitude may not be feasible in practice. We have developed a normalized nonzero-lag crosscorrelataion-based elastic FWI algorithm to maximize the similarity of the calculated and observed data. We use the first-order elastic-wave equation to simulate the propagation of seismic waves in the earth. Our proposed objective function emphasizes the matching of the phases of the events in the calculated and observed data, and thus, it is more immune to inaccuracies in the initial model and the difference between the true and modeled physics. The normalization term can compensate the energy loss in the far offsets because of geometric spreading and avoid a bias in estimation toward extreme values in the observed data. We develop a polynomial-type weighting function and evaluate an approach to determine the optimal time lag. We use a synthetic elastic Marmousi model and the BigSky field data set to verify the effectiveness of the proposed method. To suppress the short-wavelength artifacts in the estimated S-wave velocity and noise in the field data, we apply a Laplacian regularization and a total variation constraint on the synthetic and field data examples, respectively.

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 the 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.