Seismic imaging is conventionally performed using noisy data and a presumably inexact velocity model. Uncertainties in the input parameters propagate directly into the final image and therefore into any quantity of interest, or qualitative interpretation, obtained from the image. We considered the problem of uncertainty quantification in velocity building and seismic imaging using Bayesian inference. Using a reduced velocity model, a fast field expansion method for simulating recorded wavefields, and the adaptive Metropolis-Hastings algorithm, we efficiently quantify velocity model uncertainty by generating multiple models consistent with low-frequency full-waveform data. A second application of Bayesian inversion to any seismic reflections present in the recorded data reconstructs the corresponding structures’ position along with its associated uncertainty. Our analysis complements rather than replaces traditional imaging because it allows us to assess the reliability of visible image features and to take that into account in subsequent interpretations.

Cracks, joints, fluids, and other pore‐scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore‐scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presence and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low‐amplitude P wave probe by a high‐amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.

Time-lapse seismic data are widely used to monitor reservoir changes. Qualitative comparisons between baseline and monitor data sets or image volumes provide information about fluid and pressure effects within the reservoir during production. However, to perform real quantitative analysis of such reservoir changes, quantitative estimates of the elastic parameters are required as input parameters to rock-physics-based reservoir models. Full-waveform inversion has been proposed as a potential tool for retrieving subsurface properties, such as P- and S-wave velocities and density by fitting simulated waveforms to seismic data. An extension of this method to time-lapse applications seems straightforward, but, in fact, it requires more tailored processes such as double-difference waveform inversion (DDWI). We used realistic 2D synthetic pressure data examples to compare the performance of DDWI with that of two other inversion schemes: one using the same starting model for both inversions and the other starting the monitor inversion with the final baseline inversion model. The data simulation and inversion were based on acoustic theory. Although P-wave velocity changes were reliably recovered by each inversion method, DDWI was found to deliver the best results when perfectly repeated surveys were used. However, differencing the baseline and monitor data sets, as required by DDWI, could be found to be sensitive to the presence of survey nonrepeatability. To investigate the feasibility of using DDWI in practice, the dependence of DDWI on the quality of the baseline models and its robustness to survey nonrepeatability were studied with numerical tests. Various types of nonrepeatability were considered separately in the synthetic tests, including random noise, acquisition geometry mismatch, source wavelet discrepancy, and overburden velocity changes. A study of the correlation between the levels and types of nonrepeatability and the resulting contamination of the inversion results found that, for pressure data, DDWI was capable of inverting reliably for P-wave velocity changes under realistic survey nonrepeatability conditions.

Machine-learning techniques allow geoscientists to extract meaningful information from data in an automated fashion, and they are also an efficient alternative to traditional manual interpretation methods. Many geophysical problems have an abundance of unlabeled data and a paucity of labeled data, and the lithology classification of wireline data reflects this situation. Training supervised algorithms on small labeled data sets can lead to overtraining, and subsequent predictions for the numerous unlabeled data may be unstable. However, semisupervised algorithms are designed for classification problems with limited amounts of labeled data, and they are theoretically able to achieve better accuracies than supervised algorithms in these situations. We explore this hypothesis by applying two semisupervised techniques, label propagation (LP) and self-training, to a well-log data set and compare their performance to three popular supervised algorithms. LP is an established method, but our self-training method is a unique adaptation of existing implementations. The well-log data were made public through an SEG competition held in 2016. We simulate a semisupervised scenario with these data by assuming that only one of the 10 wells has labels (i.e., core samples), and our objective is to predict the labels for the remaining nine wells. We generate results from these data in two stages. The first stage is applying all the algorithms in question to the data as is (i.e., the global data), and the results from this motivate the second stage, which is applying all algorithms to the data when they are decomposed into two separate data sets. Overall, our findings suggest that LP does not outperform the supervised methods, but our self-training method coupled with LP can outperform the supervised methods by a notable margin if the assumptions of LP are met.

Much of the computational cost involved in full-waveform inversion comes from the solution of the wave equation in a large domain. These computations must be done for the entire domain through which we expect waves to pass for a particular survey, despite the fact that our region of interest is often significantly smaller. In addition to the wasted time spent propagating waves through less important parts of the model, computing updates on the entire domain may result in slower convergence of the inversion algorithm due to the larger model space. This can be especially important in 4D seismic monitoring, where we often see the majority of changes within a small subregion of the total domain, such as the reservoir. We present a local wave solver that accurately computes the solution of the wave equation within only a subdomain of the region covered by the survey, representing a significant cost saving in the computation of full-waveform inversion. We also show how this solver can improve the resulting velocity estimates in full-waveform inversion for time-lapse applications and observe that the local solver requires fewer iterations to converge than does the full-domain solver.

We have studied the problem of uncertainty quantification for migrated images. A traditional migrated image contains deterministic reconstructions of subsurface structures. However, input parameters used in migration, such as reflection data and a velocity model, are inherently uncertain. This uncertainty is carried through to the migrated images. We have used Bayesian analysis to quantify the uncertainty of the migrated structures by constructing a joint statistical distribution of the location of these structures. From this distribution, we could deduce the uncertainty in any quantity derived from these structures. We have developed the proposed framework using a simple model with velocity uncertainty in the overburden, and we estimated the absolute positions of the horizons and the relative depth of one horizon with respect to another. By quantifying the difference in the corresponding uncertainties, we found that, in this case, the relative depths of the structures could be estimated much better than their absolute depths. This analysis justifies redatuming below an uncertain overburden for the purposes of the uncertainty reduction.