ALBERT

Description: We have developed a time-lapse seismic history matching framework to assimilate production data and time-lapse seismic data for the prediction of static reservoir models. An iterative data assimilation method, the ensemble smoother with multiple data assimilation is adopted to iteratively update an ensemble of reservoir models until their predicted observations match the actual production and seismic measurements and to quantify the model uncertainty of the posterior reservoir models. To address computational and numerical challenges when applying ensemble-based optimization methods on large seismic data volumes, we develop a deep representation learning method, namely, the deep convolutional autoencoder. Such a method is used to reduce the data dimensionality by sparsely and approximately representing the seismic data with a set of hidden features to capture the nonlinear and spatial correlations in the data space. Instead of using the entire seismic data set, which would require an extremely large number of models, the ensemble of reservoir models is iteratively updated by conditioning the reservoir realizations on the production data and the low-dimensional hidden features extracted from the seismic measurements. We test our methodology on two synthetic data sets: a simplified 2D reservoir used for method validation and a 3D application with multiple channelized reservoirs. The results indicate that the deep convolutional autoencoder is extremely efficient in sparsely representing the seismic data and that the reservoir models can be accurately updated according to production data and the reparameterized time-lapse seismic data.

Description: Applying deep learning to 3D velocity model building remains a challenge due to the sheer volume of data required to train large-scale artificial neural networks. Moreover, little is known about what types of network architectures are appropriate for such a complex task. To ease the development of a deep-learning approach for seismic velocity estimation, we have evaluated a simplified surrogate problem — the estimation of the root-mean-square (rms) and interval velocity in time from common-midpoint gathers — for 1D layered velocity models. We have developed a deep neural network, whose design was inspired by the information flow found in semblance analysis. The network replaces semblance estimation by a representation built with a deep convolutional neural network, and then it performs velocity estimation automatically with recurrent neural networks. The network is trained with synthetic data to identify primary reflection events, rms velocity, and interval velocity. For a synthetic test set containing 1D layered models, we find that rms and interval velocity are accurately estimated, with an error of less than [Formula: see text] for the rms velocity. We apply the neural network to a real 2D marine survey and obtain accurate rms velocity predictions leading to a coherent stacked section, in addition to an estimation of the interval velocity that reproduces the main structures in the stacked section. Our results provide strong evidence that neural networks can estimate velocity from seismic data and that good performance can be achieved on real data even if the training is based on synthetics. The findings for the 1D problem suggest that deep convolutional encoders and recurrent neural networks are promising components of more complex networks that can perform 2D and 3D velocity model building.

Description: The injection of fluids with electromagnetic (EM) contrast is regarded as a promising tool for EM monitoring. We have developed a novel model-based inversion method, designated as a particle mapping (PM) method, as a fit-for-purpose inversion tool for EM monitoring. The PM method optimizes the location of particles while constraining a priori information on the net physical property-volume products in the inversion domain. In addition, as a regularization method for location-based inversion, a fuzzy clustering method is adopted to integrate the PM method with the geometries of an a priori anomalous distribution. The EM monitoring of hydraulic fracturing is considered as a primary application of the PM method. In particular, numerical experiments focus on the injection of magnetically enhanced proppants and the use of the fracture model as a cluster geometry. Numerical experiments also include situational assumptions of incorrect a priori injected amounts of fluids and the distribution of anomalous regions to fully investigate the practicality of the method. The results indicate not only how clear and intrinsically interpretable the imaging results can be obtained with the PM method but also how known or assumed information on injected fluids and the fracture model can be integrated with the EM inversion.

Description: Reflection full-waveform inversion (RFWI) can recover the low-wavenumber components of the velocity model along with the reflection wavepaths. However, this requires an expensive least-squares reverse time migration (LSRTM) to construct the perturbation image that can still suffer from cycle-skipping problems. As an inexpensive alternative to LSRTM, we use migration deconvolution (MD) with RFWI. To mitigate cycle-skipping problems, we develop a multiscale reflection phase inversion (MRPI) strategy that boosts the low-frequency data and should only explain the phase information in the recorded data, not its magnitude spectrum. We also use the rolling-offset strategy that gradually extends the offset range of data with an increasing number of iterations. Numerical results indicate that the MRPI + MD method can efficiently recover the low-wavenumber components of the velocity model and is less prone to getting stuck in local minima compared to conventional RFWI.

Description: The spectral element method (SEM) has gained tremendous popularity within the seismological community to solve the wave equation at all scales. Classic SEM applications mostly rely on degrees 4–8 elements in each tensorial direction. Higher degrees are usually not considered due to two main reasons. First, high degrees imply large elements, which make the meshing of mechanical discontinuities difficult. Second, the SEM’s collocation points cluster toward the edge of the elements with the degree, degrading the time-marching stability criteria and imposing a small time step and a high numerical cost. Recently, the homogenization method has been introduced in seismology. This method can be seen as a preprocessing step before solving the wave equation that smooths out the internal mechanical discontinuities of the elastic model. It releases the meshing constraint and makes use of very high degree elements more attractive. Thus, we address the question of memory and computing time efficiency of very high degree elements in SEM, up to degree 40. Numerical analyses reveal that, for a fixed accuracy, very high degree elements require less computer memory than low-degree elements. With minimum sampling points per minimum wavelength of 2.5, the memory needed for a degree 20 is about a quarter that of the one necessary for a degree 4 in two dimensions and about one-eighth in three dimensions. Moreover, for the SEM codes tested in this work, the computation time with degrees 12–24 can be up to twice faster than the classic degree 4. This makes SEM with very high degrees attractive and competitive for solving the wave equation in many situations.

Description: Simulation of wave propagation in a constant-[Formula: see text] viscoacoustic medium is an important problem, for instance, within [Formula: see text]-compensated reverse time migration (RTM). Processes of attenuation and dispersion influence all aspects of seismic wave propagation, degrading the resolution of migrated images. To improve the image resolution, we have developed a new approach for the numerical solution of the viscoacoustic wave equation in the time domain and we developed an associated viscoacoustic RTM ([Formula: see text]-RTM) method. The main feature of the [Formula: see text]-RTM approach is compensation of attenuation effects in seismic images during migration by separation of amplitude attenuation and phase dispersion terms. Because of this separation, we are able to compensate the amplitude loss effect in isolation, the phase dispersion effect in isolation, or both effects concurrently. In the [Formula: see text]-RTM implementation, an attenuation-compensated operator is constructed by reversing the sign of the amplitude attenuation and a regularized viscoacoustic wave equation is invoked to eliminate high-frequency instabilities. The scheme is tested on a layered model and a modified acoustic Marmousi velocity model. We validate and examine the response of this approach by using it within an RTM scheme adjusted to compensate for attenuation. The amplitude loss in the wavefield at the source and receivers due to attenuation can be recovered by applying compensation operators on the measured receiver wavefield. Our 2D and 3D numerical tests focus on the amplitude recovery and resolution of the [Formula: see text]-RTM images as well as the interface locations. Improvements in all three of these features beneath highly attenuative layers are evident.

Description: Full-waveform inversion (FWI) is widely used to infer earth structures and rock properties. In FWI, most of the computation arises from the repeated simulations of wave propagation. Although frequency-domain implementations have several advantages, solving the Helmholtz equation incurs a major computational cost associated with the inversion of large matrices. Hence, we have used a new model reduction technique called the generalized multiscale finite-element method (GM FEM) to perform this task rapidly for forward and backward simulations. This in turn leads to the acceleration of the FWI. In addition, the multiscale finite-element approach allows flexible, adaptive selection of modeling parameters (i.e., grid size, number of basis functions) for different target frequencies, providing further speed up. We apply this frequency-domain, multiscale FEM approach to the Marmousi-2 model, and the FWI results indicated how varying the number of basis functions can control the trade-off between the accuracy and computational speed. In addition, we introduced FWI examples applied to field data from the Gulf of Mexico. These field data examples indicate that applying our multiscale FWI with a relatively small number of basis functions can quickly construct a macrovelocity model using low frequencies. We also evaluate a strategy to optimize the FWI procedure by using frequency-adaptive multiscale basis functions based on the target frequency group. In general, we can reduce the run time by up to 30% through the application of GM FEM wave modeling in FWI.

Description: We have developed a nonlinear gravity inversion for simultaneously estimating the basement and Moho geometries, as well as the depth of the reference Moho along a profile crossing a passive rifted margin. To obtain stable solutions, we impose smoothness on basement and Moho, force them to be close to previously estimated depths along the profile and also impose local isostatic equilibrium. Different from previous methods, we evaluate the information of local isostatic equilibrium by imposing smoothness on the lithostatic stress exerted at depth. Our method delimits regions that deviate and those that can be considered in local isostatic equilibrium by varying the weight of the isostatic constraint along the profile. It also allows controlling the degree of equilibrium along the profile, so that the interpreter can obtain a set of candidate models that fit the observed data and exhibit different degrees of isostatic equilibrium. Our method also differs from earlier studies because it attempts to use isostasy for exploring (but not necessarily reducing) the inherent ambiguity of gravity methods. Tests with synthetic data illustrate the effect of our isostatic constraint on the estimated basement and Moho reliefs, especially at regions with pronounced crustal thinning, which are typical of passive volcanic margins. Results obtained by inverting satellite data over the Pelotas Basin, a passive volcanic margin in southern Brazil, agree with previous interpretations obtained independently by combining gravity, magnetic, and seismic data available to the petroleum industry. These results indicate that combined with a priori information, simple isostatic assumptions can be very useful for interpreting gravity data on passive rifted margins.

Description: Electrostatic forces acting at the particle scale can be an important drive behind water weakening of chalk. Upon the replacement of oil with brine, ions present in the imbibing brine can exchange with ions already adsorbed to the calcite surface, leading to a change in the surface potential. This can cause an increase in the disjoining pressure between particles, either reducing the cohesion of particles connected via contact cement or decreasing friction between free particles. We have assessed the effect of electrostatic forces by measuring pore-water effects on porosity in sediment columns using nuclear magnetic resonance relaxometry. Samples of calcite, quartz, or kaolinite powder were saturated with brines containing ions found in seawater ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]) at varying ionic strengths and as a nonpolar reference, with ethylene glycol. The difference in porosity between samples saturated with glycol and with brines reflects the disjoining pressure. For calcite samples, saturation with solutions containing divalent cations ([Formula: see text] and [Formula: see text]) lead to higher repulsive forces between the grains, whereas adsorption of [Formula: see text] counteracts the initially positive surface charge, lowering the repulsive forces. Calcium-based brines induced the highest repulsion, probably due to higher surface coverage of [Formula: see text] than that of [Formula: see text] due to its smaller hydrated radius. For kaolinite, differences in potential between the silica and alumina faces as well as the edges can either lead to repulsion between particles or to flocculation, depending on the ionic strength and ionic species of the fluid. Our results indicate that low-salinity water flooding may lead to kaolinite mobilization within reservoirs. A comparison of the results from our calcite powder experiments with results from mechanical tests performed on chalk samples indicates that electrical double layer-related forces can contribute to the weakening of chalk. Saturating brines for which the repulsion between grains in powder experiments was larger corresponds to weaker chalk samples.

Description: 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.