Microseismic source imaging using physics-informed neural networks with hard constraints

Microseismic source imaging plays a significant role in passive seismic monitoring. However, such a process is prone to failure due to the aliasing problem when dealing with sparse measured data. Thus, we propose a direct microseismic imaging framework based on physics-informed neural networks (PINNs), which can generate focused source images, even with very sparse recordings. We use the PINNs to represent a multi-frequency wavefield and then apply the inverse Fourier transform to extract the source image. Specially, we modify the representation of the frequency-domain wavefield to inherently satisfy the boundary conditions (the measured data on the surface) by means of the hard constraint, which helps to avoid the difficulty in balancing the data and PDE losses in PINNs. Furthermore, we propose the causality loss implementation with respect to depth to enhance the convergence of PINNs. The numerical experiments on the Overthrust model show that the method can admit reliable and accurate source imaging for single- or multiple- sources and even in passive monitoring settings. Then, we further apply our method on the hydraulic fracturing field data, and demonstrate that our method can correctly image the source

Robust data driven discovery of a seismic wave equation

Despite the fact that our physical observations can often be described by derived physical laws, such as the wave equation, in many cases, we observe data that do not match the laws or have not been described physically yet. Therefore recently, a branch of machine learning has been devoted to the discovery of physical laws from data. We test such discovery algorithms, with our own flavor of implementation D-WE, in discovering the wave equation from the observed spatial-temporal wavefields. D-WE first pretrains a neural network (NN) in a supervised fashion to establish the mapping between the spatial-temporal locations (x,y,z,t) and the observation displacement wavefield function u(x,y,z,t). The trained NN serves to generate meta-data and provide the time and spatial derivatives of the wavefield (e.g., u_tt and u_xx) by automatic differentiation. Then, a preliminary library of potential terms for the wave equation is optimized from an overcomplete library by using a genetic algorithm. We, then, use a physics-informed information criterion to evaluate the precision and parsimony of potential equations in the preliminary library and determine the best structure of the wave equation. Finally, we train the "physics-informed" neural network to identify the corresponding coefficients of each functional term. Examples in discovering the 2D acoustic wave equation validate the feasibility and effectiveness of D-WE. We also verify the robustness of this method by testing it on noisy and sparsely acquired wavefield data

Reflection Moveout Inversion For Horizontal Transverse Isotropy: Accuracy And Limitation

Horizontal transverse isotropy (HTI) is the simplest azimuthally anisotropic model used to describe vertical fracturing in an isotropic matrix. Using the elliptical variation of P-wave normal-moveout (NMO) velocity with azimuth, measured in three different source-to-receiver orientations, we can obtain the vertical velocity V[subscript Pvert], anisotropy parameter δ[superscript (V)], and the azimuth a of the symmetry-axis plane. Parameter estimation from variations in the moveout velocity in azimuthally anisotropic media is quite sensitive to the angular separation between the survey lines in 2D, or equivalently source-to-receiver azimuths in 3D, and to the set of azimuths used in the inversion procedure. The accuracy in estimating the parameter α, in particular, is also sensitive to the strength of anisotropy. The accuracy in resolving δ[superscript (V)] and [subscript Pvert] is about the same for any strength of anisotropy. In order to maximize the accuracy and stability in parameter estimation, it is best to have the azimuths for the three source-to- receiver directions 60° apart. In land seismic data acquisition having wide azimuthal coverage is quite feasible. In marine seismic data acquisition, however, where the azimuthal data coverage is limited, multiple survey directions are necessary to achieve such wide azimuthal coverage. Having more than three distinct source-to-receiver azimuths (e.g., full azimuthal coverage) provides useful data redundancy that enhances the quality of the estimates, and sets the stage for a least-square type of inversion in which the errors in the parameters estimates are minimized in a least-square sense. In layered azimuthally anisotropic media, applying Dix differentiation to obtain interval moveout velocity provides sufficient accuracy in the inversion for the medium parameters, especially where the direction of the symmetry planes is uniform. In order to obtain acceptable parameter estimates, an HTI layer overlain by an azimuthally isotropic overburden (as might happen for fractured reservoirs) should have a thickness (in time) relative to the total thickness. The total thickness should be equal to or greater than the ratio of the error in the NMO (stacking) velocity to the interval anisotropy strength of the fractured layer.Saudi AramcoMassachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumMassachusetts Institute of Technology. Earth Resources Laboratory. Reservoir Delineation Consortiu

Joint Microseismic Event Detection and Location with a Detection Transformer

Microseismic event detection and location are two primary components in microseismic monitoring, which offers us invaluable insights into the subsurface during reservoir stimulation and evolution. Conventional approaches for event detection and location often suffer from manual intervention and/or heavy computation, while current machine learning-assisted approaches typically address detection and location separately; such limitations hinder the potential for real-time microseismic monitoring. We propose an approach to unify event detection and source location into a single framework by adapting a Convolutional Neural Network backbone and an encoder-decoder Transformer with a set-based Hungarian loss, which is applied directly to recorded waveforms. The proposed network is trained on synthetic data simulating multiple microseismic events corresponding to random source locations in the area of suspected microseismic activities. A synthetic test on a 2D profile of the SEAM Time Lapse model illustrates the capability of the proposed method in detecting the events properly and locating them in the subsurface accurately; while, a field test using the Arkoma Basin data further proves its practicability, efficiency, and its potential in paving the way for real-time monitoring of microseismic events

Meta-Processing: A robust framework for multi-tasks seismic processing

Machine learning-based seismic processing models are typically trained separately to perform specific seismic processing tasks (SPTs), and as a result, require plenty of training data. However, preparing training data sets is not trivial, especially for supervised learning (SL). Nevertheless, seismic data of different types and from different regions share generally common features, such as their sinusoidal nature and geometric texture. To learn the shared features, and thus, quickly adapt to various SPTs, we develop a unified paradigm for neural network-based seismic processing, called Meta-Processing, that uses limited training data for meta learning a common network initialization, which offers universal adaptability features. The proposed Meta-Processing framework consists of two stages: meta-training and meta-testing. In the meta-training stage, each SPT is treated as a separate task and the training dataset is divided into support and query sets. Unlike conventional SL methods, here, the neural network (NN) parameters are updated by a bilevel gradient descent from the support set to the query set, iterating through all tasks. In the meta-testing stage, we also utilize limited data to fine-tune the optimized NN parameters in an SL fashion to conduct various SPTs, such as denoising, interpolation, ground-roll attenuation, image enhancement, and velocity estimation, aiming to converge quickly to ideal performance. Comprehensive numerical examples are performed to evaluate the performance of Meta-Processing on both synthetic and field data. The results demonstrate that our method significantly improves the convergence speed and prediction accuracy of the NN

Micro-seismic Elastic Reflection Full Waveform Inversion with An Equivalent Source

In micro-seismic event measurements, pinpointing the passive source's exact spatial and temporal location is paramount. This research advocates for the combined use of both P- and S-wave data, captured by geophone monitoring systems, to improve source inversion accuracy. Drawing inspiration from the secondary source concept in Elastic Reflection Full Waveform Inversion (ERFWI), we introduce an equivalent source term. This term combines source functions and source images. Our optimization strategy iteratively refines the spatial locations of the source, its temporal functions, and associated velocities using a full waveform inversion framework. Under the premise of an isotropic medium with consistent density, the source is defined by two spatial and three temporal components. This offers a nuanced source representation in contrast to the conventional seismic moment tensor. To address gradient computation, we employ the adjoint-state method. However, we encountered pronounced non-linearity in waveform inversion of micro-seismic events, primarily due to the unknown source origin time, resulting in cycle skipping challenges. To counteract this, we devised an objective function that is decoupled from the source origin time. This function is formulated by convolving reference traces with both observed and predicted data. Through the concurrent inversion of the source image, source time function, and velocity model, our method offers precise estimations of these parameters, as validated by a synthetic 2D example based on a modified Marmousi model. This nested inversion approach promises enhanced accuracy in determining the source image, time function, and velocity model

A prior regularized full waveform inversion using generative diffusion models

Full waveform inversion (FWI) has the potential to provide high-resolution subsurface model estimations. However, due to limitations in observation, e.g., regional noise, limited shots or receivers, and band-limited data, it is hard to obtain the desired high-resolution model with FWI. To address this challenge, we propose a new paradigm for FWI regularized by generative diffusion models. Specifically, we pre-train a diffusion model in a fully unsupervised manner on a prior velocity model distribution that represents our expectations of the subsurface and then adapt it to the seismic observations by incorporating the FWI into the sampling process of the generative diffusion models. What makes diffusion models uniquely appropriate for such an implementation is that the generative process retains the form and dimensions of the velocity model. Numerical examples demonstrate that our method can outperform the conventional FWI with only negligible additional computational cost. Even in cases of very sparse observations or observations with strong noise, the proposed method could still reconstruct a high-quality subsurface model. Thus, we can incorporate our prior expectations of the solutions in an efficient manner. We further test this approach on field data, which demonstrates the effectiveness of the proposed method