This paper introduces novel deep recurrent neural network architectures for Velocity Model Building (VMB), which is beyond what Araya-Polo et al 2018 pioneered with the Machine Learning-based seismic tomography built with convolutional non-recurrent neural network. Our investigation includes the utilization of basic recurrent neural network (RNN) cells, as well as Long Short Term Memory (LSTM) and Gated Recurrent Unit (GRU) cells. Performance evaluation reveals that salt bodies are consistently predicted more accurately by GRU and LSTM-based architectures, as compared to non-recurrent architectures. The results take us a step closer to the final goal of a reliable fully Machine Learning-based tomography from pre-stack data, which when achieved will reduce the VMB turnaround from weeks to days.
Seismic traveltime tomography using transmission data is widely used to image the Earth's interior from global to local scales. In seismic imaging, it is used to obtain velocity models for subsequent depth-migration or full-waveform inversion. In addition, cross-hole tomography has been successfully applied for a variety of applications, including mineral exploration, reservoir monitoring, and CO2 injection and sequestration. Conventional tomography techniques suffer from a number of limitations, including the use of a smoothing regularizer that is agnostic to the physics of wave propagation. …
Seismic tomography is a methodology to image the interior of solid or fluid media, and is often used to map properties in the subsurface of the Earth. In order to better interpret the resulting images it is important to assess imaging uncertainties. Since tomography is significantly nonlinear, Monte Carlo sampling methods are often used for this purpose, but they are generally computationally intractable for large datasets and high-dimensional parameter spaces. To extend uncertainty analysis to larger systems we use variational inference methods to conduct seismic tomography. In contrast to Mo…
Reservoir characterization involves the estimation petrophysical properties from well-log data and seismic data. Estimating such properties is a challenging task due to the non-linearity and heterogeneity of the subsurface. Various attempts have been made to estimate petrophysical properties using machine learning techniques such as feed-forward neural networks and support vector regression (SVR). Recent advances in machine learning have shown promising results for recurrent neural networks (RNN) in modeling complex sequential data such as videos and speech signals. In this work, we propose an…
We introduce a `double-difference' method for the inversion for seismic wavespeed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systematic uncertainties. To alleviate the corresponding nonuniqueness in the inverse problem, we construct differential measurements between stations, thereby reducing the influence of the source signature and systematic errors. We minimize the discrepancy…
Seismotectonics and Slip Behavior of a Submarine Plate Boundary Fault from Seismicity Repeaters and Tomography using a high-resolution earthquake catalog from machine learning
The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, $\ell_2$ penalties are compared to so-called sparsity promoting $\ell_1$ and $\ell_0$ penalties, and a total variation penalty. Which of these algorithms is judged optimal depends on the specific requirements of the scientific experiment. If the correct reproduction of model amplitudes is important, classical damping towards a smooth model using an $\ell_2$ norm works almost as well as minimizing the total variation but is much more efficient. If gradients (e…
Recent applications of deep learning in the seismic domain have shown great potential in different areas such as inversion and interpretation. Deep learning algorithms, in general, require tremendous amounts of labeled data to train properly. To overcome this issue, we propose a semi-supervised framework for acoustic impedance inversion based on convolutional and recurrent neural networks. Specifically, seismic traces and acoustic impedance traces are modeled as time series. Then, a neural-network-based inversion model comprising convolutional and recurrent neural layers is used to invert seis…
A recently proposed method of constructing seismic networks from 'record breaking events' from the earthquake catalog of California (Phy. Rev. E, 77 6,066104, 2008) was successfull in establishing causal features to seismicity and arrive at estimates for rupture length and its scaling with magnitude. The results of our implementation of this procedure on the earthquake catalog of Japan establishes the robustness of the procedure. Additionally, we find that the temporal distributions are able to detect heterogeneties in the seismicity of the region.
In exploration seismology, seismic inversion refers to the process of inferring physical properties of the subsurface from seismic data. Knowledge of physical properties can prove helpful in identifying key structures in the subsurface for hydrocarbon exploration. In this work, we propose a workflow for predicting acoustic impedance (AI) from seismic data using a network architecture based on Temporal Convolutional Network by posing the problem as that of sequence modeling. The proposed workflow overcomes some of the problems that other network architectures usually face, like gradient vanishi…
In this article, we develop a 1-D traveltime tomography method to calculate the seismic P-wave velocity of a medium. We use the results of 1-D tomography to obtain linear inhomogeneity parameters in a specific layer. To get the trustworthiness of the method, we perform several synthetic experiments. We show that the inverted model parameters are reasonably accurate and stable. To examine the results of linear inhomogeneity parameters using a different method, we also develop an inversion method based on a two-parameter velocity model. Finally, we apply both the methods to Vertical Seismic Prof…
The purpose of this work is to generalize the frozen Gaussian approximation (FGA) theory to solve the 3-D elastic wave equation and use it as the forward modeling tool for seismic tomography with high-frequency data. FGA has been previously developed and verified as an efficient solver for high-frequency acoustic wave propagation (P-wave). The main contribution of this paper consists of three aspects: 1. We derive the FGA formulation for the 3-D elastic wave equation. Rather than standard ray-based methods (e.g. geometric optics and Gaussian beam method), the derivation requires to do asymptot…
Deep Earth imaging through neutrino and seismic tomography
Institute of Physics（印度物理研究所）；Homi Bhabha National Institute（霍米·巴巴国立学院）；Indian Institute of Science Education and Research, Pune（印度科学教育研究学院浦那分校）；Tata Institute of Fundamental Research（塔塔基础研究院）；CSIR Fourth Paradigm Institute（印度科学工业研究理事会第四范式研究所）；Department of Physics, Aligarh Muslim University（阿利加尔穆斯林大学物理系）
Real time, accurate passive seismic event detection is a critical safety measure across a range of monitoring applications from reservoir stability to carbon storage to volcanic tremor detection. The most common detection procedure remains the Short-Term-Average to Long-Term-Average (STA/LTA) trigger despite its common pitfalls of requiring a signal-to-noise ratio greater than one and being highly sensitive to the trigger parameters. Whilst numerous alternatives have been proposed, they often are tailored to a specific monitoring setting and therefore cannot be globally applied, or they are to…
We propose a local earthquake tomography method that applies a structured regularization technique to determine sharp changes in Earth's seismic velocity structure using arrival time data of direct waves. Our approach focuses on the ability to better image two common features that are observed in Earth's seismic velocity structure: sharp changes in velocities that correspond to material boundaries, such as the Conrad and Moho discontinuities; and gradual changes in velocity that are associated with pressure and temperature distributions in the crust and mantle. We employ different penalty term…
Seismic Traveltime Tomography with Label-free Learning
College of Big Data and Software Engineering, Zhejiang Wanli University（浙江万里学院大数据与软件工程学院）；Key Laboratory of Geoscience Big Data and Deep Resource of Zhejiang Province, School of Earth Sciences, Zhejiang University（浙江大学地球科学学院浙江省地球科学大数据与深部资源重点实验室）
Recent applications of machine learning algorithms in the seismic domain have shown great potential in different areas such as seismic inversion and interpretation. However, such algorithms rarely enforce geophysical constraints - the lack of which might lead to undesirable results. To overcome this issue, we have developed a semi-supervised sequence modeling framework based on recurrent neural networks for elastic impedance inversion from multi-angle seismic data. Specifically, seismic traces and elastic impedance (EI) traces are modeled as a time series. Then, a neural-network-based inversio…
We propose a method to search for signs of causal structure in spatiotemporal data making minimal a priori assumptions about the underlying dynamics. To this end, we generalize the elementary concept of recurrence for a point process in time to recurrent events in space and time. An event is defined to be a recurrence of any previous event if it is closer to it in space than all the intervening events. As such, each sequence of recurrences for a given event is a record breaking process. This definition provides a strictly data driven technique to search for structure. Defining events to be nod…
I demonstrate that the conventional seismic full-waveform inversion algorithm can be constructed as a recurrent neural network and so implemented using deep learning software such as TensorFlow. Applying another deep learning concept, the Adam optimizer with minibatches of data, produces quicker convergence toward the true wave speed model on a 2D dataset than Stochastic Gradient Descent and than the L-BFGS-B optimizer with the cost function and gradient computed using the entire training dataset. I also show that the cost function gradient calculation using reverse-mode automatic differentiat…
The Elman artificial neural network (ANN) (feedback connection) was used for seismic data filtering. The recurrent connection that characterizes this network offers the advantage of storing values from the previous time step to be used in the current time step. The proposed structure has the advantage of training simplicity by a back-propagation algorithm (steepest descent). Several trials were addressed on synthetic (with 10% and 50% of random and Gaussian noise) and real seismic data using respectively 10 to 30 neurons and a minimum of 60 neurons in the hidden layer. Both an iteration number…
Time-lapse seismic data acquisition is an essential tool to monitor changes in a reservoir due to fluid injection, such as CO$_2$ injection. By acquiring multiple seismic surveys in the exact location, we can identify the reservoir changes by analyzing the difference in the data. However, such analysis can be skewed by the near-surface seasonal velocity variations, inaccuracy in the acquisition parameters, and other inevitable noise. The common practice (cross-equalization) to address this problem uses the part of the data where changes are not expected to design a matching filter and then app…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective function. This is the case for objective functions like minimizing RMS of amplitude, residual traveltime error in tomography, cross correlation and sometimes mixing different norms (e.g. L1 of model + L2 of RMS error). Algebraic objective function assumes that the optimal solution will come up with the correct geometry. It is sometimes difficult to understa…
Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are key prerequisites for reverse-time migration and other high-resolution seismic imaging techniques. Such velocity information has traditionally been derived by tomography or full-waveform inversion (FWI), which are time consuming and computationally expensive, and they rely heavily on human interaction and quality control. We investigate a novel method based on the supervised deep fully convolutional neural network (FCN) for velocity-model building (VMB) directly from raw seismogra…
California Institute of Technology（加州理工学院）；Purdue University（普渡大学）
Seismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of research. This is exacerbated by the fact that new simulations must be performed when the velocity structure or source location is perturbed. Here, we explore a prototype framework for learning general solutions using a recently developed machine learning paradigm called Neural Operator. A trained Neural Operator can compute a solution in negligible time for any velocity structure or source location. We develop a scheme…
In current seismic acquisition practice, there is an increasing drive for sparsely (in space) acquired data, often in irregular geometry. These surveys can trade off subsurface information for efficiency/cost - creating a problem of "missing seismic data" that can greatly hinder subsequent processing and interpretation. Reconstruction of regularly sampled dense data from highly sparse, irregular data can therefore aid in processing and interpretation of these far sparser, more efficient seismic surveys. Here, two methods are compared to solve the reconstruction problem in both space-time and w…
The accurate and fast estimation of velocity models is crucial in seismic imaging. Conventional methods, like Tomography and Full-Waveform Inversion (FWI), obtain appropriate velocity models; however, they require intense and specialized human supervision and consume much time and computational resources. In recent years, some works investigated deep learning(DL) algorithms to obtain the velocity model directly from shots or migrated angle panels, obtaining encouraging predictions of synthetic models. This paper proposes a new flow to increase the complexity of velocity models recovered with D…
In Earthquake Early Warning (EEW), every sufficiently impulsive signal is potentially the first evidence for an unfolding large earthquake. More often than not, however, impulsive signals are mere nuisance signals. One of the most fundamental - and difficult - tasks in EEW is to rapidly and reliably discriminate real local earthquake signals from all other signals. This discrimination is necessarily based on very little information, typically a few seconds worth of seismic waveforms from a small number of stations. As a result, current EEW systems struggle to avoid discrimination errors, and s…
Enhanced Seismicity Monitoring in the Rapid Scientific Response to the 2025 Santorini Crisis
The Lyell Centre, British Geological Survey（英国地质调查局利尔中心）；School of GeoSciences, The University of Edinburgh（爱丁堡大学地球科学学院）；Department of Geophysics, Stanford University（斯坦福大学地球物理学系）；GFZ Helmholtz Centre for Geosciences（GFZ德国地学研究中心赫尔姆霍茨）；RWTH Aachen University（亚琛工业大学）；Dipartimento di Fisica Ettore Pancini, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学埃托雷·潘奇尼物理系）；Istituto Nazionale di Geofisica e Vulcanologia (INGV)（意大利国家地球物理学和火山学研究所）；U.S. Geological Survey, Volcano Disaster Assistance Program（美国地质调查局火山灾害援助计划）；Department of Earth Sciences, University of Oxford（牛津大学地球科学系）；Department of Civil and Environmental Engineering, University of Southern California（南加州大学土木与环境工程系）；Division of Natural Sciences, Academy of Athens（雅典科学院自然科学部）；U.S. Geological Survey, Pacific Coastal and Marine Science Center（美国地质调查局太平洋沿海与海洋科学中心）；Institute of Geodynamics, National Observatory of Athens（雅典国立天文台地球动力学研究所）；Dipartimento di Geoscienze, Università degli Studi di Padova（帕多瓦大学地球科学系）；Dipartimento di Scienze della Terra, dell’ Ambiente e delle Risorse, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学地球、环境与资源科学系）
We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution $m$ that contains no more fine-scale structure than is necessary to fit the data $d$ to within its assigned errors.
We have formulated elastic seismic full waveform inversion (FWI) within a deep learning environment. In our formulation, a recurrent neural network is set up with rules enforcing elastic wave propagation, with the wavefield projected onto a measurement surface acting as the synthetic data to be compared with observed seismic data. Gradients for iterative updating of an elastic model, with a variety of parameterizations and misfit functionals, can be efficiently constructed within the network through the automatic differential method. With this method, the inversion based on complex misfits can…
