Earth Science and Engineering Program
For more information visit: https://pse.kaust.edu.sa/study/academicprograms/earthscienceandengineering/Pages/home.aspx
Recent Submissions

Rayleigh Wave Dispersion Spectrum Inversion Across Scales(Surveys in Geophysics, Springer Science and Business Media LLC, 20211019) [Article]Traditional approaches of using dispersion curves for Swave velocity reconstruction have limitations, principally, the 1Dlayered model assumption and the automatic/manual picking of dispersion curves. At the same time, conventional fullwaveform inversion (FWI) can easily converge to a nonglobal minimum when applied directly to complicated surface waves. Alternatively, the recently introduced wave equation dispersion spectrum inversion method can avoid these limitations, by applying the adjoint state method on the dispersion spectra of the observed and predicted data and utilizing the local similarity objective function to depress cycle skipping. We apply the wave equation dispersion spectrum inversion to three real datasets of different scales: tens of meters scale activesource data for estimating shallow targets, tens of kilometers scale ambient noise data for reservoir characterization and a continentalscale seismic array data for imaging the crust and uppermost mantle. We use these three open datasets from exploration to crustal scale seismology to demonstrate the effectiveness of the inversion method. The dispersion spectrum inversion method adapts well to the differentscale data without any special tuning. The main benefits of the proposed method over traditional methods are that (1) it can handle lateral variations; (2) it avoids direct picking dispersion curves; (3) it utilizes both the fundamental and higher modes of Rayleigh waves, and (4) the inversion can be solved using gradientbased local optimizations. Compared to the conventional 1D inversion, the dispersion spectrum inversion requires more computational cost since it requires solving the 2D/3D elastic wave equation in each iteration. A good match between the observed and predicted dispersion spectra also leads to a reasonably good match between the observed and predicted waveforms, though the inversion does not aim to match the waveforms.

Machine Learning Enabled Traveltime Inversion Based on the Horizontal Source Location Perturbation(GEOPHYSICS, Society of Exploration Geophysicists, 20211017) [Article]Gradient based traveltime tomography, which aims to minimize the difference between modeled and observed first arrival times, is a highly nonlinear optimization problem. Stabilization of this inverse problem often requires employing regularization. While regularization helps avoid local minima solutions, it might cause low resolution tomograms because of its inherent smoothing property. On the other hand, although conventional raybased tomography can be robust in terms of the uniqueness of the solution, it suffers from the limitations inherent in ray tracing, which limits its use in complex media. To mitigate the aforementioned drawbacks of gradient and raybased tomography, we approach the problem in a completely novel way leveraging datadriven inversion techniques based on training deep convolutional neural networks (DCNN). Since DCNN often face challenges in detecting high level features from the relatively smooth traveltime data, we use this type of network to map horizontal changes in observed first arrival traveltimes caused by a source shift to lateral velocity variations. The relationship between them is explained by a linearized eikonal equation. Construction of the velocity models from this predicted lateral variation requires information from, for example, a vertical welllog in the area. This vertical profile is then used to build a tomogram from the output of the network. Both synthetic and field data results verify that the suggested approach estimates the velocity models reliably. Because of the limited depth penetration of first arrival traveltimes, the method is particularly favorable for nearsurface applications.

Ensemble Kalman filtering with colored observation noise(Quarterly Journal of the Royal Meteorological Society, Wiley, 20211015) [Article]The Kalman filter (KF) is derived under the assumption of timeindependent (white) observation noise. Although this assumption can be reasonable in many ocean and atmospheric applications, the recent increase in sensors coverage such as the launching of new constellations of satellites with global spatiotemporal coverage will provide high density of oceanic and atmospheric observations that are expected to have timedependent (colored) error statistics. In this situation, the KF update has been shown to generally provide overconfident probability estimates, which may degrade the filter performance. Different KFbased schemes accounting for timecorrelated observation noise were proposed for small systems by modeling the colored noise as a firstorder autoregressive model driven by white Gaussian noise. This work introduces new ensemble Kalman filters (EnKFs) that account for colored observational noises for efficient data assimilation into largescale oceanic and atmospheric applications. More specifically, we follow the standard and the onestepahead smoothing formulations of the Bayesian filtering problem with colored observational noise, modeled as an autoregressive model, to derive two (deterministic) EnKFs. We demonstrate the relevance of the colored observational noiseaware EnKFs and analyze their performances through extensive numerical experiments conducted with the Lorenz96 model.

Enhancing Fracture Network Characterization: A DataDriven, OutcropBased Analysis(Wiley, 20211011) [Preprint]The stochastic discrete fracture network (SDFN) model is a practical approach to model complex fracture systems in the subsurface. However, it is impossible to validate the correctness and quality of an SDFN model because the comprehensive subsurface structure is never known. We utilize a pixelbased fracture detection algorithm to digitize 80 published outcrop maps of different scales at different locations. The key fracture properties, including fracture lengths, orientations, intensities, topological structures, clusters and flow are then analyzed. Our findings provide significant justifications for statistical distributions used in SDFN modellings. In addition, the shortcomings of current SDFN models are discussed. We find that fracture lengths follow multiple (instead of single) powerlaw distributions with varying exponents. Large fractures tend to have large exponents, possibly because of a small coalescence probability. Most smallscale natural fracture networks have scattered orientations, corresponding to a small κ value (κ<3) in a von MisesFisher distribution. Large fracture systems collected in this research usually have more concentrated orientations with large κ values. Fracture intensities are spatially clustered at all scales. A fractal spatial density distribution, which introduces clustered fracture positions, can better capture the spatial clustering than a uniform distribution. Natural fracture networks usually have a significant proportion of Ttype nodes, which is unavailable in conventional SDFN models. Thus a rulebased algorithm to mimic the fracture growth and form Ttype nodes is necessary. Most outcrop maps show good topological connectivity. However, sealing patterns and stress impact must be considered to evaluate the hydraulic connectivity of fracture networks.

Mathematical modeling of immune responses against sarscov2 using an ensemble kalman filter(Mathematics, MDPI AG, 20210930) [Article]In this paper, a mathematical model was developed to simulate SARSCoV2 dynamics in infected patients. The model considers both the innate and adaptive immune responses and consists of healthy cells, infected cells, viral load, cytokines, natural killer cells, cytotoxic Tlymphocytes, Blymphocytes, plasma cells, and antibody levels. First, a mathematical analysis was performed to discuss the model’s equilibrium points and compute the basic reproduction number. The accuracy of such mathematical models may be affected by many sources of uncertainties due to the incomplete representation of the biological process and poorly known parameters. This may strongly limit their performance and prediction skills. A stateoftheart data assimilation technique, the ensemble Kalman filter (EnKF), was then used to enhance the model’s behavior by incorporating available data to determine the best possible estimate of the model’s state and parameters. The proposed assimilation system was applied on the real viral load datasets of six COVID19 patients. The results demonstrate the efficiency of the proposed assimilation system in improving the model predictions by up to 40%.

PINNup: Robust neural network wavefield solutions using frequency upscaling and neuron splitting(arXiv, 20210929) [Preprint]Solving for the frequencydomain scattered wavefield via physicsinformed neural network (PINN) has great potential in seismic modeling and inversion. However, when dealing with highfrequency wavefields, its accuracy and training cost limits its applications. Thus, we propose a novel implementation of PINN using frequency upscaling and neuron splitting, which allows the neural network model to grow in size as we increase the frequency while leveraging the information from the pretrained model for lowerfrequency wavefields, resulting in fast convergence to highaccuracy solutions. Numerical results show that, compared to the commonly used PINN with random initialization, the proposed PINN exhibits notable superiority in terms of convergence and accuracy and can achieve neuron based highfrequency wavefield solutions with a twohiddenlayer model.

Seismic velocity modeling in the digital transformation era: a review of the role of machine learning(Journal of Petroleum Exploration and Production Technology, Springer Science and Business Media LLC, 20210928) [Article]Seismic velocity modeling is a crucial step in seismic processing that enables the use of velocity information from both seismic and wells to map the depth and thickness of subsurface layers interpreted from seismic images. The velocity can be obtained in the form of normal moveout (NMO) velocity or by an inversion (optimization) process such as in fullwaveform inversion (FWI). These methods have several limitations. These limitations include enormous time consumption in the case of NMO due to manual and heavy human involvement in the picking. As an optimization problem, it incurs high cost and suffers from nonlinearity issues. Researchers have proposed various machine learning (ML) techniques including unsupervised, supervised, and semisupervised learning methods to model the velocity more efficiently. The focus of the studies is mostly to automate the NMO velocity picking, improve the convergence in FWI, and apply FWI using ML directly from the data. In the purview of the digital transformation roadmap of the petroleum industry, this paper presents a chronologic review of these studies, appraises the progress made so far, and concludes with a set of recommendations to overcome the prevailing challenges through the implementation of more advanced ML methodologies. We hope that this work will benefit experts, young professionals, and ML enthusiasts to help push forward their research efforts to achieving complete automation of the NMO velocity and further enhancing the performance of ML applications used in the FWI framework.

Seasonal Simulations of Summer Aerosol Optical Depth over the Arabian Peninsula using WRFChem : Validation, Climatology, and Variability(International Journal of Climatology, Wiley, 20210927) [Article]This study investigates the climatology and variability of summer Aerosol Optical Depth (AOD) over the Arabian Peninsula (AP) using a longterm highresolution Weather Research and Forecasting model coupled with the chemistry module (WRFChem) simulation, available groundbased and satellite observations, and reanalysis products from 2008 to 2018. The simulated spatial distribution of the summer AOD agrees well with the satellite observations and reanalysis over the AP, with spatial correlation coefficients of 0.81/0.83/0.89 with MODISA/MODIST/MERRA2, respectively. Higher values of summertime AOD are broadly found over the eastern AP regions and the southern Red Sea and minima over the northern Red Sea and northwest AP, consistent with observational datasets. The WRFChem simulation suggests that the two regions of high AOD are associated with dust advected from the Tigris–Euphrates by the northwesterly summer Shamal wind in the eastern AP and from the African Sahara via Sudan by westerly winds through the Tokar Gap for the southern AP. The high AOD over the southcentral east AP is due to locally generated dust by the action of northerly winds, modulated by variations in relative humidity, vertical motion, soil moisture, and soil temperature over the desert regions. The vertical extent of this dust is primarily driven by upward motion triggered by thermal convection over the local source region. In terms of interannual variability, summer AOD exhibits significant yeartoyear variations over the AP region. In particular, enhanced (reduced) AOD over the southern AP (Persian Gulf) is observed during La Niña conditions, favored by stronger (weaker) Tokar westerly (northwesterly summer Shamal) winds.

Preconditioned BFGSbased Uncertainty Quantification in Elastic Full Waveform Inversion(Geophysical Journal International, Oxford University Press (OUP), 20210921) [Article]Full Waveform Inversion (FWI) has become an essential technique for mapping geophysical subsurface structures. However, proper uncertainty quantification is often lacking in current applications. In theory, uncertainty quantification is related to the inverse Hessian (or the posterior covariance matrix). Even for common geophysical inverse problems its calculation is beyond the computational and storage capacities of the largest highperformance computing systems. In this study, we amend the BroydenFletcherGoldfarbShanno (BFGS) algorithm to perform uncertainty quantification for largescale applications. For seismic inverse problems, the limitedmemory BFGS (LBFGS) method prevails as the most efficient quasiNewton method. We aim to augment it further to obtain an approximate inverse Hessian for uncertainty quantification in FWI. To facilitate retrieval of the inverse Hessian, we combine BFGS (essentially a fullhistory LBFGS) with randomized singular value decomposition to determine a lowrank approximation of the inverse Hessian. Setting the rank number equal to the number of iterations makes this solution efficient and memoryaffordable even for largescale problems. Furthermore, based on the GaussNewton method, we formulate different initial, diagonal Hessian matrices as preconditioners for the inverse scheme and compare their performances in elastic FWI applications. We highlight our approach with the elastic Marmousi benchmark model, demonstrating the applicability of preconditioned BFGS for largescale FWI and uncertainty quantification.

Shear wave velocity structure beneath Northeast China from joint inversion of receiver functions and Rayleigh wave group velocities: Implications for intraplate volcanism(Wiley, 20210917) [Preprint]A highresolution 3D crustal and uppermantle shearwave velocity model of Northeast China is established by joint inversion of receiver functions and Rayleigh wave group velocities. The teleseismic data for obtaining receiver functions are collected from 107 CEA permanent sites and 118 NECESSArray portable stations. Rayleigh wave dispersion measurements are extracted from an independent tomographic study. Our model exhibits unprecedented detail in Svelocity structure. Particularly, we discover a low Svelocity belt at 7.512.5 km depth covering entire Northeast China (except the Songliao basin), which is attributed to a combination of anomalous temperature, partial melts and fluidfilled faults related to Cenozoic volcanism. Localized crustal fast Svelocity anomaly under the Songliao basin is imaged and interpreted as lateMesozoic mafic intrusions. In the upper mantle, our model confirms the presence of low velocity zones below the Changbai mountains and Lesser Xing’an mountain range, which agree with models invoking sublithospheric mantle upwellings. We observe a positive Svelocity anomaly at 5090 km depth under the Songliao basin, which may represent a depleted and more refractory lithosphere inducing the absence of Cenozoic volcanism. Additionally, the average lithosphereasthenosphere boundary depth increases from 5070 km under the Changbai mountains to 100 km below the Songliao basin, and exceeds 125 km beneath the Greater Xing’an mountain range in the west. Furthermore, compared with other Precambrian lithospheres, Northeast China likely has a rather warm crust (~480970 °C) and a slightly warm uppermost mantle (~1200 °C), probably associated with active volcanism. The Songliao basin possesses a moderately warm uppermost mantle (~1080 °C).

Fracture Permeability Estimation Under Complex Physics: A DataDriven Model Using Machine Learning(SPE, 20210915) [Conference Paper]Abstract The permeability of fractures, including natural and hydraulic, are essential parameters for the modeling of fluid flow in conventional and unconventional fractured reservoirs. However, traditional analytical cubic law (CLbased) models used to estimate fracture permeability show unsatisfactory performance when dealing with different dynamic complexities of fractures. This work presents a datadriven, physicsincluded model based on machine learning as an alternative to traditional methods. The workflow for the development of the datadriven model includes four steps. Step 1: Identify uncertain parameters and perform Latin Hypercube Sampling (LHS). We first identify the uncertain parameters which affect the fracture permeability. We then generate training samples using LHS. Step 2: Perform training simulations and collect inputs and outputs. In this step, highresolution simulations with parallel computing for the NavierStokes equations (NSEs) are run for each of the training samples. We then collect the inputs and outputs from the simulations. Step 3: Construct an optimized datadriven surrogate model. A datadriven model based on machine learning is then built to model the nonlinear mapping between the inputs and outputs collected from Step 2. Herein, Artificial Neural Network (ANN) coupling with Bayesian optimization algorithm is implemented to obtain the optimized surrogate model. Step 4: Validate the proposed datadriven model. In this step, we conduct blind validation on the proposed model with highfidelity simulations. We further test the developed surrogate model with newly generated fracture cases with a broad range of roughness and tortuosity under different Reynolds numbers. We then compare its performance to the reference NSEs solutions. Results show that the developed datadriven model delivers good accuracy exceeding 90% for all training, validation, and test samples. This work introduces an integrated workflow for developing a datadriven, physicsincluded model using machine learning to estimate fracture permeability under complex physics (e.g., inertial effect). To our knowledge, this technique is introduced for the first time for the upscaling of rock fractures. The proposed model offers an efficient and accurate alternative to the traditional upscaling methods that can be readily implemented in reservoir characterization and modeling workflows.

CO2 Leakage Rate Forecasting Using Optimized Deep Learning(SPE, 20210915) [Conference Paper]Abstract Geologic CO2 Sequestration (GCS) is a promising engineering technology to reduce global greenhouse emissions. Realtime forecasting of CO2 leakage rates is an essential aspect of largescale GCS deployment. This work introduces a datadriven, physicsfeaturing surrogate model based on deeplearning technique for CO2 leakage rate forecasting. The workflow for the development of datadriven, physicsfeaturing surrogate model includes three steps: 1) Datasets Generation: We first identify uncertainty parameters that affect the objective of interests (i.e., CO2 leakage rates). For the identified uncertainty parameters, various realizations are then generated based on Latin Hypercube Sampling (LHS). Highfidelity simulations based on a twophase blackoil solver within MRST are performed to generate the objective functions. Datasets including inputs (i.e., the uncertainty parameters) and outputs (CO2 leakage rates) are collected. 2) Surrogate Development: In this step, a timeseries surrogate model using long shortterm memory (LSTM) is constructed to map the nonlinear relationship between these uncertainty parameters as inputs and CO2 leakage rates as outputs. We perform Bayesian optimization to automate the tuning of hyperparameters and network architecture instead of the traditional trialerror tuning process. 3) Uncertainty Analysis: This step aims to perform Monte Carlo (MC) simulations using the successfully trained surrogate model to explore uncertainty propagation. The sampled realizations are collected in the form of distributions from which the probabilistic forecast of percentiles, P10, P50, and P50, are evaluated. We propose a datadriven, physicsfeaturing surrogate model based on LSTM for CO2 leakage rate forecasting. We demonstrate its performance in terms of accuracy and efficiency by comparing it with groundtruth solutions. The proposed deeplearning workflow shows promising potential and could be readily implemented in commercialscale GCS for realtime monitoring applications.

The potential of selfsupervised networks for random noise suppression in seismic data(arXiv, 20210915) [Preprint]Noise suppression is an essential step in any seismic processing workflow. A portion of this noise, particularly in land datasets, presents itself as random noise. In recent years, neural networks have been successfully used to denoise seismic data in a supervised fashion. However, supervised learning always comes with the often unachievable requirement of having noisyclean data pairs for training. Using blindspot networks, we redefine the denoising task as a selfsupervised procedure where the network uses the surrounding noisy samples to estimate the noisefree value of a central sample. Based on the assumption that noise is statistically independent between samples, the network struggles to predict the noise component of the sample due to its randomnicity, whilst the signal component is accurately predicted due to its spatiotemporal coherency. Illustrated on synthetic examples, the blindspot network is shown to be an efficient denoiser of seismic data contaminated by random noise with minimal damage to the signal; therefore, providing improvements in both the image domain and downtheline tasks, such as inversion. To conclude the study, the suggested approach is applied to field data and the results are compared with two commonly used random denoising techniques: FXdeconvolution and Curvelet transform. By demonstrating that blindspot networks are an efficient suppressor of random noise, we believe this is just the beginning of utilising selfsupervised learning in seismic applications.

The potential of selfsupervised networks for random noise suppression in seismic data(arXiv, 20210915) [Preprint]Noise suppression is an essential step in any seismic processing workflow. A portion of this noise, particularly in land datasets, presents itself as random noise. In recent years, neural networks have been successfully used to denoise seismic data in a supervised fashion. However, supervised learning always comes with the often unachievable requirement of having noisyclean data pairs for training. Using blindspot networks, we redefine the denoising task as a selfsupervised procedure where the network uses the surrounding noisy samples to estimate the noisefree value of a central sample. Based on the assumption that noise is statistically independent between samples, the network struggles to predict the noise component of the sample due to its randomnicity, whilst the signal component is accurately predicted due to its spatiotemporal coherency. Illustrated on synthetic examples, the blindspot network is shown to be an efficient denoiser of seismic data contaminated by random noise with minimal damage to the signal; therefore, providing improvements in both the image domain and downtheline tasks, such as inversion. To conclude the study, the suggested approach is applied to field data and the results are compared with two commonly used random denoising techniques: FXdeconvolution and Curvelet transform. By demonstrating that blindspot networks are an efficient suppressor of random noise, we believe this is just the beginning of utilising selfsupervised learning in seismic applications.

Cycleskipping mitigation using misfit measurements based on differentiable dynamic time warping(arXiv, 20210909) [Preprint]The dynamic time warping (DTW) distance has been used as a misfit function for waveequation inversion to mitigate the local minima issue. However, the original DTW distance is not smooth; therefore it can yield a strong discontinuity in the adjoint source. Such a weakness does not help nonlinear inverse problems converge to a plausible minimum by any means. We therefore introduce for the first time in geophysics the smooth DTW distance, which has demonstrated its performance in time series classification, clustering, and prediction as the loss function. The fundamental idea of such a distance is to replace the $\min$ operator with its smooth relaxation. Then it becomes possible to define the analytic derivative of DTW distance. The new misfit function is entitled to the differentiable DTW distance. Moreover, considering that the warping path is an indicator of the traveltime difference between the observed and synthetic trace, a penalization term is constructed based on the warping path such that the misfit accumulation by the penalized differentiable DTW distance is weighted in favor of the traveltime difference. Numerical examples demonstrate the advantage of the penalized differentiable DTW misfit function over the conventional nondifferentiable one.

Dualband generative learning for lowfrequency extrapolation in seismic land data(Society of Exploration Geophysicists, 20210901) [Conference Paper]The presence of lowfrequency energy in seismic data can help mitigate cycleskipping problems in fullwaveform inversion. Unfortunately, the generation and recording of lowfrequency signals in seismic exploration remains a nontrivial task. Extrapolation of missing lowfrequency content in field data might be addressed in a datadriven framework. In particular, deep learning models trained on synthetic data could be used for inference on the field data. Such an implementation of switching application domains remains challenging. We, therefore, propose the concept of generative dualband learning to facilitate the knowledge transfer between synthetic and field seismic data applications of lowfrequency data extrapolation. We first explain the twostep procedure for training a generative adversarial network (GAN) that extrapolates low frequencies. Then, we describe the workflow for synthetic dataset generation. Finally, we explore the feasibility of the dualband learning concept on real nearsurface land data acquired in Saudi Arabia. The presence of lowfrequency energy in seismic data can help mitigate cycleskipping problems in fullwaveform inversion. Unfortunately, the generation and recording of lowfrequency signals in seismic exploration remains a nontrivial task. Extrapolation of missing lowfrequency content in field data might be addressed in a datadriven framework. In particular, deep learning models trained on synthetic data could be used for inference on the field data. Such an implementation of switching application domains remains challenging. We, therefore, propose the concept of generative dualband learning to facilitate the knowledge transfer between synthetic and field seismic data applications of lowfrequency data extrapolation. We first explain the twostep procedure for training a generative adversarial network (GAN) that extrapolates low frequencies. Then, we describe the workflow for synthetic dataset generation. Finally, we explore the feasibility of the dualband learning concept on real nearsurface land data acquired in Saudi Arabia.

Highdimensional wavefield solutions based on neural network functions(Society of Exploration Geophysicists, 20210901) [Conference Paper]Waveﬁeld solutions are critical for applications ranging from imaging to full waveform inversion. These waveﬁelds are often large, especially for 3D media, and multiple p o int sources, like Green’s functions. A recently introduced framework based on neu ra l networks admitting functional solutions to partial differential equations(PDEs) o↵ers the opportunity to solve the Helmholtz equation with a neural network (NN) model. The input to such an NN is a location in space and the output are the real and imaginary parts of the scattered waveﬁeldat that location, thus, acting like a function. The network is trained on random input points in space and a variance of the Helmh o lt z equation for the scatteredwaveﬁeld is used as the loss function to update the network parameters. In spite of the methods ﬂexibility, like handling irregular surfaces and complex media, and its potential for velocity model building, the cost of training the network far exceeds that of numerical solutions. Relying on the network’s ability to learn waveﬁeld features, we extend the dimension of this NN function to learn the waveﬁeld for many sources and frequencies, simultaneously. We show, in this preliminary study, that reasonable waveﬁeld solutions can be predicted using smaller networks. This includes waveﬁelds for frequencies not within the training range. The new NN function has the potential to eﬃciently represent the waveﬁeld as a function of location in space, as well as source location and frequency.

Selfsupervised learning for random noise suppression in seismic data(Society of Exploration Geophysicists, 20210901) [Conference Paper]A staunch companion to seismic signals, noise consistently hinders processing and interpretation of seismic data. Borrowing ideas from the field of computer vision, we propose the use of selfsupervised deep learning for the task of random noise suppression. These techniques require no clean training data and therefore remove any requirement of precleaning of field data or the generation of realistic synthetic datasets for training purposes. Through the use of blindspot networks, we show that selfsupervised Noise2Void (N2V) procedure can be adapted to the seismic context, and trained solely on noisy data. An initial validation performed on a synthetic dataset corrupted by additive, white, Gaussian noise confirms that N2V can be trained to accurately separate the correlated seismic signal from the uncorrelated noise. Furthermore, when correlated and random noise are both present in the data, whilst the model cannot remove the majority of the correlated noise, a portion of it is suppressed alongside the random noise. Finally, the network is validated on a field dataset that is heavily contaminated with strong random noise caused by the surface conditions. The N2V denoising approach is shown to drastically reduce the random noise in the data. Through these examples, we have validated the effectiveness of blindspot networks on highly oscillating signals, such as seismic data. This pave the way for the application of other selfsupervised procedures to seismic data that go beyond the assumption of statistically independent noise.

Misfit functions based on differentiable dynamic time warping for waveform inversion(Society of Exploration Geophysicists, 20210901) [Conference Paper]Misfit functions based on differentiable dynamic time warping (DTW) have demonstrated an excellent performance in various sequencerelated tasks. We introduce this concept in the context of waveform inversion and discuss a fast algorithm to calculate the first and second derivatives of such misfits. The DTW distance is originally calculated by solving a series of min sorting problems, thus it is not differentiable. The fundamental idea of differentiable DTW is replacing the min operator with its smooth relaxation. It is then straightforward to solve the derivatives following the differentiation rules, which results in both the differentiable misfit measurements and warping path. This path weights the traveltime mismatch more than its amplitude counterpart. We can construct a penalization term based on this warping path. The penalized misfit function is adaptable to measure traveltime and amplitude separately. Numerical examples show the flexibility and the performance of the proposed misfit function in mitigating local minima issues and retrieving the longwavelength model features

Tomographic deconvolution of reflection tomograms(Society of Exploration Geophysicists, 20210901) [Conference Paper]We present a tomographic deconvolution procedure for highresolution imaging of velocity anomalies between reflecting interfaces. The key idea is to first invert reflection or transmission traveltimes for the background velocity model. A convolutional neural network (CNN) model is then trained to estimate the inverse to the blurred tomogram consisting of small scatterers in the background velocity model. We call this CNN a tomographic deconvolution operator because it deconvolves the blurring artifacts in traveltime slowness tomograms. This procedure is similar to that of migration deconvolution which deconvolves the migration butterfly artifacts in migration images. Results with synthetic examples show the effectiveness of this procedure in significantly sharpening the tomographic images of small scatterers.