# Browsing by Subject "Seismic inversion"

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Item Advanced methods for subsurface velocity estimation : trans-dimensional inversion and machine learning(2019-12) Biswas, Reetam; Sen, Mrinal K.; Arnulf, Adrien F.; Spikes, Kyle T.; Grand, Stephen P.; Bennett, NicholasShow more Inversion is a widely adopted tool to estimate the subsurface elastic properties of the Earth from seismic data. However, it faces several obstacles due to lack of adequate data coverage, and various assumptions made in forward modeling and inversion algorithms resulting often in sub-optimal results. One such assumption is the choice of parameterization of the model. In general, it is assumed to be known a priori and kept fixed. This can lead to either over or under parameterization, causing either overfitting or underfitting the data. In the first part of my thesis, I address the problem of model parameterization. Along with searching for models that fit the data, I also solve for the optimum number of model parameters required as dictated by the data. In a deterministic approach, I use the Basis Pursuit Inversion (BPI), which imposes sparsity in the model parameterization by adding a regularization term of L₁ norm of the model vector. The weight of the regularization term plays a dominant role, and I propose an approach for automatic calculation of this weighting factor. Alternately, I also develop a stochastic method, using Bayesian framework to solve my inverse problem in which the model parameters are treated as unknown. Unlike BPI, this method also provides us with estimates of uncertainty. Here, I make use of the Reversible Jump Markov Chain Monte Carlo (RJMCMC) framework, which allows changing the number of model parameters. However, the conventional RJMCMC is generally very slow as it attempts to sample a variable dimensional model space. To address this, I propose a new method called the Reversible Jump Hamiltonian Monte Carlo (RJHMC), which improves the efficiency by combining RJMCMC with a gradient-based Hamiltonian Monte Carlo (HMC). The gradient-based steps ensure quick convergence by allowing the sampling to take large steps guided by the gradient instead of complete random steps. I represent my model space using a layer-based earth model for the 1D problem and using an adaptive ensemble of nuclei along with Voronoi partition for a 2D problem. Subsequently, I use the method to solve the deconvolution problem in 1D, and tomography and Full Waveform Inversion problems in a 2D setting. It also provides estimates of the elastic parameters and marginal distribution of the number of model parameters. I use the 1D RJHMC to estimate density, along with P- and Swave velocities from a pre-stack angle gather. The region contains paleo-residual gas (PRG), which shows same signature as that of normal gas saturation, and can be better differentiated using density. Additionally, I applied trans-dimensional tomography to invert for P-wave velocity structure at an Axial Seamount, which is one of the most volcanically active regions in northeastern Pacific. In addition to BPI and RJMHC, I develop workflows, which take advantage of the hybrid schemes and Machine Learning (ML) algorithms. Solving an elastic FWI problem can be challenging, as it is very computationally expensive in comparison to the more commonly used acoustic formulation. I propose a hybrid scheme, where the initial P-wave velocity result from an acoustic FWI can be used to perform less expensive pre-stack Amplitude vs. Angle (AVA) inversion. This provides us with all three elastic parameters: P-wave velocity, S-wave velocity, and Density. Several inverse problems can be mapped into a neural network architecture, which can be solved using the currently developed deep learning algorithms. The last part of my dissertation describes two machine learning (ML) algorithms that I have developed for seismic inversion. I use a Convolutional Neural Network (CNN) to perform seismic inversion, in which instead of using the traditional way of using input-output pairs to train the network, I use the physics of the forward wave-propagation to guide the training. It circumvents the need for providing the label data during training and makes it unsupervised. In addition to this, I propose to use a Recurrent Neural Network (RNN) to estimate NMO velocities, which is a basic seismic processing technique. Generally, the NMO velocity is hand-picked and requires a lot of human intervention and computation time. Using this workflow with only 10% of data used as training, the network estimates NMO velocities almost instantly for the rest of the datasetShow more Item Characterization of the Cana-Woodford Shale using fractal-based, stochastic inversion, Canadian County, Oklahoma(2016-05) Borgman, Barry Michael; Spikes, Kyle; Sen, Mrinal K; Wilson, Clark RShow more The past decade has seen a surge in unconventional hydrocarbon exploration and production, driven by advances in horizontal drilling and hydraulic fracturing. Even with such advances, reliable models of the subsurface are crucial in all phases of exploitation. This study focuses on the methods used for estimation of the elastic properties (density, velocity, and impedance), which play a key role in targeting reservoir zones ideal for hydraulic fracturing. Well-log data provides high-resolution vertical measurements of elastic properties, but a relatively shallow depth of investigation imposes spatial limitations. Seismic data provides broader horizontal coverage at lower cost, but sacrifices vertical resolution. Thin beds present in many unconventional reservoirs fall below seismic resolution. In addition, the band-limited nature of seismic data results in the absence of low-frequency content of the Earth model, as well as the high-frequency content present in well logs. Seismic inversion is a process that provides estimates of elastic properties given input seismic and well data. Stochastic inversion is a method that uses well-log data as a priori information, with an added aspect of randomness. The method generates many realizations using the same input model and takes an average of those realizations. We implement two separate stochastic inversion algorithms to estimate P-impedance in the Cana-Woodford Shale in west-central Oklahoma. First, we use a fractal-based, very fast simulated annealing algorithm that exploits the fractal characteristics found in well-log data to build a prior model. The method of very fast simulated annealing optimizes our elastic model by searching for the minimum misfit between observed and synthetic seismic traces. Next, we use a principal component analysis (PCA) based stochastic inversion algorithm to invert for impedance at all traces simultaneously. Comparison of the results with traditional deterministic inversion results shows improved vertical resolution while honoring the low-frequency content of the Earth model. The PCA-based inversion results also show improved lateral continuity of the elastic profile along our 2D line. The impedance profile from the PCA-based approach provides a better representation of the vertical and horizontal variability of the reservoir, allowing for improved targeting of frackable zones.Show more Item Full-waveform inversion in three-dimensional PML-truncated elastic media : theory, computations, and field experiments(2015-05) Fathi, Arash; Kallivokas, Loukas F.; Dawson, Clinton N; Demkowicz, Leszek F; Ghattas, Omar; Manuel, Lance; Stokoe II, Kenneth HShow more We are concerned with the high-fidelity subsurface imaging of the soil, which commonly arises in geotechnical site characterization and geophysical explorations. Specifically, we attempt to image the spatial distribution of the Lame parameters in semi-infinite, three-dimensional, arbitrarily heterogeneous formations, using surficial measurements of the soil's response to probing elastic waves. We use the complete waveforms of the medium's response to drive the inverse problem. Specifically, we use a partial-differential-equation (PDE)-constrained optimization approach, directly in the time-domain, to minimize the misfit between the observed response of the medium at select measurement locations, and a computed response corresponding to a trial distribution of the Lame parameters. We discuss strategies that lend algorithmic robustness to the proposed inversion schemes. To limit the computational domain to the size of interest, we employ perfectly-matched-layers (PMLs). The PML is a buffer zone that surrounds the domain of interest, and enforces the decay of outgoing waves. In order to resolve the forward problem, we present a hybrid finite element approach, where a displacement-stress formulation for the PML is coupled to a standard displacement-only formulation for the interior domain, thus leading to a computationally cost-efficient scheme. We discuss several time-integration schemes, including an explicit Runge-Kutta scheme, which is well-suited for large-scale problems on parallel computers. We report numerical results demonstrating stability and efficacy of the forward wave solver, and also provide examples attesting to the successful reconstruction of the two Lame parameters for both smooth and sharp profiles, using synthetic records. We also report the details of two field experiments, whose records we subsequently used to drive the developed inversion algorithms in order to characterize the sites where the field experiments took place. We contrast the full-waveform-based inverted site profile against a profile obtained using the Spectral-Analysis-of-Surface-Waves (SASW) method, in an attempt to compare our methodology against a widely used concurrent inversion approach. We also compare the inverted profiles, at select locations, with the results of independently performed, invasive, Cone Penetrometer Tests (CPTs). Overall, whether exercised by synthetic or by physical data, the full-waveform inversion method we discuss herein appears quite promising for the robust subsurface imaging of near-surface deposits in support of geotechnical site characterization investigations.Show more Item Gas-hydrates saturation estimation in Krishna-Godavari basin, India(2013-05) Das, Kumar Sundaram; Sen, Mrinal K.; Tatham, Robert; Spikes, KyleShow more Gas hydrates are an unconventional energy resource. They may become an important source of energy for India in the future. They occur offshore along the continental margin. They are currently in exploratory and evaluation stages and their quantification is an important task. The goal of this thesis is to demonstrate a new technique for the estimation of gas hydrates volumes. The region of study is the Krishna-Godavari basin. It is located on the eastern offshore areas of India. The presence of gas hydrates has been proven by drilling into marine sediments as a part of the Indian National Gas Hydrates Program. Borehole subsurface and surface seismic data were collected during this expedition. I use a 2D seismic reflection line and borehole log data for my study. The method I use for estimation of gas hydrates saturation uses a combination of inversion of seismic reflection data and development of seismic attributes. My approach can be broadly described by following steps: 1. Process the seismic data to remove noise. Use stacked and migrated data along with well logs to perform poststack seismic inversion to obtain impedance information in volumetric portions of the subsurface. 2. Use NMO corrected CDP gather records of the seismic reflection data along with subsurface well logs to perform prestack seismic inversion to obtain impedance volumes. 3. Compare the results from step1 and step 2 and use the best results to perform multi-attribute analysis using a neural network method to predict resistivity and porosity logs at the well location. Use the transform equations obtained at the well location to predict the well logs throughout the seismic section in the desired zone of interest. 4. Use an anisotropic equivalent of Archie’s law that relates resistivity and porosity to saturation to predict saturation throughout the seismic reflection section. The majority of the previous work done in the region is limited to gas hydrates quantification only at the well location. By using neural networks for multi-attribute analysis, I have demonstrated a statistical based method for the prediction of log properties away from well location. My results suggest gas hydrates saturation in the range of 50-80% in the zone of interest. The estimated saturation of gas hydrates matches up very closely with the saturation estimates obtained from the cores recovered during coring of the boreholes. Hence my method provides a reliable method of quantification of gas hydrates by making best possible use of seismic and well log data. The unique combination of impedance derived attributes and neural-network includes the non-linear behavior in the predictive transform relationships. The use of an anisotropic formulation of Archie’s law to estimate saturation also produces accurate results confirmed with the observed gas-hydrates saturation.Show more Item Machine learning algorithms for solving some seismic inversion challenges(2021-05-03) Phan, Son Dang Thai; Sen, Mrinal K.; Spikes, Kyle; Fomel, Sergey; Jackson, Charles; Foster, DouglasShow more Seismic inversion is a popular quantitative approach to extract some of the subsurface properties from seismic amplitudes by utilizing the physics of the wave propagation through earth layers, in forms of the empirical formulations that simulate the energy distribution phenomenon. Typical inversions are performed with limited offset angles, and in a small time-window, within which the wavelet is assumed to be stationary, and the property contrasts are small across the boundaries. These exposes the process to several major problems: (1) the limited resolution due to wavelet effects, (2) the dependence on some rock physics models when inverting for petrophysical properties, and (3) the resolution discrepancy between the time domain seismic signal and well logs in depth domain. The primary goal of this research is to use machine learning to solve these challenges, by designing and applying proper neural network structures and suitable training schematics. Firstly, a single-layer Boltzmann machine is implemented as an unsupervised learning algorithm to predict the elastic properties at higher resolution than that can be achieved by conventional approaches, while still retaining the physical relationship between the seismic amplitudes and reflectivity series. The high-resolution results are produced from the accurate post-inversion reflectivity series, which is not bounded by the wavelet effects, and novel model update schemes. Secondly, a new multimodal Cross-shape deep Boltzmann machine is designed to simultaneously capture six possible relationships between four different input training data to invert for petrophysical properties from the pre-stack seismic amplitudes in datasets with limited well coverages. This algorithm has a significant advantage in avoiding the uncertainties associated with the data fitting algorithms to create the rock physics models to guide the solution. Last but not the least, a novel multimodal deep learning network is applied to predict the posterior distribution of the subsurface elastic properties from a seismic gather, to resolve the resolution discrepancy challenge, by a smart preparation of the training label in the form of time dependent probability distributions. The biggest advantage of this algorithm is the avoidance of the heuristic calculation of the partition function, which is required to calculate the posterior distributions of common neural network outputs. While the first algorithm requires an input wavelet to constraint the results, the other two algorithms do not, which make them appropriate for inversion in depth domain, or with nonstationary signalsShow more Item Mechanisms of lithospheric failure during late continental rifting and early subduction(2021-08-13) Shuck, Brandon Douglas; Van Avendonk, Harm J. A.; Gulick, Sean P. S.; Bangs, Nathan L.B.; Becker, Thorsten W.; Lavier, Luc L.; Shillington, Donna J.Show more Two fundamental components of plate tectonics are the separation of continents, leading to new ocean basins, and the initiation of subduction zones, which facilitate recycling of the Earth's outer shell into its interior. In order for continental rifting and subduction initiation to succeed, tectonic driving forces must overcome resisting forces and strength of the lithosphere. If achieved, the lithosphere undergoes failure and a new plate boundary is established, wherein subsequent strain is localized along a narrow weak zone, such as a subduction zone megathrust or seafloor spreading center. Though these processes are conceptually straightforward, many aspects remain elusive. In particular, intact lithospheric strength is thought to be far greater than available tectonic forces, yet observationally continental breakup and subduction initiation occur frequently throughout Earth's history. The goal of this dissertation is to further investigate this force paradox by exploring the weakening mechanisms that assist lithospheric failure during late continental rifting and early subduction. Active-source seismic data are used to image geologic processes and the tectonic evolution along two study areas - the Eastern North American Margin and the Puysegur Margin, New Zealand. Along the Eastern North American Margin, I show that new mafic crust was emplaced above a thinning subcontinental mantle lithosphere that resisted breakup despite abundant magmatism. I propose a new model in which continental crust separated before the lithosphere and complete breakup was not achieved for ~25 Myrs after the arrival of melts. I then image mantle dynamics near the lithosphere-asthenosphere boundary during final stages of rifting and show that rupture was enabled by highly organized crystallographic textures that focused melt and deformation into a narrow weak zone. At the Puysegur Margin, I argue that subduction initiation was aided by previous phases of continental rifting and strike-slip. Rifting stretched continental crust of Zealandia and later dextral strike-slip translated thin and dense oceanic crust from farther south and juxtaposed it with thick continental crust at a collisional restraining bend. Ideal conditions ensued, where buoyancy contrasts and pre-existing fault zones weakened the lithosphere and facilitated subduction nucleation. Since initial underthrusting, subduction initiation became more efficient as the trench propagated southward over time. I conclude with a novel 4D model where subduction initiation is resisted at the site of nucleation but followed by mechanically easier and faster initiation and lateral propagation as the plate boundary develops along-strike. Inherited lithospheric heterogeneities and weak zones are the dominant mechanism allowing the plate tectonic cycle to persist on Earth.Show more Item Novel stochastic inversion methods and workflow for reservoir characterization and monitoring(2013-12) Xue, Yang, active 2013; Sen, Mrinal K.Show more Reservoir models are generally constructed from seismic, well logs and other related datasets using inversion methods and geostatistics. It has already been recognized by the geoscientists that such a process is prone to non-uniqueness. Practical methods for estimation of uncertainty still remain elusive. In my dissertation, I propose two new methods to estimate uncertainty in reservoir models from seismic, well logs and well production data. The first part of my research is aimed at estimating reservoir impedance models and their uncertainties from seismic data and well logs. This constitutes an inverse problem, and we recognize that multiple models can fit the measurements. A deterministic inversion based on minimization of the error between the observation and forward modeling only provides one of the best-fit models, which is usually band-limited. A complete solution should include both models and their uncertainties, which requires drawing samples from the posterior distribution. A global optimization method called very fast simulated annealing (VFSA) is commonly used to approximate posterior distribution with fast convergence. Here I address some of the limitations of VFSA by developing a new stochastic inference method, named Greedy Annealed Importance Sampling (GAIS). GAIS combines VFSA with greedy importance sampling (GIS), which uses a greedy search in the important regions located by VFSA to attain fast convergence and provide unbiased estimation. I demonstrate the performance of GAIS on post- and pre-stack data from real fields to estimate impedance models. The results indicate that GAIS can estimate both the expectation value and the uncertainties more accurately than using VFSA alone. Furthermore, principal component analysis (PCA) as an efficient parameterization method is employed together with GAIS to improve lateral continuity by simultaneous inversion of all traces. The second part of my research involves estimation of reservoir permeability models and their uncertainties using quantitative joint inversion of dynamic measurements, including synthetic production data and time-lapse seismic related data. Impacts from different objective functions or different data sets on the model uncertainty and model predictability are investigated as well. The results demonstrate that joint inversion of production data and time-lapse seismic related data (water saturation maps here) reduces model uncertainty, improves model predictability and shows superior performance than inversion using one type of data alone.Show more Item Pre-stack inversion for porosity estimation from seismic data in an oil field, Eastern Saudi Arabia(2008) AlMuhaidib, Abdulaziz Mohammad; Sen, Mrinal K.Show more The main objective of seismic inversion is to obtain earth model parameters from seismic reflection data. In other words, it is the process of determining what physical characteristics of rocks and fluids (i.e., P-impedance, shear impedance, and density) could have produced the seismic record. The aim of this study is to obtain reservoir properties, such as porosity both at the well locations and in the inter-well regions from seismic data and incorporated well logs. The target is a Jurassic carbonate reservoir from an oil field located to the East of Saudi Arabia. The purpose was to investigate the reliability of inferring the elastic properties (Zp, Zs, ρ) from seismic data in this field, and to build a geologic framework for flow simulation for better reservoir production forecasting and management. The seismic data were processed with special attention to preserving the true reflection amplitudes, and were time migrated before stack. Residual moveout from multiples after NMO, however, is almost horizontal at near offset, and constructively add to the stacked amplitude. Therefore, we applied a pre-stack inversion technique on the seismic data, after careful processing, including removal of residual internal multiples. Such an inversion incorporates all of the offsets to obtain an optimum acoustic impedance model. We also investigated the stability of inverting shear impedance and density in the field of study. The seismic inversion results were overall very good and stable for P-impedance. The match between borehole log and seismic impedance profiles was excellent for the high-contrast events and variable for the low contrast in acoustic impedance, depending on the location within the field. Inverted shear impedance results were less stable compared to P-Impedance, while density was totally unstable and has not been resolved. In general, areas of poor inversion coincided with the zones of poor quality seismic data. The borehole log data showed a good impedance-porosity relationship. The Raymer-Hunt-Gardner impedance-porosity empirical relation fits the borehole data very well. Thus, I used the Raymer-Hunt-Gardner relation, with coefficients for this field derived from the log data, to convert inverted acoustic impedance into a porosity model for the field. Based on the new quantitative seismic reservoir characterization, I was able to identify additional areas of potentially good reservoir qualityShow more Item Regularizing seismic inverse problems : transdimensional and machine learning based strategies(2023-12) Dhara, Arnab; Sen, Mrinal K.; Spikes, Kyle; Zhao, Zeyu; Fomel, SergeyShow more Seismic inversion is a well-established technique in geophysics used to generate quantitative estimates of subsurface rock properties, such as lithology, porosity, fluid content and density from seismic data. It is an iterative process where an initial model is updated based on the comparison between the observed data and the synthetic data generated by simulating the propagation of seismic waves using approximations of the wave equation. However, such inverse problems are high-dimensional and highly non-linear. These problems are mathematically ill-posed resulting in non-uniqueness.The non-uniqueness can be attributed to incomplete data coverage, inaccurate forward model and noise in the data. In this thesis, I address the problem of regularizing such inverse problems. Regularization aims to mitigate the effect of noise and incomplete data coverage by introducing addtional constraints in the inverse problems, thus improving the stability of the problem and preventing unrealistic or erratic results. I study both stochastic and deterministic inverse algorithms. Stochastic seismic inversion takes into consideration the ill-posedness and uncertainty by incorporating probabilistic methods into the inversion process. The Bayesian approach to stochastic inversion provides a natural framework for uncertainty quantification. Markov Chain Monte Carlo (MCMC) sampling is the most common Bayesian inference method. Traditional MCMC algorithms when applied to the same problem, presume and fix the model parameterization, which leads to an overfitting problem to the noise in the data. Hence, in order to reduce the overfitting, a subjective regularization is imposed on the problem. Conventional MCMC algorithms widely used for geophysical inverse problems presume and fix the number of model parameters. However, reversible jump MCMC (RJMCMC) allows the number of model parameters (model dimensionality) to vary during the inversion process and thus appropriate model complexity is directly inferred from data and the prior distribution. However, current implementation of the transdimensional RJMCMC algorithms do not take into account the multimodal distribution of elastic properties and honour the rock physics relationship among themelastic properties. To address this problem, I extend the RJMCMC method to the problem of discrete-continuous seismic inverse problem where I simultaneously invert for facies and elastic reservoir properties from pre-stack seismic data. Secondly, I looked into the application of machine learning algorithms for seismic inverse problems. Conventional machine learning algorithms designed directly to map seismic data to desired properties donot take into account physics based constraints or produce robust uncertainty estimates. Moreover, they require a large amount of training data. To overcome this issue, an Invertible Neural Network is designed to estimate elastic and petrophysical properties from seismic data. INN establishes bijective mappings between the input (physical model) and the output (observed data) and introduces an additional latent output variable to capture the information that is otherwise lost during the forward modeling process. The latent variable can be used to estimate the complete posterior distribution of model parameters. Finally, I designed workflows based on Physics Guided Machine Learning paradigm for full waveform inversion. Unlike traditional machine learning algorithms where one trains the network using labelled seismic data-velocity pairs, I use the physics of wave propagation to train the network. My physics guided network overcomes several issues faced by conventional full waveform inversion algorithms like cycle skipping and inter parameter crosstalk. Cycle skipping refers to situations where FWI fails to find the correct solution due to inadequate initial model assumptions, absence of low frequencies or the presence of highly complex subsurface features. The cycle-skipping issue is further exacerbated in case of multiparameter full waveform inversion. Interparameter crosstalk occurs due to coupling effects between different parameters. The coupling effects between different parameters impedes convergence to global minima since the misfit caused by the inaccuracy in the estimate of one model parameter are wrongly ascribed to a different model parameter.Show more