ItemLocating and Monitoring Microseismicity, Hydraulic Fracture and Earthquake Rupture Using Elastic Time-Reversal Imaging(Oxford Univ Press on behalf of The Royal Astronomical Society, 2019-01) Yang, Jidong; Zhu, Hejun; 0000-0002-7452-075X (Zhu, H); Yang, Jidong; Zhu, HejunLocating and monitoring passive seismic sources provides us important information for studying subsurface rock deformation, injected fluid migration, regional stress conditions as well as fault rupture mechanism. In this paper, we present a novel passive-source monitoring approach using vector-based elastic time-reversal imaging. By solving the elastic wave equation using observed multicomponent records as boundary conditions, we first compute back-propagated elastic wavefields in the subsurface. Then, we separate the extrapolated wavefields into compressional (P-wave) and shear (S-wave) modes using the vector Helmholtz decomposition. A zero-lag cross-correlation imaging condition is applied to the separated pure-mode vector wavefields to produce passive-source images. We compare imaging results using three implementations, that is dot-product, energy and power. Numerical experiments demonstrate that the power imaging condition gives us the highest resolution and is less sensitive to the presence of random noises. To capture the propagation of microseismic fracture and earthquake rupture, we modify the traditional zero-lag cross-correlation imaging condition by summing the multiplication of the separated P and S wavefields within local time windows, which enables us to capture the temporal and spatial evolution of earthquake rupture. 2-D and 3-D numerical examples demonstrate that the proposed method is capable of accurately locating point sources, as well as delineating dynamic propagation of hydraulic fracture and earthquake rupture. ItemElastic Wavefield Separation in Anisotropic Media Based on Eigenform Analysis and Its Application in Reverse-Time Migration(Oxford University Press, 2019-02-13) Yang, Jidong; Zhang, H.; Zhao, Y.; Zhu, Hejun; 0000-0002-7452-075X (Zhu, H); Yang, Jidong; Zhu, HejunSeparating compressional and shear wavefields is an important step in elastic reverse-time migration, which can remove wave-mode crosstalk artefacts and improve imaging quality. In vertical (VTI) and titled (TTI) transversely isotropic media, the state-of-the-art techniques for wavefield separation are based on either non-stationary filter or low-rank approximation. They both require intensive Fourier transforms for models with strong heterogeneity. Based on the eigenform analysis, we develop an efficient pseudo-Helmholtz decomposition method for the VTI and TTI media, which produces vector P and S wavefields with the same amplitudes, phases and physical units as the input elastic wavefields. Starting from the elastic VTI wave equations, we first derive the analytical eigenvalues and eigenvectors, then use the Taylor expansion to approximate the square-root term in the eigenvalues, and finally obtain a zero-order and a first-order pseudo-Helmholtz decomposition operator. Because the zero-order operator is the true solution for the case of ϵ = δ, it produces accurate wavefield separation results for elliptical anisotropic media. The first-order separation operator is more accurate for non-elliptical anisotropy. Since the proposed pseudo-Helmholtz decomposition requires solving an anisotropic Poisson's equation, we propose two fast numerical solvers. One is based on the sparse lower-upper (LU) factorization, which can be repeatedly applied to the input elastic wavefields once computing the lower and upper triangular matrices. The second solver assumes the model parameters are laterally homogeneous within a given migration aperture. This assumption allows us to efficiently solve the anisotropic Poisson's equation in the z k x domain, where k x and z denote the horizontal wavenumber and depth, respectively. Using the coordinate transform, we extend the pseudo-Helmholtz decomposition to the TTI media. The separated vector wavefields are used to produce PP and PS images by applying a dot-product imaging condition. Several numerical examples demonstrate the feasibility and applicability of the proposed methods. © The Author(s) 2019. Published by Oxford University Press on behalf of The Royal Astronomical Society. ItemTime-Domain Least-Squares Migration Using the Gaussian Beam Summation Method(Oxford University Press) Yang, Jidong; Zhu, Hejun; McMechan, George A.; Yue, Yubo; 0000-0002-7452-075X (Zhu, H); 103911551 (McMechan, GA); Yang, Jidong; Zhu, Hejun; McMechan, George A.With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modelling rather than the inverse operator.We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modelling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a pre-conditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration. © The Author(s) 2018. Published by Oxford University Press on behalf of The Royal Astronomical Society. ItemCrustal Wave Speed Structure of North Texas and Oklahoma Based on Ambient Noise Cross-Correlation Functions and Adjoint Tomography(Oxford University Press) Zhu, Hejun; Zhu, HejunRecently, seismologists observed increasing seismicity in NorthTexas and Oklahoma. Based on seismic observations and other geophysical measurements, numerous studies have suggested links between the increasing seismicity andwastewater injection during unconventional oil and gas exploration. To better monitor seismic events and investigate their triggering mechanisms, we need an accurate 3-D crustalwave speed model for the study region. Considering the uneven distribution of earthquakes in this area, seismic tomography with local earthquake records has difficulties achieving even illumination. To overcome this limitation, in this study, ambient noise cross-correlation functions are used to constrain subsurface variations in wave speeds. I use adjoint tomography to iteratively fit frequency-dependent phase differences between observed and predicted band-limited Green's functions. The spectral element method is used to numerically calculate the band-limited Green's functions and the adjoint method is used to calculate misfit gradients with respect to wave speeds. A total of 25 preconditioned conjugate gradient iterations is used to updatemodel parameters and minimize datamisfits. Features in the new crustal model TO25 correlate well with geological provinces in the study region, including the Llano uplift, the Anadarko basin, the Ouachita orogenic front, etc. In addition, there are relatively good correlations between seismic results with gravity and magnetic observations. This new crustal model can be used to better constrain earthquake source parameters in North Texas and Oklahoma, such as epicentre location as well as moment tensor solutions, which are important for investigating triggering mechanisms between these induced earthquakes and unconventional oil and gas exploration activities. © The Author(s) 2018. Published by Oxford University Press on behalf of The Royal Astronomical Society. ItemSeismogram Registration via Markov Chain Monte Carlo Optimization and Its Applications in Full Waveform Inversion(Oxford Univ Press, 2018-11-05) Zhu, Hejun; 0000-0003-3556-8096 (Zhu, H); Zhu, HejunCycle skipping is a serious issue in full waveform inversion (FWI) since it leads to local minima. To date, most FWI algorithms depend on local gradient based optimization approaches, which cannot guarantee convergence towards the global minimum if the misfit function involves local minima and the starting model is far from the true solution. In this study, I propose a misfit function based on non-stationary time warping functions, which can be calculated by solving a seismogram registration problem. Considering the inherent cycle skipping and local minima issues of the registration problem, I use a Markov chain Monte Carlo (MCMC) method to solve it. With this global optimization approach, I am able to directly sample the global minimum and measure non-stationary traveltime differences between observed and predicted seismograms. The a priori constraint about the sparsity of the local warping functions is incorporated to eliminate unreasonable solutions. No window selections are required in this procedure. In comparison to other approaches for measuring traveltime differences, the proposed method enables us to align signals with different numbers of events. This property is a direct consequence of the usage of MCMC optimization and sparsity constraints. Several numerical examples demonstrate that the proposed misfit function allows us to tackle the cycle skipping problem and construct accurate long-wavelength velocity models even without low frequency data and good starting models. ItemRadial Anisotropy of the North American Upper Mantle Based on Adjoint Tomography with Usarray(Oxford Univ Press, 2017-07-31) Zhu, Hejun; Komatitsch, Dimitri; Tromp, Jeroen; 0000-0003-3556-8096 (Zhu, H); Zhu, HejunWe use seismic data from USArray to image the upper mantle underneath the United States based on a so-called 'adjoint tomography', an iterative full waveform inversion technique. The inversion uses data from 180 regional earthquakes recorded by 4516 seismographic stations, resulting in 586 185 frequency-dependent measurements. Three-component short-period body waves and long-period surface waves are combined to simultaneously constrain deep and shallow structures. The transversely isotropic model US₂₂ is the result of 22 pre-conditioned conjugate-gradient iterations. Approximate Hessian maps and point-spread function tests demonstrate good illumination of the study region and limited trade-offs among different model parameters. We observe a distinct wave-speed contrast between the stable eastern US and the tectonically active western US. This boundary is well correlated with the Rocky Mountain Front. Stable cratonic regions are characterized by fast anomalies down to 250-300 km, reflecting the thickness of the North American lithosphere. Several fast anomalies are observed beneath the North American lithosphere, suggesting the possibility of lithospheric delamination. Slow wave-speed channels are imaged beneath the lithosphere, which might indicate weak asthenosphere. Beneath the mantle transition zone of the central US, an elongated north-south fast anomaly is observed, which might be the ancient subducted Farallon slab. The tectonically active western US is dominated by prominent slow anomalies with magnitudes greater than -6 per cent down to approximately 250 km. No continuous lower to upper mantle upwellings are observed beneath Yellowstone. In addition, our results confirm previously observed differences between oceans and continents in the anisotropic parameter. xi (beta(h)/beta(v))(2). A slow wave-speed channel with xi > 1 is imaged beneath the eastern Pacific at depths from 100 to 200 km, reflecting horizontal shear within the asthenosphere. Underneath continental areas, regions with. > 1 are imaged at shallower depths around 100 km. They are characterized by fast shear wave speeds, suggesting different origins of anisotropy underneath oceans and continents. The wave speed and anisotropic signatures of the western Atlantic are similar to continental areas in comparison with the eastern Pacific. Furthermore, we observe regions with xi < 1 beneath the tectonically active western US at depths between 300 and 400 km, which might reflect vertical flows induced by subduction of the Farallon and Juan de Fuca Plates. Comparing US₂₂ with several previous tomographic models, we observe relatively good correlations for long-wavelength features. However, there are still large discrepancies for small-scale features. ItemFull-Waveform Inversion Using Seislet Regularization(Society of Exploration Geophysicists, 2017-06-21) Xue, Z.; Zhu, Hejun; Fomel, S.; 0000-0002-7452-075X (Zhu, H); Zhu, HejunBecause of inaccurate, incomplete, and inconsistent waveform records, full-waveform inversion (FWI) in the framework of a local optimization approach may not have a unique solution, and thus it remains an ill-posed inverse problem. To improve the robustness of FWI, we have developed a new model regularization approach that enforced the sparsity of solutions in the seislet domain. The construction of seislet basis functions requires structural information that can be estimated iteratively from migration images.We implement FWI with seislet regularization using nonlinear shaping regularization and impose sparseness by applying soft thresholding on the updated model in the seislet domain at each iteration of the data-fitting process. The main extra computational cost of the method relative to standard FWI is the cost of applying forward and inverse seislet transforms at each iteration. This cost is almost negligible compared with the cost of solving wave equations. Numerical tests using the synthetic Marmousi model demonstrate that seislet regularization can greatly improve the robustness of FWI by recovering high-resolution velocity models, particularly in the presence of strong crosstalk artifacts from simultaneous sources or strong random noise in the data. © The Authors. Published by the Society of Exploration Geophysicists.