Liangguo Dong

Sensitivity kernels for seismic Fresnel volume tomography

Fresnel volume tomography FVT offers higher resolution and better accuracy than conventional seismic raypath tomography. A key problem in FVT is the sensitivity kernel. We propose amplitude and traveltime sensitivity kernels expressed directly with Green’s functions for transmitted waves for 2D/3D homogeneous/heterogeneous media. The Green’s functions are calculated with a finite-difference operator of the full wave equation in the frequency-space domain. In the special case of homogeneous media, we analyze the properties of the sensitivity kernels extensively and gain new insight into these properties. According to the constructive interference of waves, the spatial distribution ranges of the monochromatic sensitivity kernels in FVT differ from each other greatly and are 1 / 8, 2/ 8, 3/ 8 and 4 / 8 periods of seismic waves, respectively, for 2D amplitude, 3D amplitude, 2D traveltime, and 3D traveltime conditions. We also have a new understanding of the relationship between raypath tomography and FVT. Within the first Fresnel volume of the dominant frequency, the band-limited sensitivity kernels of FVT in homogeneous media or smoothly heterogeneous media are very close to those of the dominant frequency. Thus, it is practical to replace the band-limited sensitivity kernel with a few selected frequencies or even the single dominant frequency to save computation when performing band-limited FVT. The numerical experiment proves that FVT using our sensitivity kernels can achieve more accurate results than traditional raypath tomography.

Full Waveform Inversion Based on Envelope Objective Function

Full waveform inversion has been a successful tool to build high resolution velocity models, but it suffers from local minima problem. We propose an envelope based method allowing the updating of long wavelength components of the velocity model. The gradient of the misfit function can be efficiently computed through adjoint-state technique. We use simple models to prove that the envelope objective function is more convex than the traditional FWI objective function and is not as sensitive to the frequency components of the data as traditional FWI. Finally we compare the new approach to the traditional FWI through an application on a simple 2D synthetic data set to illustrate our method can be a supplement to traditional FWI approach when initial model is far from the true model and low-frequency data is missing.

An eigenvalue decomposition method to construct absorbing boundary conditions for acoustic and elastic wave equations

A new approach to constructing absorbing boundary conditions (ABCs) for acoustic and elastic wave equations (in transversely isotropic media) is presented. The eigenvalue decomposition method (ED method) is used to calculate the eigenvalues and eigenvectors of the coefficient matrix in the wave equations, which can be used to construct the outgoing and incoming waves along any direction. For different boundary regions, the outgoing waves are kept unchanged, but the amplitudes of the incoming waves are kept constant in time. As well as ABCs at the four lines in 2D and six surfaces in 3D, the ABCs at the four corners in 2D and eight corners and 12 lines in 3D are constructed. The vibration curves show that these conditions have nearly the same effect as perfectly matched layer (PML) absorbing boundary conditions, and are much better than Clayton–Enquist (CE) absorbing boundary conditions.

Elastic envelope inversion using multicomponent seismic data with filtered-out low frequencies

The absence of low-frequency information in seismic data is one of the most difficult problems in elastic full waveform inversion. Without low-frequency data, it is difficult to recover the long-wavelength components of subsurface models and the inversion converges to local minima. To solve this problem, the elastic envelope inversion method is introduced. Based on the elastic envelope operator that is capable of retrieving lowfrequency signals hidden in multicomponent data, the proposed method uses the envelope of multicomponent seismic signals to construct a misfit function and then recover the longwavelength components of the subsurface model. Numerical tests verify that the elastic envelope method reduces the inversion nonlinearity and provides better starting models for the subsequent conventional elastic full waveform inversion and elastic depth migration, even when low frequencies are missing in multicomponent data and the starting model is far from the true model. Numerical tests also suggest that the proposed method is more effective in reconstructing the long-wavelength components of the S-wave velocity model. The inversion of synthetic data based on the Marmousi-2 model shows that the resolution of conventional elastic full waveform inversion improves after using the starting model obtained using the elastic envelope method. Finally, the limitations of the elastic envelope inversion method are discussed.

Improved hybrid iterative optimization method for seismic full waveform inversion

In full waveform inversion (FWI), Hessian information of the misfit function is of vital importance for accelerating the convergence of the inversion; however, it usually is not feasible to directly calculate the Hessian matrix and its inverse. Although the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) or Hessian-free inexact Newton (HFN) methods are able to use approximate Hessian information, the information they collect is limited. The two methods can be interlaced because they are able to provide Hessian information for each other; however, the performance of the hybrid iterative method is dependent on the effective switch between the two methods. We have designed a new scheme to realize the dynamic switch between the two methods based on the decrease ratio (DR) of the misfit function (objective function), and we propose a modified hybrid iterative optimization method. In the new scheme, we compare the DR of the two methods for a given computational cost, and choose the method with a faster DR. Using these steps, the modified method always implements the most efficient method. The results of Marmousi and over thrust model testings indicate that the convergence with our modified method is significantly faster than that in the L-BFGS method with no loss of inversion quality. Moreover, our modified outperforms the enriched method by a little speedup of the convergence. It also exhibits better efficiency than the HFN method.

Sensitivity kernels and Fresnel volumes for transmitted waves

Twoand three-dimensional sensitivity kernels corresponding to an incident plane wave (denoted by plw hereinafter) and a point source (denoted by ps hereinafter) in a homogeneous medium are derived according to the Born and Rytov approximations for traveltime and amplitude tomography. Furthermore, using the idea of constructive interference of waves, the spatial distribution ranges and properties of transmitted Fresnel volumes are summarized. These studies are important for seismic modeling and inversion based on Fresnel volume theory such as Fresnel volume tomography.

A Multi-parameter Full Waveform Inversion Strategy in Acoustic Media

Full waveform inversion (FWI) is a challenging data-matching procedure that exploits the full information from the seismic data to obtain high-resolution models of the subsurface. To best fit the observed seismograms, the forward modeling should correctly account for the wave propagation phenomena present in the recorded data, especially for the wide-aperture acquisition geometry. Thus, the mono-parameter acoustic FWI should be extended to multi-parameter FWI, such as P-wave velocity, shear-wave velocity, density, attenuation, anisotropy, or other related parameters. In this study, we propose a multi-parameter full waveform inversion strategy that can simultaneously recover the velocity and density in acoustic media. The strategy consists of two stages and the acoustic wave equation is parameterized by velocity and density. In the first stage, the velocity and density are simultaneously inverted. In this case, the inverted velocity is reasonable while the density profile is deviated from the true one. During the second stage, the recovered velocity model in the first stage is reused as the initial velocity model. Then, the velocity and density are reconstructed at the same time. The final results show that both the velocity and density are reconstructed well. The synthetic numerical examples prove the validity of the method.

Time-windowed Frequency Domain Full Waveform Inversion Using Phase-encoded Simultaneous Sources

Full-waveform inversion (FWI) is a powerful tool to reconstruct the complex subsurface geologic structures. A major numerical difficulty of FWI is the presence of local minima in the least-squares misfit. To overcome this problem, we propose a time-windowed and phase-encoded frequency domain FWI scheme. This new approach implements multi-scale strategy both in time domain and in frequency domain. Meanwhile, the encoded simultaneous-source technique is used to reduce the computational cost. Numerical examples prove the validity of this approach.

Regularizations in First Arrival Tomography

Ambiguity has always been an unavoidable problem in seismic inversion. How to make efficiently use of the a prior information to complement the observed data is discussed in this paper. The a prior information can be divided into three types. Usually, the three types of information are used to modify the model parameters directly after it is updated. However, ray-based tomography theory is developed under the linear approximation. So if the model is modified twice successively, it is very likely that the hypothesis is violated. If the a prior information can be integrated into the inverse equations, the constraint modification can be avoided. Regularization is a mean of achieving this task. Regularization has always been studied in inverse problems, but it is usually used to overcome the instability of the inverse algorithms. Clap and Fomel make use of regularization to incorporate geologic information into inversion. In this paper, basing on the category of the a prior information summarized above, we proposed the regularization methods relating with different kinds of the a prior information and expressed them in a formula.

Truncated Gauss-Newton Method with a Modified Scattering-integral Approach for Multi-parameter FWI in Acoustic Media

Density is difficult to reconstruct in multi-parameter full waveform inversion, due to the cross-talk effects between velocity and density. In this study, we implement the truncated Gauss-Newton method to multi-parameter FWI in acoustic media, in which we incorporate the inverse of the approximate Hessian where the off-diagonal blocks reflect the trade-off effects between different parameters, to decouple the velocity and density during the reconstruction procedure. The model update is computed through the matrix-free conjugate gradient (CG) solution of the Newton linear system. We adopt a modified scattering-integral approach to calculate the gradient of the misfit function with respect to the model parameters and the Hessian-vector product instead of the widely accepted adjoint-state method. The numerical examples prove the feasibility of our method.