Jizhong Yang

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.

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.

Reflection Fresnel Volume Tomography and Its Application

According to the finite-frequency theory, for a single source-receiver pair, not only the points on the ray-path, but also those outside the ray affect wave propagation. This kind of effect can be described by a sensitivity kernel. On the basis of earlier studies of the Fresnel Volume tomography (FVT) of transmitted waves, a new approach, Fresnel Volume tomography of reflected waves (RFVT), is proposed here. In addition, the traveltime sensitivity kernel of RFVT for homogeneous media is analyzed. To overcome the coupling between velocity and depth of layered media, a decoupling strategy is proposed which inverts the velocity and depth alternatively using an iterative approach. This strategy makes use of the zero-offset or near-offset stack section of the seismic records and can be performed on one layer at a time. Finally, using existing calculation methods on the boundaries of a band-limited Fresnel Volume, RFVT is performed on a synthesized data set. The inverse results indicate that RFVT can achieve higher accuracy and better vertical resolution than conventional reflection ray-path tomography (RRT), with both methods using the same decoupling strategy.

Least-squares Reverse Time Migration with Variable Density

Least-squares reverse time migration (LSRTM) aims to match the amplitudes of the simulated data with the observed data. The amplitude of reflected seismic wave is dominantly affected by contrasts in acoustic impedance, which is a product of velocity and density. Therefore, if the P-wave velocity is the only variable parameter in LSRTM, the seismic amplitudes will not be correctly modelled. In this study, we present a LSRTM scheme applicable in the presence of density variations. Reflectivity models associated with velocity and density perturbations are simultaneously retrieved to generate simulated data better matches the recorded data in amplitudes. Numerical examples based on a two-layer model verified the effectiveness of the proposed method.

Elastic Multi-parameter FWI Based on the Truncated Gauss-Newton Method Using an Improved Scattering-integral Algorithm

Elastic full-waveform inversion of multicomponent seismic data is a powerful tool to simultaneously reconstruct subsurface quantitative parameters, and suffers from the limited frequency components in records, the incomplete survey geometry, and the trade-off effects between different parameters. To deal with this, a well estimation of the inverse Hessian operator is requires. We introduce the truncated Gauss-Newton method in EFWI based on the improved scattering-integral algorithm. We firstly introduce the computation of the gradient vector, and then the implementation of the approximate Hessian operator in a matrix-free conjugate gradient approach. Finally, we present a numerical experiment to prove the effectiveness of this method.

Least-squares Reverse Time Migration with Truncated Gauss-Newton Method

Least-squares migration (LSM) generates better quality migration images than conventional migration by removing migration artifacts, balancing reflector amplitudes, and improving the spatial resolution. Accurate consideration of the inverse Hessian is of great importance in the context of LSM, because the convergence rate would be accelerated to some extent. In this study, we adapt the truncated Gauss-Newton method to LSM, in which the Gauss-Newton normal equation is iteratively solved with a matrix-free conjugate gradient algorithm. The Hessian-vector product is calculated based on a demigration/migration procedure. The numerical example proves the feasibility of our method.

Joint Inversion of VTI Parameters Using Nonlinear Traveltime Tomography

In this paper,we use a nonlinear tomographic method to jointly invert for the multiple parameters in VTI media.It is based on the harmonic series of group velocity to calculate the Frechet kernels of traveltime with respect to model parameters.Two parameterizations are used.Through theoretically analysis and numerical experiments,we find that the parameterization of vertical slowness,horizontal slowness,and NMO slowness is more appropriate for joint traveltime tomography,compared with the traditional Thomsen parameterization.To overcome the insensitivity of traveltime to epsilon,a double-round strategy is employed in double-parameter inversion,through which epsilon as well as vertical velocity is successfully obtained.The extension from double-round to triple-round strategy also shows great potential to construct all of the three parameters.

Reflection Fresnel Volume Tomography

According to the finite-frequency theory, for a single source-receiver pair, not only the points on the ray-path, but also those outside the ray affect wave propagation. This kind of effect can be described by a sensitivity kernel. On the basis of earlier studies of the Fresnel Volume tomography (FVT) of transmitted waves, a new approach, Fresnel Volume tomography of reflected waves (RFVT), is proposed here. In addition, the traveltime sensitivity kernel of RFVT for homogeneous media is analyzed. To overcome the coupling between velocity and depth of layered media, a decoupling strategy is proposed which inverts the velocity and depth alternatively using an iterative approach. This strategy makes use of the zero-offset or near-offset stack section of the seismic records and can be performed on one layer at a time. Finally, using existing calculation methods on the boundaries of a band-limited Fresnel Volume, RFVT is performed on a synthesized data set. The inverse results indicate that RFVT can achieve higher accuracy and better vertical resolution than conventional reflection ray-path tomography (RRT), with both methods using the same decoupling strategy.