Meigen Zhang

Scalar Seismic-Wave Equation Modeling by a Multisymplectic Discrete Singular Convolution Differentiator Method

High-precision modeling of seismic-wave propagation in heterogeneous media is very important to seismological investigation. However, such modeling is one of the difficult problems in the seismological research fields. For developing methods of seismic inversion and high-resolution seismic-wave imaging, the modeling problem must be solved as perfectly as possible. Moreover, for long-term computations of seismic waves (e.g., Earth’s free-oscillations modeling and seismic noise-propagation modeling), the capability of seismic modeling methods for long-time simulations is in great demand. In this paper, an alternative method for accurately and efficiently modeling seismic wave fields is presented; it is based on a multisymplectic discrete singular convolution differentiator scheme (MDSCD). This approach uses optimization and truncation to form a localized operator, which preserves the fine structure of the wave field in complex media and avoids noncausal interaction when parameter discontinuities are present in the medium. The approach presented has a structure-preserving property, which is suitable for treating questions of high-precision or long-time numerical simulations. Our numerical results indicate that this method can suppress numerical dispersion and allow for research into long-time numerical simulations of wave fields. These numerical results also show that the MDSCD method can effectively capture the inner interface without any special treatment at the discontinuity.

Seismic scalar wave equation with variable coefficients modeling by a new convolutional differentiator

Studying seismic wavefields in the Earths interior requires an accurate calculation of wave propagation using accurate and efficient numerical techniques. In this paper, we present an alternative method for accurately and efficiently modeling seismic wavefields using a convolutional generalized orthogonal polynomial differentiator. Our approach uses optimization and truncation to form a localized operator. This preserves the fine structure of the wavefield in complex media and avoids non-causal interaction when parameter discontinuities are present in the medium. We demonstrate this approach for scalar wavefield modeling in heterogeneous media and conclude that the method could be readily extended to elastic wavefield calculations. Our numerical results indicate that this method can suppress numerical dispersion and allow for the study of wavefields in heterogeneous structures. The results hold promise not only for future seismic studies, but also for any field that requires high-precision numerical solution of partial differential equation with variable coefficients.

Time-domain inversion of GPR data containing attenuation due to conductive losses

Many seismic data processing and inversion techniques have been applied to ground-penetrating radar (GPR) data without including the wave field attenuation caused by conductive ground. Neglecting this attenuation often reduces inversion resolution. This paper introduces a GPR inversion technique that accounts for the effects of attenuation. The inversion is formulated in the time domain with the synthetic GPR waveforms calculated by a finite-element method (FEM). The Jacobian matrix can be computed efficiently with the same FEM forward modeling procedure. Synthetic data tests show that the inversion can generate high-resolution subsurface velocity profiles even with data containing strong random noise. The inversion can resolve small objects not readily visible in the waveforms. Further, the inversion yields a dielectric constant that can help to determine the types of material filling underground cavities.

Finite-element implementation of reverse-time migration for anisotropic media

Reverse-time migration for post-stack seismic data in anisotropic media is implemented using the finite-element method. As an accurate digital method, the finite-element method is flexible for dealing with complicated geological structures, inner and man-made boundaries despite its intensive computation. Applying it in reverse-time migration may produce accurate images for anisotropic media. To eliminate man-made boundary reflections, the absorbing boundary condition for anisotropic elastic waves is also studied. An efficient and stable absorbing boundary scheme is presented combining a discrete transparent boundary condition with an attenuation boundary condition.

Pre-stack full wavefield inversion for elastic parameters of TI media

Pre-stack full wavefield inversion for the elastic parameters of transversely isotropical media is implemented. The Jacobian matrix is derived directly with the finite element method, just like the full wavefield forward modelling. An absorbing boundary scheme combining Liaos transparent boundary condition with Sarmas attenuation boundary condition is applied to the forward modelling and Jacobian calculation. The input data are the complete ground-recorded wavefields containing full kinematic and dynamic information for the seismic waves. Inversion with such data is desirable as it should improve the accuracy of the estimated parameters and also reduce data pre-processing, such as wavefield identification and separation. A scheme called energy grading inversion is presented to deal with the instability caused by the large energy difference between different arrivals in the input data. With this method, parameters in the shallow areas, which mainly affect wave patterns with strong energy, converge before those of deeper media. Thus, the number of unknowns in each inversion step is reduced, and the stability and reliability of the inversion process is greatly improved. As a result, the scheme is helpful to reduce the non-uniqueness in the inversion. Two synthetic examples show that the inversion system is reliable and accurate even though initial models deviate significantly from the actual models. Also, the system can accurately invert for transversely isotropic model parameters even with the introduction of strong random noise.

2D efficient ray tracing with a modified shortest path method

The computation effort of ray tracing with the shortest path method (SPM) is strongly dependent on the number of the discretized nodes in a model and the number of ray directions emanating from a secondary source node. In the traditional SPM, a secondary source emanates rays to all the surrounding nodes. Obviously, most of them are not minimal traveltime raypaths. As a result, the efficiency of SPM can be greatly improved if some measures are taken to avoid those unnecessary computations. In the current study, we apply the traveltime information of neighbouring nodes and the incident rays to determine the effective target propagation directions of secondary source nodes in 2D case. Generally, the effective propagation directions are narrow bands with few surrounding nodes. Thus, most unnecessary ray directions of secondary source nodes are avoided. 2D model tests show that the computational speed of the improved method is about several to tens of times of that of the traditional SPM with the increase of network nodes and cells.

Ray tracing with the improved shortest path method

The shortest path ray tracing is a kind of efficient and flexible method to calculate global minimum traveltimes and raypaths. However, the derived zigzag raypaths can generate errors in both traveltimes and loci. Increasing the number of nodes and propagation directions from a secondary source can improve the situation. But it also increases much computation. Here, several measures are presented to improve the efficiency and accuracy of the shortest path method (SPM). First, Snell’s law is considered when searching wave propagation directions from a secondary source. Thus, a large number of unnecessary directions are discarded. Second, when tracing reflections, a measure is applied to keep from tracing areas below interfaces. Third, traveltimes and raypath loci are corrected with a nonlinear interpolation scheme. In addition, a special SPM, named interface point method, is presented. It can tracing blocky models with high efficiency and accuracy.

Fine Reconstruction of Seismic Data Using Localized Fractals

Seismology requires accurate (fine) data reconstruction from sparsely (or irregularly) sampled data sets, but such results are usually not possible with conventional (non-fractal) methods. To produce a highprecision reconstruction of seismic data, a more accurate localized fractal reconstruction approach can be used provided the data is self-similar on local and global spatial scales. In this paper, a novel localized fractal reconstruction approach has been presented. This method is a data-driven algorithm that does not require any geological or geophysical assumptions concerning the data. Here, we report our results of using the approach to reconstruct sparsely sampled seismic data. Our results indicate that the fine structure associated with seismic data can be easily and accurately reconstructed using the localized fractal approach, indicating that seismic data is indeed self-similar on local and global spatial scales. This result holds promise not only for future seismic studies, but also for any field that requires fine reconstruction from sparsely sampled data sets.

TIME-DOMAIN FINITE-ELEMENT WAVE FORM INVERSION OF ACOUSTIC WAVE EQUATION

The paper derives the finite element equation for acoustic wave in time domain and presents a transparent-plus-attenuation boundary condition. Forward modeling demonstrates that the boundary condition absorbs boundary reflection wave very well. On these bases, we derive the equation satisfied by elements of Jacobi matrix used in the inversion of the physical property parameters of acoustic media. In fact, the equation is the same as that of forward modeling in form. Only the right force item is different. So with the same method of forward modeling, we can get the elements of Jacobi matrix. Because the elements are variable with time and the present inversion does not permit too many unknowns. We integrate the finite elements with the same physical property as one unknown structure unit (for example, a horizontal layer or an oblique layer, etc.) and inverse the physical property parameters of these unknown structure units instead all elements unknown parameters. The method greatly reduces calculation time and saves computer memory. Also, it improves the accuracy of the inversion results and improves the stability of the solving process. The inversion equations are solved with QR decomposition method. Model results prove that the full wave equation inversion method in time domain is effective.