Chao-ying Bai

3D Local Earthquake Hypocenter Determination with an Irregular Shortest-Path Method

A simple but robust method for joint (multiple) earthquake location in arbitrary 3D velocity media is presented in this article. It exploits the advantages of the irregular shortest-path method (irregular spm) for the raytracing, and uses a damped minimum norm, constrained least-squares solution for the source parameter (hypocenter and origin time) update. Special features of the scheme, made possible by the irregular spm, are that the raytracing needs to be carried out only once and the elements of the Jacobian matrix are calculated directly. Six supplementary sources are added around a trial (to be updated) source and trilinear interpolation used to form the travel times and the derivatives. Comparison tests against the regular spm and the finite-difference method show that the newly developed procedure is able to achieve comparable accuracy in both the travel-time calculation and in the hypocentral location solution, but at considerable computational economy. Further numerical tests for a complex 3D model indicate that the method is accurate, with a location error in depth comparable to that in the horizontal plane, at least for the station distribution used. In a practical sense, there is no requirement to have a close initial guess of the source coordinates and origin time before the location process is undertaken if the sources are not too far from the seismic network. The results show that this approach is fairly insensitive to modest levels of random noise, but like all hypocenter determination algorithms, it strongly depends on having the correct velocity model.

2D/3D Seismic Simultaneous Inversion for the Velocity and Interface Geometry Using Multiple Classes of Arrivals

By utilizing our newly developed multiple arrival (transmitted, reflected, refracted, and mode‐converted) tracking algorithm (multistage irregular shortest‐path method), in combination with the conjugate gradient method to solve the damped minimum norm, constrained least‐squares problem, we present a simultaneous inversion algorithm to recover both the velocity information and the subsurface interface geometry. In the inversion process, we introduce different weighting factors according to the different picking errors for the various seismic arrivals and normalize the two types of model parameters that form the elements of the Jacobian matrix so as to balance the influence on the travel times of the different velocity variations and reflector depths. From numerical tests and by comparison with a subspace inversion algorithm, we show the new approach to be a practical and efficient way to improve the spatial resolution and reduce artifacts in the reconstructed image.

3D Simultaneous Traveltime Inversion for Velocity Structure, Hypocenter Locations, and Reflector Geometry Using Multiple Classes of Arrivals

Traditionally, traveltime tomography entails inversion of either the velocity field and the reflector geometry sequentially, or the velocity field and the hypocenter locations simultaneously or in a cascaded fashion, but seldom are all three types (velocities, geometry of reflectors, and source locations) updated simultaneously because of the compromise between the different classes of model variable and the lack of different seismic phases to constrain these variables. By using a state-of-the-art ray-tracing algorithm for the first and later arrivals combined with a popular linearized inversion solver, it is possible to simultaneously recover the three classes of model variables. In the work discussed in this paper we combined the multistage irregular shortest-path ray-tracing algorithm with a subspace inversion solver to achieve simultaneous inversion of multi-class variables, using arrival times for different phases to concurrently obtain the velocity field, the reflector shapes, and the hypocenter locations. Simulation and comparison tests for two sets of source–receiver arrangements (one the ideal case and the other an approximated real case) indicate that the combined triple-class inversion algorithm is capable of obtaining nearly the same results as the double-class affect inversion scheme (velocity and reflector geometry, or velocity and source locations) even if a lower ray density and irregular source-receiver geometry are used to simulate the real situation. In addition, the new simultaneous inversion method is not sensitive to a modest amount of picking error in the traveltime data and reasonable uncertainty in earthquake hypocenter locations, which shows it to be a feasible and promising approach in real applications.

Extracting the Virtual Reflected Wavelet from TEM Data Based on Regularizing Method

A pseudo-seismic interpretation method is an alternative way to process and explain transient electromagnetic (TEM) data, and has become a popular research field in recent years. TEM signals which satisfy the diffusion equation can be converted by means of a mathematical transformation into ones which obey the wave equation. For an ill-posed problem of this kind of transformation, a sub-regularization algorithm is developed in this paper to extract a virtual wavelet of the TEM field. According to the conventional designation of TEM recordings, the entire integration period is divided into seven time intervals. In order to avoid low accuracy in the calculations, high-density wavefield data has been calculated based on the former sub-division. Therefore, the virtual wavelet can be extracted successfully by using an optimized algorithm to obtain high-density integral coefficients for all time windows, and a satisfactory condition number of the coefficient matrix while taking a different channel number in each time period. The Tikhonov regularization inversion scheme is used to determine the optimal parameters based on minimizing a least squares misfit, and the Newton iterative formula is used to obtain optimal regularization parameters. Both synthetic model simulations and a real data interpretation example indicate that the proposed pseudo-seismic wavefield method is a suitable alternative way to interpret TEM data.

Multiple arrival tracking within irregular triangular or tetrahedral cell model

The focus of this research is to introduce a triangular shortest-path method incorporating a multistage scheme for tracking multiple arrivals composed of any kind of combinations of transmissions, conversions and reflections in complex 2D or 3D layered media, in which a triangular (2D) or a tetrahedral (3D) cell is used to parameterize the velocity model. The basic principle is to divide a layered model into several different computational domains using irregular triangular (or tetrahedral) cells in model parameterization, and then to apply the multistage technique to trace the multiple arrivals. Meanwhile, a second level of forward star technique (where a forward star represents a geometric arrangement of network connections, or possible ray branching points into adjacent nodes), previously defined in gridded model, is first introduced into the triangular (or tetrahedral) cell model. The results show that using irregular triangular (or tetrahedral) cells can effectively approximate the undulated subsurface and velocity discontinuity, easily define the velocity distribution across the irregular subsurface interface, and hence greatly improve the computational accuracy. Several examples (including the Marmousi model) are used to demonstrate the viability and versatility of the multistage triangular shortest-path method in heterogeneous media, even in the presence of high-velocity contrasts involving interfaces of relatively high curvature. With the introduction of the second level of the forward star scheme, the total number of nodes is reduced sufficiently (normally by half), and therefore the computer memory required is less. Most important is that the computing accuracy with the second level forward star scheme can be greatly improved (say, 2?3 times in general) over those with the first level of forward star scheme applied.

Simultaneous Inversion for Velocity and Reflector Geometry Using Multi-phase Fresnel Volume Rays

Traditional ray tomography methods based on the high frequency assumption are sometimes unable to obtain a high resolution tomographic picture due to a deficient coverage of ray paths in real applications, especially for low velocity anomalous regions. In contrast, finite-frequency ray theory is more suitable for handling real seismic propagation problems because the travel time depends not only on the velocity distribution along a central ray (or traditional geometric ray), but also on the velocity values within a region (referred to as the first Fresnel Volume) which incorporates the central ray. In this study, we develop an algorithm to calculate multi-phase Fresnel Volume finite-frequency rays, and then present an inversion method to simultaneous invert for both velocity and reflector geometry by using these multi-phase Fresnel Volume finite-frequency rays. Using synthetic data examples, we compare the reconstructions of the velocity field and the reflector orientation using the Fresnel Volume ray tomographic methods and the traditional ray tomography approach. Results show that the former is advantageous over the latter, especially when the ray density is relatively low. An additional benefit of the Fresnel Volume finite-frequency ray tomographic method is that it can start with a low frequency to capture the coarse velocity structure, thereby mitigating the local minimum trapping problem, and then be tuned to a high frequency for delineating the fine velocity structure.

Seismic wavefield simulation in 2D elastic and viscoelastic tilted transversely isotropic media: comparisons between four different kinds of finite-difference grid schemes

In this paper, we use the staggered grid, the auxiliary grid, the rotated staggered grid and the non-staggered grid finite-difference methods to simulate the wavefield propagation in 2D elastic tilted transversely isotropic (TTI) and viscoelastic TTI media, respectively. Under the stability conditions, we choose different spatial and temporal intervals to get wavefront snapshots and synthetic seismograms to compare the four algorithms in terms of computational accuracy, CPU time, phase shift, frequency dispersion and amplitude preservation. The numerical results show that: (1) the rotated staggered grid scheme has the least memory cost and the fastest running speed; (2) the non-staggered grid scheme has the highest computational accuracy and least phase shift; (3) the staggered grid has less frequency dispersion even when the spatial interval becomes larger.

Multi-valued reflection arrival tracking via an extremal solution of the summed ray field

In heterogeneous media involving large velocity contrasts and/or strongly curved interfaces, the seismic wavefronts may self-intersect, implying that the rays follow multi-paths between source and receiver. In order to simulate such multi-valued reflection arrivals, we present here an algorithm to trace the various events. We refer to this as an extremal solution based on the summed ray field, one emanating from the source to the reflecting interface and the other from the receiver to the reflecting interface. Two popular grid-based algorithms, the fast marching method and the irregular shortest path method, are used in the ray tracing process. The steps involved in the extremal solution method are: (1) conduct downwind ray tracing from both the source and receiver to the reflecting interfaces and record the traveltimes and the raypaths at each sampled point along the interface, and then sum up the traveltime value at each sampled point on the interface to form a stacked ‘traveltime–distance’ curve along the interface (or subsurface interface for 3D case); (2) solve for the extremal values of this stacked ‘traveltime–distance’ curve (or subsurface interface), to obtain the locations of the extremal points which are the actual reflection points; (3) link the raypaths and the traveltimes from the source to those reflection points, and then to the receiver, by which the multi-valued reflected arrivals are successfully traced. This algorithm has a simple principle, high accuracy and easy adaptation for complex media. Several numerical simulations and an angular error analysis indicate that it is a feasible, accurate and efficient way to track the multi-valued reflected arrivals.

Simultaneous travel time tomography for updating both velocity and reflector geometry in triangular/tetrahedral cell model

To conduct forward and simultaneous inversion in a complex geological model, including an irregular topography (or irregular reflector or velocity anomaly), we in this paper combined our previous multiphase arrival tracking method (referred as triangular shortest-path method, TSPM) in triangular (2D) or tetrahedral (3D) cell model and a linearized inversion solver (referred to as damped minimum norms and constrained least squares problem solved using the conjugate gradient method, DMNCLS-CG) to formulate a simultaneous travel time inversion method for updating both velocity and reflector geometry by using multiphase arrival times. In the triangular/tetrahedral cells, we deduced the partial derivative of velocity variation with respective to the depth change of reflector. The numerical simulation results show that the computational accuracy can be tuned to a high precision in forward modeling and the irregular velocity anomaly and reflector geometry can be accurately captured in the simultaneous inversion, because the triangular/tetrahedral cell can be easily used to stitch the irregular topography or subsurface interface.

Simultaneous elastic parameter inversion in 2-D/3-D TTI medium combined later arrival times

Traditional traveltime inversion for anisotropic medium is, in general, based on a “weak” assumption in the anisotropic property, which simplifies both the forward part (ray tracing is performed once only) and the inversion part (a linear inversion solver is possible). But for some real applications, a general (both “weak” and “strong”) anisotropic medium should be considered. In such cases, one has to develop a ray tracing algorithm to handle with the general (including “strong”) anisotropic medium and also to design a non-linear inversion solver for later tomography. Meanwhile, it is constructive to investigate how much the tomographic resolution can be improved by introducing the later arrivals. For this motivation, we incorporated our newly developed ray tracing algorithm (multistage irregular shortest-path method) for general anisotropic media with a non-linear inversion solver (a damped minimum norm, constrained least squares problem with a conjugate gradient approach) to formulate a non-linear inversion solver for anisotropic medium. This anisotropic traveltime inversion procedure is able to combine the later (reflected) arrival times. Both 2-D/3-D synthetic inversion experiments and comparison tests show that (1) the proposed anisotropic traveltime inversion scheme is able to recover the high contrast anomalies and (2) it is possible to improve the tomographic resolution by introducing the later (reflected) arrivals, but not as expected in the isotropic medium, because the different velocity (qP, qSV and qSH) sensitivities (or derivatives) respective to the different elastic parameters are not the same but are also dependent on the inclination angle.