Xiao-Bi Xie

Wave-equation-based seismic illumination analysis

We present a wave-equation-based method for seismic illumination analysis. A one-way wave-equation-based, generalized screen propagator is used to extrapolate the wavefields from sources and receivers to the subsurface target. A local plane-wave analysis is used at the target to calculate localized,directionalenergyfluxesforbothsourceandreceiver wavefields. We construct an illumination matrix using these energy fluxes to quantify the target illumination conditions. The target geometry information is used to manipulate the illumination matrix and generate different types of illumination measures. The wave-equation-based approach can properly handle forward multiple-scattering phenomena, including focusing/defocusing, diffraction, and interference effects.Itcanbedirectlyappliedtocomplexvelocitymodels. Velocity-model smoothing and Fresnel-zone smoothing are not required. Different illumination measurements derived from this method can be applied to target-oriented or volumetric illumination analyses. This new method is flexible and practical for illumination analysis in complex 2D and 3D velocity models with nontrivial acquisition and target

Extracting Angle Domain Information From Migrated Wavefield

The recent development of wave equation based migration methods provided accurate propagators for seismic wave extrapolation. These propagators brought the possibility that many analysis and inversion can be made at the depth using migrated wavefield. In this study, we propose an approach for extracting angle domain information from migrated wavefield. The method is based on localized plane wave analysis and can be used for almost any migration method. Then, using the concept of the local image matrix, useful information (angle domain image gathers, reflector dips, etc.) can be further extracted from this angle related information. Numerical examples are conducted to demonstrate the applications of this method.

The finite-frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis

We have derived a broadband sensitivity kernel that relates the residual moveout (RMO) in prestack depth migration (PSDM) to velocity perturbations in the migration-velocity model. We have compared the kernel with the RMO directly measured from the migration image. The consistency between the sensitivity kernel and the measured sensitivity map validates the theory and the numerical implementation. Based on this broadband sensitivity kernel, we propose a new tomography method for migration-velocity analysis and updating — specifically, for the shot-record PSDM and shot-index common-image gather. As a result, time-consuming angle-domain analysis is not required. We use a fast one-way propagator and multiple forward scattering and single backscattering approximations to calculate the sensitivity kernel. Using synthetic data sets, we can successfully invert velocity perturbations from the migration RMO. This wave-equation-based method naturally incorporates the wave phenomena and is best teamed with the wave-...

Acquisition Aperture Correction In Angle-domain And True-amplitude Imaging For Wave Equation Migration

Summary Based on beamlet decomposition of wave field and Green’s function, we formulated an amplitude correction method in angle domain. The formulation relates the local image matr ix (LIM), which bears the footprints of the acquisition apertur e and propagation path effects, and the local scattering mat rix (LSM), which is directly related to the medium propert y. From the formulation, two types of amplitude correction ar e proposed: one is the correction for common reflection-angle image for AVA analysis. The other is the correction fo r total strength image. From the imaging results of the four-laye r model and the SEG/EAGE model, we see significant improvement in amplitude fidelity and image quality.

Modeling elastic wave forward propagation and reflection using the complex screen method

Formulation for calculating forward propagation and reflection in a 3D elastic structure based on the complex-screen method is given in this paper. The calculation of reflections is formulated based on the local Born approximation. When using a small angle approximation, the backscattering operator reduces to a screen operator which is similar to the forward screen propagator. Combining the forward propagator and backscattering operator together, the new method can properly handle the multiple forward scattering and single backscattering in a 3D heterogeneous model. Using a dual-domain technique, the new method is highly efficient in CPU time and memory savings. For models where reverberation and resonance scattering can be neglected, this method provides a fast and accurate algorithm. Synthetic seismograms for two-dimensional elastic models are calculated with this method and compared with those generated by the finite-difference method. The results show that the method works well for small to medium scattering angles and medium velocity contrasts.

Regional Seismic Characteristics of the 9 October 2006 North Korean Nuclear Test

We investigate the regional seismic signature of the 9 October 2006 North Korean nuclear test. Broadband regional data for the nuclear test and a group of earthquakes close to the test site were obtained between December 2000 and No- vember 2006. Epicentral distances from the stations to the test site are between 371 and 1153 km. We first use these regional events to calibrate the Lg-wave magnitude in the network. Then the network is used to calculate mbLg �� 3:93 for the North Ko- rean nuclear explosion. Using a modified fully coupled magnitude-yield relation, the yield of the North Korean nuclear test is estimated to be 0.48 kt. Because of large uncertainties in the source depth, the estimate is preliminary. The P=S-type spectral ratios Pg=Lg, Pn=Lg, and Pn=Sn are calculated for the nuclear explosion and a group of earthquakes close to the test site. At frequencies above 2 Hz, the network-averaged P=S spectral ratios clearly separate the 9 October 2006 explosion from the regional earthquakes. Our result indicates that a single-blast explosion in the North Korea re- gion shows different seismic characteristics from an earthquake. Any well-coupled single-blast explosion detonated in this region with yield similar to that for the North Korean nuclear test has a large probability of being identified by a regional seismic network such as the one adopted in this study.

Multicomponent prestack depth migration using the elastic screen method

A 3D multicomponent prestack depth-migration method is presented. An elastic-screen propagator based on one-way wave propagation with a wide-angle correction is used to extrapolate both source and receiver wavefields. The elastic-screen propagator neglects backscattered waves but can handle forward multiple-scattering effects, such as focusing/defocusing, diffraction, interference, and conversions between P- and S-waves. Vector-imaging conditions are used to generate a P-P image and a P-S converted-wave image. The application of the multicomponent elastic propagator and vector-imaging condition preserves more information carried by the elastic waves. It also solves the polarization problem of converted-wave imaging. Partial images from different sources with correct polarizations can be stacked to generate a final image. Numerical examples using 2D synthetic data sets are presented to show the feasibility of this method.

Geometric Spreading of Pn and Sn in a Spherical Earth Model

Geometric spreading of Pn and Sn waves in a spherical Earth model is different than that of classical headwaves and is frequency dependent. The behavior cannot be fully represented by a frequency-independent power-law model, as is com- monly assumed. The lack of an accurate representation of Pn andSn geometric spread- ing in a spherical Earth model impedes our ability to characterize Earth properties including anelasticity. We conduct numerical simulations to quantify Pn and Sn geometric spreading in a spherical Earth model with constant mantle-lid velocities. Based on our simulation results, we present new empirical Pn and Sn geometric- spreading models in the form Gr;f ��� 10 n3� f� =r0�� r0=rn1� flogr0=r�� n2� fand nif �� ni1� logf=f0�� 2 � ni2 logf=f0 �� ni3, where i � 1 ,2 , or 3;r is epicentral distance; f is frequency; r0 � 1 km; and f0 � 1 Hz. We derive values of coefficients nij by fitting the model to computed Pn and Sn amplitudes for a spherical Earth model having a 40-km-thick crust, generic values of P and S velocities, and a constant-ve- locity uppermost mantle. We apply the new spreading model to observed data in Eur- asia to estimate average Pn attenuation, obtaining more reasonable results compared to using a standard power-law model. Our new Pn and Sn geometric-spreading models provide generally applicable reference behavior for spherical Earth models with con- stant uppermost-mantle velocities.

Seismic Wave Propagation and Scattering in Heterogeneous Crustal Waveguides Using Screen Propagators: I SH Waves

The great advantages of one-way propagation methods, such as the gen- eralized screen propagators (GSP) method, are the fast speed of computation, often several orders of magnitude faster than the full-wave finite difference and finite element methods, and the huge savings in internal memory. In this article, a half- space GSP is formulated for the SH half-space problem. Two versions of the half- space GSP are derived: the wide-angle pseudo-screen and the phase-screen. The Moho discontinuity is treated as parameter perturbations from the crustal back- ground. The validity and limitations of this treatment are discussed. It is shown that half-space screen propagators can accurately propagate guided crustal waves that are composed of small-angle waves with respect to the horizontal direction. Comparisons of numerical results with a wavenumber integration method for flat crustal models and a finite difference algorithm for heterogeneous models show excellent agree- ments. For a model with propagation distance of 250 km, dominant frequency at 0.5 Hz, the GSP method is about 300 times faster than a finite difference algorithm with a similar accuracy. These comparisons demonstrate the accuracy and efficiency of the method. We apply our method to simulate regional wave propagation in different types of complex crustal waveguides including those with small-scale random het- erogeneities. The influence of these heterogeneities on Lg amplitude attenuation and Lg coda formation is significant.

One-way and one-return approximations (de wolf approximation) for fast elastic wave modeling in complex media

The De Wolf approximation has been introduced to overcome the limitation of the Born and Rytov approximations in long range forward propagation and backscattering calculations. The De Wolf approximation is a multiple-forescattering-single-backscattering (MFSB) approximation, which can be implemented by using an iterative marching algorithm with a single backscattering calculation for each marching step (a thin-slab). Therefore, it is also called a one-return approximation. The marching algorithm not only updates the incident field step-by-step, in the forward direction, but also the Greens function when propagating the backscattered waves to the receivers. This distinguishes it from the first order approximation of the asymptotic multiple scattering series, such as the generalized Bremmer series, where the Greens function is approximated by an asymptotic solution. The De Wolf approximation neglects the reverberations (internal multiples) inside thin-slabs, but can model all the forward scattering phenomena, such as focusing/defocusing, diffraction, refraction, interference, as well as the primary reflections. In this chapter, renormalized MFSB (multiple-forescattering–single-backscattering) equations and the dual-domain expressions for scalar, acoustic and elastic waves are derived by using a unified approach. Two versions of the one-return method (using MFSB approximation) are given: one is the wide-angle, dual-domain formulation (thin-slab approximation) (compared to the screen approximation, no small-angle approximation is made in the derivation); the other is the screen approximation. In the screen approximation, which involves a small-angle approximation for the wave-medium interaction, it can be clearly seen that the forward scattered, or transmitted waves are mainly controlled by velocity perturbations; while the backscattered or reflected waves, are mainly controlled by impedance perturbations. Later in this chapter the validity of the thin-slab and screen methods, and the wide-angle capability of the dual-domain implementation are demonstrated by numerical examples. Reflection coefficients of a plane interface, derived from numerical simulations by the wide-angle method, are shown to match the theoretical curves well up to critical angles. The methods are applied to the fast calculation of synthetic seismograms. The results are compared with finite difference (FD) calculations for the elastic French model. For weak heterogeneities ( ± 15 % perturbation), good agreement between the two methods verifies the validity of the one-return approach. However, the one-return approach is about 2–3 orders of magnitude faster than the elastic FD algorithm. The other example of application is the modeling of amplitude variation with angle (AVA) responses for a complex reservoir with heterogeneous overburdens. In addition to its fast computation speed, the one return method (thin-slab and complex-screen propagators) has some special advantages when applied to the thin-bed and random layer responses.