Elastic Kirchhoff migration of vectorial wave-fields

Based on Kuo and Dai＇s vectorial wave-field extrapolation equations, we derive new Kirchhoff migration equations by introducing unit vectors which represent the ray directions at the imaging points of the reflected P- and PS converted-waves. Furthermore, using the slope of the events on shot records and a ray racing procedure, mirror-image reflection points are found and the reflection data are smeared along the Fresnel zone. The migration method proposed in this paper solves two troublesome imaging problems caused by limited receiving aperture and migration artifacts resulting from wave propagation at the velocities of non original wave type. The migration method is applied successfully with model data, demonstrating that the new method is effective and correct.

Application of Amplitude Ratio Profiles Extracted with Prestack Kirchhoff Integral Migration

The Z component and X component profiles of seismic waves extracted with the prestack Kirchhoff integral migration could approximate to the primary wave （P wave） and converted shear wave （PS wave） profiles under certain conditions. The relative change of their reflection amplitude reflects the formation stress anomaly and subsurface media anisotropy. The principle and method for extracting amplitude ratios were studied and the application of amplitude ratio profiles was also examined when processing and interpreting actual seismic data. The amplitude ratio profile is an effective supplementary means of identifying the stratigraphic boundary and lithology.

Method for extracting angle-domain common image gathers in Kirchhoff beam migration

Kirchhoff beam migration is a simplified Gaussian beam migration,which omits the dynamic information and can calculate multi-arrival traveltime,so it is a high-precision and fast seismic imaging method.In the imaging process,extracting common image gathers can be used for velocity analysis,improving the accuracy of modeling and imaging quality.Compared with the conventional common image gathers extracting methods,the angle-domain common image gathers extracting method can avoid the artifacts caused by multi-arrival seismic waves.The authors present a new method of extracting common image gathers in angle-domain from Kirchhoff beam migration and verify the method by numerical calculations.

Super-resolution least-squares prestack Kirchhoff depth migration using the L_0-norm

Least-squares migration （LSM） is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground reflectivity models. LSM reduces the migration artifacts, enhances the spatial resolution of the migrated images, and yields a more accurate subsurface reflectivity distribution than that of standard migration. The introduction of regularization constraints effectively improves the stability of the least-squares offset. The commonly used regularization terms are based on the L2-norm, which smooths the migration results, e.g., by smearing the reflectivities, while providing stability. However, in exploration geophysics, reflection structures based on velocity and density are generally observed to be discontinuous in depth, illustrating sparse reflectance. To obtain a sparse migration profile, we propose the super-resolution least-squares Kirchhoff prestack depth migration by solving the L0-norm-constrained optimization problem. Additionally, we introduce a two-stage iterative soft and hard thresholding algorithm to retrieve the super-resolution reflectivity distribution. Further, the proposed algorithm is applied to complex synthetic data. Furthermore, the sensitivity of the proposed algorithm to noise and the dominant frequency of the source wavelet was evaluated. Finally, we conclude that the proposed method improves the spatial resolution and achieves impulse-like reflectivity distribution and can be applied to structural interpretations and complex subsurface imaging.

Combined migration velocity model-building and its application in tunnel seismic prediction

We propose a combined migration velocity analysis and imaging method based on Kirchhoff integral migration and reverse time migration,using the residual curvature analysis and layer stripping strategy to build the velocity model.This method improves the image resolution of Kirchhoff integral migration and reduces the computations of the reverse time migration.It combines the advantages of efficiency and accuracy of the two migration methods.Its application in tunnel seismic prediction shows good results.Numerical experiments show that the imaging results of reverse time migration are better than the imaging results of Kirchhoff integral migration in many aspects of tunnel prediction.Field data show that this method has efficient computations and can establish a reasonable velocity model and a high quality imaging section.Combination with geological information can make an accurate prediction of the front of the tunnel geological structure.

Kirchhoff PSDM angle-gather generation based on the traveltime gradient

Angle-domain common-image gathers（ADCIGs） are the basic data in migration velocity analysis（MVA） and amplitude variation with angle（AVA） analysis. We propose a common-angle gather-generating scheme using Kirchhoff PSDM based on the traveltime gradient field. The scheme includes three major operations：（1） to calculate the traveltime field of the source and the receiver based on the dynamic programming approach;（2） to obtain the refl ection angle according to the traveltime gradient field in the image space; and（3） to generate the ADCIGs during the migration process. Because of the computation approach, the method for generating ADCIGs is superior to conventional ray-based methods. We use the proposed ADCIGs generation method in 3D large-scale seismic data. The key points of the method are the following.（1） We use common-shot datasets for migration,（2） we load traveltimes based on the shot aperture, and（3） we use the MPI and Open Mp memory sharing to decrease the amount of input and output（I/O）. Numerical examples using synthetic data suggest that the ADCIGs improve the quality of the velocity and the effectiveness of the 3D angle-gather generation scheme.

Study on virtual source method under complex overburden in horizontal well

In conventional seismic exploration,complex overburden prevents us from imaging the deeper underground structure,because near-surface velocity model cannot be efficiently simplified and accurately established. The virtual source method provides a promising solution,which images below a complex overburden without the knowledge of overburden velocities and near-surface changes. In this paper,the authors simulate the forward modeling under complex overburden with sources on the surface and receivers in the horizontal well,and reset the real sources into the horizontal well using the virtual source method,which subtly avoid the distortion effects of the complex overburden. Finally the underground structure can be imaged using Kirchhoff migration,so the feasibility and advantages of the virtual source method are verified.

Rupture pattern of the Oct 23,2011 Van-Merkez,Eastern Turkey earthquake

High-frequency rupture process of the Oct 23, 2011 Van-Merkez earthquake is imaged by back-projection method using high-quality teleseismic P wave data from the US Array, and prestack Kirchhoff migration using P wave data from a subarray of global seismic networks. The rupture model with two asperities is confirmed by previous two methods. In low-frequency imaging, a large asperity derived from the migration method corresponds to the second one from the high-frequency P waves. The con- sistency of the locations of asperities from datasets with different frequency bands indicates that there is possible insignificance of the frequency-dependent feature for the earthquake. The resultant images illustrate the spatial and temporal evolution of the rupture, which mainly propa- gated WSW over a length of 33 km during the first 18 s, accompanying with bursts of two asperities at 3 and 11-13 s. The rupture direction is confirmed by the S wave comer frequency variations of strong ground accelerations. The rupture fronts are mainly located at the updip of the causative fault. Based on polarities of the P waveforms and focal mechanisms of the mainshock and aftershocks, the failure of these two asperities is determined to have occurred on a reverse fault with a dip angle of 47°. Hence, the rupture pattern of the 2011 Van-Merkez earthquakewas dominated by a unilateral rupture toward the west- southwest direction.

Finite-difference calculation of traveltimes based on rectangular grid

To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to improve calculating efficiency and adaptability, the calculation method of first-arrival traveltime of finite-difference is de- rived based on any rectangular grid and a local plane wavefront approximation. In addition, head waves and scat- tering waves are properly treated and shadow and caustic zones cannot be encountered, which appear in traditional ray-tracing. The testes of two simple models and the complex Marmousi model show that the method has higher accuracy and adaptability to complex structure with strong vertical and lateral velocity variation, and Kirchhoff prestack depth migration based on this method can basically achieve the position imaging effects of wave equation prestack depth migration in major structures and targets. Because of not taking account of the later arrivals energy, the effect of its amplitude preservation is worse than that by wave equation method, but its computing efficiency is higher than that by total Green′s function method and wave equation method.

Least-Squares Seismic Inversion with Stochastic Conjugate Gradient Method

With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.