scholarly journals Fast least-squares prestack time migration via accelerating the explicit calculation of Hessian matrix with dip-angle Fresnel zone

2021 ◽  
Author(s):  
Bo-Wu Jiang ◽  
Jiang-Jie Zhang ◽  
Hao Zhang ◽  
Wen-Kai Lu
Keyword(s):  
Least Squares ◽  
Fresnel Zone ◽  
Hessian Matrix ◽  
Explicit Calculation ◽  
Time Migration ◽  
Prestack Time Migration ◽  
Dip Angle

High-resolution imaging: An approach by incorporating stationary-phase implementation into deabsorption prestack time migration

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S317-S331 ◽  
Author(s):  
Jianfeng Zhang ◽  
Zhengwei Li ◽  
Linong Liu ◽  
Jin Wang ◽  
Jincheng Xu
Keyword(s):  
Stationary Phase ◽  
Fresnel Zone ◽  
Computational Cost ◽  
Computational Effort ◽  
Propagation Path ◽  
Time Migration ◽  
Resolution Imaging ◽  
Prestack Time Migration ◽  
Dip Angle ◽  
Absorption And Dispersion

We have improved the so-called deabsorption prestack time migration (PSTM) by introducing a dip-angle domain stationary-phase implementation. Deabsorption PSTM compensates absorption and dispersion via an actual wave propagation path using effective [Formula: see text] parameters that are obtained during migration. However, noises induced by the compensation degrade the resolution gained and deabsorption PSTM requires more computational effort than conventional PSTM. Our stationary-phase implementation improves deabsorption PSTM through the determination of an optimal migration aperture based on an estimate of the Fresnel zone. This significantly attenuates the noises and reduces the computational cost of 3D deabsorption PSTM. We have estimated the 2D Fresnel zone in terms of two dip angles through building a pair of 1D migrated dip-angle gathers using PSTM. Our stationary-phase QPSTM (deabsorption PSTM) was implemented as a two-stage process. First, we used conventional PSTM to obtain the Fresnel zones. Then, we performed deabsorption PSTM with the Fresnel-zone-based optimized migration aperture. We applied stationary-phase QPSTM to a 3D field data. Comparison with synthetic seismogram generated from well log data validates the resolution enhancements.

Least-squares migration with a blockwise Hessian matrix: A prestack time-migration approach

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. R625-R640 ◽  
Author(s):  
Bowu Jiang ◽  
Jianfeng Zhang
Keyword(s):  
Least Squares ◽  
Field Data ◽  
Hessian Matrix ◽  
Total Variation Regularization ◽  
Data Sets ◽  
Reflection Point ◽  
Inverse Approach ◽  
Time Migration ◽  
Prestack Time Migration ◽  
Least Squares Migration

We have developed an explicit inverse approach with a Hessian matrix for the least-squares (LS) implementation of prestack time migration (PSTM). A full Hessian matrix is divided into a series of computationally tractable small-sized matrices using a localized approach, thus significantly reducing the size of the inversion. The scheme is implemented by dividing the imaging volume into a series of subvolumes related to the blockwise Hessian matrices that govern the mapping relationship between the migrated result and corresponding reflectivity. The proposed blockwise LS-PSTM can be implemented in a target-oriented fashion. The localized approach that we use to modify the Hessian matrix can eliminate the boundary effects originating from the blockwise implementation. We derive the explicit formula of the offset-dependent Hessian matrix using the deconvolution imaging condition with an analytical Green’s function of PSTM. This avoids the challenging task of estimating the source wavelet. Moreover, migrated gathers can be generated with the proposed scheme. The smaller size of the blockwise Hessian matrix makes it possible to incorporate the total-variation regularization into the inversion, thus attenuating noises significantly. We revealed the proposed blockwise LS-PSTM with synthetic and field data sets. Higher quality common-reflection-point gathers of the field data are obtained.

scholarly journals Viscoacoustic least-squares migration with a blockwise Hessian matrix: an effective Q approach

2020 ◽  
Author(s):  
Mingpeng Song ◽  
Jianfeng Zhang ◽  
Jiangjie Zhang
Keyword(s):  
Least Squares ◽  
Field Data ◽  
Hessian Matrix ◽  
Data Sets ◽  
Matrix Approach ◽  
Inverse Approach ◽  
Time Migration ◽  
Q Model ◽  
Prestack Time Migration ◽  
Least Squares Migration

Abstract We present an explicit inverse approach using a Hessian matrix for least-squares migration (LSM) with Q compensation. The scheme is developed by incorporating an effective Q-based solution of the viscoacoustic wave equation into a blockwise approximation to the Hessian in LSM, which is implemented after the so-called deabsorption prestack time migration (PSTM). The effective Q model used fully accounts for frequency-dependent traveltime and amplitude at the same imaging location. We can extract the effective Q parameters by scanning during previous deabsorption PSTM. This avoids the challenging task of building the Q model. The blockwise Hessian matrix approach decomposes the full Hessian matrix into a series of computationally tractable small-sized matrices using a localised approach. We derive the explicit formula of the offset-dependent Hessian matrix using an analytical Green's function obtained from deabsorption PSTM. In this way, we can approximate a reflectivity imaging for the targeted zone by a spatial deconvolution of the migrated result with an explicit inverse. The resulting scheme broadens the frequency-band of imaging by deabsorption, and improves the subsurface illumination and spatial resolution through the inverse Hessian. A high-resolution, true-amplitude migrated gather can then be obtained. Synthetic and field data sets demonstrate the proposed blockwise LS-QPSTM.

Imaging 3-D faults using diffractions with modified dip-angle gathers

2019 ◽  
Vol 220 (3) ◽  
pp. 1569-1584
Author(s):  
Zhengwei Li ◽  
Jianfeng Zhang
Keyword(s):  
Fresnel Zone ◽  
Specular Reflection ◽  
Small Scale ◽  
Accurate Identification ◽  
Time Migration ◽  
Diffraction Imaging ◽  
Prestack Time Migration ◽  
Dip Angle ◽  
Angle Gather ◽  
Fresnel Zones

SUMMARY Accurate identification of the locations and orientations of small-scale faults plays an important role in seismic interpretation. We have developed a 3-D migration scheme that can image small-scale faults using diffractions in time. This provides a resolution beyond the classical Rayleigh limit of half a wavelength in detecting faults. The scheme images weak diffractions by building a modified dip-angle gather, which is obtained by replacing the two dip angles dimensions of the conventional 2-D dip-angle gather with tangents of the dip angles. We build the modified 2-D dip-angle gathers by calculating the tangents of dip angles following 3-D prestack time migration (PSTM). In the resulting modified 2-D dip-angle gathers, the Fresnel zone related to the specular reflection exhibits an ellipse. Comparing with the conventional 2-D dip-angle gather, diffraction event related a fault exhibits a straight cylinder shape with phase-reversal across a line related the orientation of the fault. As a result, we can not only mute the Fresnel zones related to reflections, correct phase for edge diffractions and obtain the image of faults, but also detect the orientations of 3-D faults using the modified dip-angle gathers. Like the conventional dip-angle gathers, the modified dip-angle gathers can also be used to image diffractions resulting from other sources. 3-D Field data tests demonstrate the validity of the proposed diffraction imaging scheme.

Prestack time migration from 3D irregular surfaces with near-surface-related deabsorption

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. S21-S32
Author(s):  
Jincheng Xu ◽  
Jianfeng Zhang ◽  
Linong Liu ◽  
Wei Zhang ◽  
Hui Yang
Keyword(s):  
Fresnel Zone ◽  
Signal To Noise Ratio ◽  
Data Sets ◽  
Effective Parameters ◽  
Near Surface ◽  
Intrinsic Attenuation ◽  
Effective Velocity ◽  
Time Migration ◽  
Prestack Time Migration ◽  
Absorption And Dispersion

We have developed a 3D prestack time migration (PSTM) approach that can directly migrate nonplanar data with near-surface-related deabsorption using three effective parameters. The proposed scheme improves the so-called topography PSTM approach by adding a near-surface effective [Formula: see text] parameter that compensates for the absorption and dispersion of waves propagating through near-surface media. The two effective velocity parameters above and below the datum can be estimated by flattening events in imaging gathers, and the additional near-surface effective [Formula: see text] parameter can be obtained using scanning technology. Hence, no knowledge with respect to near-surface media is needed in advance for implementing the proposed scheme. The proposed topography-deabsorption PSTM method can be applied to seismic data recorded on a 3D irregular surface without statics corrections. Consequently, traveltimes are obtained with improved accuracy because the raypath bends away from the vertical in the presence of high near-surface velocities, and the absorption and dispersion caused by strong intrinsic attenuation in near-surface media are correctly compensated. Moreover, we attenuated the migrated noise by smearing each time sample only along the Fresnel zone rather than along the entire migration aperture. As a result, an image with a higher resolution and superior signal-to-noise ratio is achieved. The performance of the proposed topography-deabsorption PSTM scheme has been verified using synthetic and field data sets.

Least-squares reverse time migration method using the factorization of the Hessian matrix

2021 ◽  
Vol 18 (1) ◽  
pp. 94-100
Author(s):  
Sun Xiao-Dong ◽  
Teng Hou-Hua ◽  
Ren Li-Juan ◽  
Wang Wei-Qi ◽  
Li Zhen-Chun
Keyword(s):  
Least Squares ◽  
Hessian Matrix ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Method

Improving prestack time migration by least-squares equivalent offset method

2021 ◽  
pp. 1-10
Author(s):  
Dan Wu ◽  
Haili Wu ◽  
Qun Li ◽  
Congbin Wang ◽  
Yufeng Lu
Keyword(s):  
Least Squares ◽  
Time Migration ◽  
Prestack Time Migration

3D diffraction imaging with Kirchhoff time migration using vertical traveltime difference gathers

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S555-S566 ◽  
Author(s):  
Zhengwei Li ◽  
Jianfeng Zhang
Keyword(s):  
Fresnel Zone ◽  
Lateral Position ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Small Scale ◽  
Imaging Method ◽  
Time Migration ◽  
Diffraction Imaging ◽  
Dip Angle ◽  
Angle Gather

We have built a vertical traveltime difference (VTD) gather to image diffractions in the 3D time domain. This significantly improves detection of small-scale faults and heterogeneities in 3D seismic data. The VTD gather is obtained using 3D Kirchhoff prestack time migration based on the traveltime-related inline and crossline dip angles, which is closely related to the 2D dip-angle gather. In VTD gathers, diffraction events exhibit flattening, whereas reflection events have convex upward-sloping shapes. Different from the 2D dip-angle gather, Fresnel zone-related specular reflections are precisely focused on the given regions over all offsets and azimuths, thus leaving more diffraction energy after muting. To image linear diffractors, such as faults in three dimensions, the VTD gather can be extended into two dimensions by adding a dip-azimuth dimension. This makes it possible to correct phases of edge diffractions and detect the orientations of the linear diffractors. The memory requirement of the VTD or VTD plus azimuth gathers is much less than that of the 2D dip-angle gathers. We can store the gathers at each lateral position and then correct the phase and enhance the weak diffractions in 3D cases. Synthetic and field data tests demonstrate the effectiveness of our 3D diffraction imaging method.

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