Zaitian Ma

Sensitivity kernels for seismic Fresnel volume tomography

Fresnel volume tomography FVT offers higher resolution and better accuracy than conventional seismic raypath tomography. A key problem in FVT is the sensitivity kernel. We propose amplitude and traveltime sensitivity kernels expressed directly with Green’s functions for transmitted waves for 2D/3D homogeneous/heterogeneous media. The Green’s functions are calculated with a finite-difference operator of the full wave equation in the frequency-space domain. In the special case of homogeneous media, we analyze the properties of the sensitivity kernels extensively and gain new insight into these properties. According to the constructive interference of waves, the spatial distribution ranges of the monochromatic sensitivity kernels in FVT differ from each other greatly and are 1 / 8, 2/ 8, 3/ 8 and 4 / 8 periods of seismic waves, respectively, for 2D amplitude, 3D amplitude, 2D traveltime, and 3D traveltime conditions. We also have a new understanding of the relationship between raypath tomography and FVT. Within the first Fresnel volume of the dominant frequency, the band-limited sensitivity kernels of FVT in homogeneous media or smoothly heterogeneous media are very close to those of the dominant frequency. Thus, it is practical to replace the band-limited sensitivity kernel with a few selected frequencies or even the single dominant frequency to save computation when performing band-limited FVT. The numerical experiment proves that FVT using our sensitivity kernels can achieve more accurate results than traditional raypath tomography.

3D Kirchhoff prestack time migration in average illumination-azimuth and incident-angle domain for isotropic and vertical transversely isotropic media

Conventional offset domain prestack migration tends to bring ambiguity and migration artifacts because it smears energy from different angles at the image point. To avoid this, prestack depth migration implementations in angle domain have been investigated in the past decades. As an efficient imaging tool, angle domain Kirchhoff prestack time migration is still useful and was proposed recently. However, existing algorithms cannot handle ray bending and anisotropy correctly. Practically, azimuth analysis for fractured reservoirs should be carried out after migration for most geological settings. Unfortunately, the existing migration algorithm implicitly involves some kind of binning to source-receiver azimuth, which may not be the real wave-path azimuth, especially for side-scattering or out-of-plane waves. In this paper, we present an algorithm for 3D Kirchhoff prestack time migration in average illumination azimuth and incident angle domain, which matches true wave path naturally and more accurately. To handle ray bending and vertical transversely isotropy, we propose several approaches to estimate two-way traveltime and the corresponding angular attributes through extended offset-to-angle mapping. Based upon these approaches, our 3D prestack time migration can provide high-quality common-image gathers for amplitude variation with incident angle and/or amplitude variation with offset and azimuth analyses, even in media with slight to moderate lateral heterogeneity. The 2D and 3D synthetic examples prove the validity of our methods.

An eigenvalue decomposition method to construct absorbing boundary conditions for acoustic and elastic wave equations

A new approach to constructing absorbing boundary conditions (ABCs) for acoustic and elastic wave equations (in transversely isotropic media) is presented. The eigenvalue decomposition method (ED method) is used to calculate the eigenvalues and eigenvectors of the coefficient matrix in the wave equations, which can be used to construct the outgoing and incoming waves along any direction. For different boundary regions, the outgoing waves are kept unchanged, but the amplitudes of the incoming waves are kept constant in time. As well as ABCs at the four lines in 2D and six surfaces in 3D, the ABCs at the four corners in 2D and eight corners and 12 lines in 3D are constructed. The vibration curves show that these conditions have nearly the same effect as perfectly matched layer (PML) absorbing boundary conditions, and are much better than Clayton–Enquist (CE) absorbing boundary conditions.

Quantitative estimation of seismic imaging resolution

Summary The seismic resolution has been investigated for a long time, but most authors focus on the vertical and horizontal resolutions of the migrated seismic image. In this paper we discuss the generalized seismic spatial resolution and further derive the general formulae to quantitatively estimate the 2D and 3D spatial resolutions for both prestack and poststack migrations in any direction, including the vertical and the horizontal directions.

Application of an integrated wave-equation datuming scheme to overthrust data: A case history from the Chinese foothills

An integrated wave-equation datuming scheme improves the imaging quality of seismic data from overthrust areas. It can be regarded as integrated because upward-layer replacement is included. In this scheme, data are downward continued to a nonplanar datum (such as the base of the weathering layer), followed by upward continuation from the nonplanar datum to a final planar datum using a one-way extrapolator. When compared with a Kirchhoff integral, this method can deal better with the strong lateral velocity variation within the near surface. After a test on synthetic data, the scheme is applied successfully to real 2D overthrust data acquired in the Qi-Lian foothills, western China. Compared with results using static corrections, integrated wave-equation datuming results lead to better reconstruction of the diffractions and reflections, more reliable migration-velocity analyses, and stronger stack and final depth images.

Azimuth-preserved Local Angle Domain Imaging and Its Application to Prestack Time Migration

Employing 3D prestack migration in azimuthal analysis allows for some structural dip and provides for higher signal to noise ratio in the measurements. Standard common-offset migration does not preserve azimuthal information. Recent attempts to move this analysis into migrated space concern source-receiver azimuth and offset on the surface, and generally involve some form of data sectoring. In fact, surface-azimuth and offset may be poor representations of the direction of wave path in the subsurface. Sectored migration may produce noisy prestack images owing to limited fold within the sectors and often requires large sectors leading to poor statistics for analysis of anisotropic properties. To tackle these problems, we present an azimuth-preserved local angle domain imaging approach that honors the local directional characteristics of the subsurface wave path in isotropic and vertical transversely isotropic media. The example has shown the advantage of our azimuth-preserved local angle domain Kirchhoff prestack time migration algorithm for azimuthal analysis.

A fast converted wave dip moveout in f-k domain

Summary Converted wave (C-wave) dip moveout (DMO) is one of the main procedures for multi-component seismic data processing. In this work, we derive a C-wave DMO formula based upon a second-order approximate trajectory equation of conversion-points, and further propose a fast algorithm in frequency-wavenumber (f-k) domain. With Cwave DMO process, the common-conversion-point (CCP) migrates to the common-middle-point (CMP). Impuse responses and a real OBC data example are presented.

Azimuth‐preserved local angle domain imaging in azimuthally anisotropic media

For seismic data with low fold and poor azimuthal sampling, more reliable imaging and azimuthal analysis can be achieved using azimuthal migration of full 3D data, rather than sectored isotropic migration of the azimuth-limited or common offset vector data. However, most routinely used prestack migration techniques only concern source-receiver azimuth and offset on the surface, which may be a poor representation of subsurface direction of the wavepath. To extract high-resolution angle-dependent reflectivity and detailed information from geologic targets, we present an azimuth-preserved local angle domain Kirchhoff prestack time migration approach which can tackle azimuthal anisotropy of the overburden and reservoir. Real data example is presented to prove the necessity of imaging in subsurface angle domain for properly focusing and revealing azimuthand angle-dependent variations of residual moveout and migrated amplitude.

Target-oriented curved-wave prestack depth migration by controlled illumination

Conventional prestack depth migration (PSDM) based on full prestack data involves many computations for wavefield extrapolation. Areal shot-record technology offers an attractive alternative for efficient PSDM because its synthesis process greatly decreases the amount of prestack data required for migration. Constructing its synthesis operator is key to the image quality of the migrated areal shot record. Curved-wave PSDM technology expands areal shot-record migration. It constructs synthesis operators by defining a complex function as a base kernel of curved wavefields multiplied by a factor of its illumination perturbation related to ray parameter and then synthesizes curved wavefields for migrations. Based on curved-wave-migration theory, we propose an efficient and accurate curved-wave, controlled-illumination method to migrate in a target-oriented way. We construct tar-get-oriented synthesis operators by wave theory, combined with rotation or perturbation of the illuminating direction of a base-kerne...

2-D frequency-space domain finite-difference elastic-wave modeling using compressed storage format

Summary Numerical simulations are widely used in seismic forward and inversion, Simulation in frequency space domain has its inherent advantages. It can simulate multiple source; each frequency component can be computed independently, thus parallel computation can be easily implemented;It has no accumulative errors; It is more suitable for simulating wave propagation in viscoelastic media. Unfortunately, the frequency domain finite-difference method is an implicit method which needs a huge storage space. Base on Stekl’s discussion [1] , a new compressed format to store the mass matrix in the process of solving the differential equation is used, which can reduce the storage space dramatically. we adopt the PML boundary condition. In order to reduce numerical dispersion, we calculate the optimal finite-difference coefficient. With the derived 9-point finite-difference format, numerical experiments demonstrate the numerical simulation method in this paper is effective, it can be used in the elastic wave migration and inversion.