Least-squares reverse time migration using analytic-signal-based wavefield decomposition

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. S149-S157 ◽  
Author(s):  
Young Seo Kim ◽  
Ali Almomin ◽  
Woodon Jeong ◽  
Constantine Tsingas
Keyword(s):  
Least Squares ◽  
Fourier Transforms ◽  
Early Stage ◽  
Vertical Direction ◽  
Analytic Signal ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Inversion Process ◽  
Time Migration ◽  
Wavefield Decomposition

An intrinsic problem during migration and imaging of seismic wavefields using the two-way wave equation is the crosstalk interference between the up/down propagation of the corresponding source and receiver wavefields. To mitigate this crosstalk, the downgoing source and upgoing receiver wavefield imaging condition (IC) is adopted at an early stage of the inversion process, improving convergence and obtaining cleaner reflection images. A wavefield decomposition methodology can also be incorporated into a least-squares reverse time migration (LSRTM) algorithm. The separation of wavefields based on the propagation direction in the early iterations of LSRTM is to reduce interference noise during the inversion process given that the IC considers only primary reflections. Wavefields decomposed with respect to the vertical direction can be easily obtained by Fourier transforms on the time and vertical axes; however, they usually require significantly higher computational effort especially for 3D applications. Vertical wavefield decomposition by a complex-valued analytic signal is an alternative method implemented by the Hilbert transform, which can be conducted by 1D Fourier transform only on the vertical axis. An LSRTM algorithm adopting this decomposition method has a disadvantage in that it requires two additional wave modelings at each iteration. However, by adapting the deprimary IC into LSRTM, only one more modeling is additionally required in the backward wavefield propagation as compared with conventional LSRTM. Our LSRTM using wavefield decomposition has the ability to produce broader band reflectivity images than conventional LSRTM. This is demonstrated with numerical examples using synthetic and real data resulting artifact-free migration results and broadband reflectivity images.

2D least-squares elastic reverse time migration of multicomponent seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S523-S538 ◽  
Author(s):  
Bingluo Gu ◽  
Jianguang Han ◽  
Zhiming Ren ◽  
Zhenchun Li
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Adjoint Operator ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Multicomponent Seismic ◽  
Isotropic Media ◽  
Wavefield Decomposition

Elastic reverse time migration (ERTM) is a state-of-the-art imaging technique used for determining complicated subsurface structures. However, the migrated images often suffer from low spatial resolution, low signal-to-noise ratio (S/N), and unbalanced amplitudes because the theoretical hypothesis of ERTM cannot be satisfied in practice. Although elastic least-squares reverse time migration (ELSRTM) has been proposed to address the issues of ERTM, the resulting images are generally represented by parameter perturbations such as P- and S-velocity perturbations, which have the different physical meanings from the ERTM images. To produce improved ERTM images, we used a least-squares RTM method for elastic data in isotropic media by applying least-squares inversion to ERTM. In the least-squares ERTM method, the forward operator generates multicomponent seismic data from the migrated images by applying elastic wavefield decomposition, scalar wavefield extrapolation, and wavefield recomposition operators. Additionally, the adjoint operator generates PP and PS images using ERTM, at which point the wavefield decomposition operator and scalar imaging condition are applied in the imaging process. Compared to conventional ERTM, our least-squares ERTM method enables us to produce improved ERTM images with higher resolution, more balanced amplitudes, and fewer artifacts. Several synthetic and field data examples were used to validate the effectiveness of the proposed least-squares ERTM method.

Multidirectional slowness vector for computing angle gathers from reverse time migration

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. S55-S68 ◽  
Author(s):  
Chen Tang ◽  
George A. McMechan
Keyword(s):  
Fourier Transforms ◽  
Grid Point ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Slowness Vector ◽  
Migration Velocity Analysis ◽  
Wavefield Decomposition ◽  
Complex Valued

Angle gathers are important for true-amplitude migration, migration velocity analysis, and angle-dependent inversion. Among existing methods, calculating the [Formula: see text] direction vector is efficient, but it can give only one direction per grid point and fails to give multiple directions for overlapping wavefields associated with multipaths and reflections. The slowness vectors (SVs) in [Formula: see text] and [Formula: see text] can be connected by Fourier transforms (FTs); the forward FT from [Formula: see text] to [Formula: see text] decomposes the wavefields into different vector components, and the inverse FT sums these components into a unique direction. Therefore, the SV has multiple directions in [Formula: see text], but it has only one direction in [Formula: see text]. Based on this relation, we have separated the computation of propagation direction into two steps: First, we used the forward FT, [Formula: see text] binning, and several inverse FTs to separate the wavefields into vector subsets with different approximate propagation angles, which contained much less wave overlapping; then, we computed [Formula: see text] SVs for each separated wavefield, and the set of these single-direction SVs constituted a multidirectional SV (MSV). In this process, the FTs between [Formula: see text] and [Formula: see text] domains required a large input/output (I/O) time. We prove the conjugate relation between the decomposition results using positive- and negative-frequency wavefields, and we use complex-valued modeling to obtain the positive-frequency wavefields. Thus, we did wavefield decomposition in [Formula: see text] instead of [Formula: see text], and avoided the huge I/O caused by the FT between the [Formula: see text] and [Formula: see text] domains. Our tests demonstrated that the MSV can give multiple directions for overlapping wavefields and improve the quality of angle gathers.

From acoustic to elastic inverse extended Born modeling: a first insight in the marine environment

Geophysics ◽  
2021 ◽  
pp. 1-73
Author(s):  
Milad Farshad ◽  
Hervé Chauris
Keyword(s):  
Least Squares ◽  
Marine Environment ◽  
Computational Cost ◽  
Physical Parameters ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Physical Density ◽  
Acoustic Approximation

Elastic least-squares reverse time migration is the state-of-the-art linear imaging technique to retrieve high-resolution quantitative subsurface images. A successful application requires many migration/modeling cycles. To accelerate the convergence rate, various pseudoinverse Born operators have been proposed, providing quantitative results within a single iteration, while having roughly the same computational cost as reverse time migration. However, these are based on the acoustic approximation, leading to possible inaccurate amplitude predictions as well as the ignorance of S-wave effects. To solve this problem, we extend the pseudoinverse Born operator from acoustic to elastic media to account for the elastic amplitudes of PP reflections and provide an estimate of physical density, P- and S-wave impedance models. We restrict the extension to marine environment, with the recording of pressure waves at the receiver positions. Firstly, we replace the acoustic Green's functions by their elastic version, without modifying the structure of the original pseudoinverse Born operator. We then apply a Radon transform to the results of the first step to calculate the angle-dependent response. Finally, we simultaneously invert for the physical parameters using a weighted least-squares method. Through numerical experiments, we first illustrate the consequences of acoustic approximation on elastic data, leading to inaccurate parameter inversion as well as to artificial reflector inclusion. Then we demonstrate that our method can simultaneously invert for elastic parameters in the presence of complex uncorrelated structures, inaccurate background models, and Gaussian noisy data.

Q least-squares reverse time migration based on the first-order viscoacoustic quasidifferential equations

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Yingming Qu ◽  
Yixin Wang ◽  
Zhenchun Li ◽  
Chang Liu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Surface Topography ◽  
Density Perturbation ◽  
Second Order ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Grid Scheme

Seismic wave attenuation caused by subsurface viscoelasticity reduces the quality of migration and the reliability of interpretation. A variety of Q-compensated migration methods have been developed based on the second-order viscoacoustic quasidifferential equations. However, these second-order wave-equation-based methods are difficult to handle with density perturbation and surface topography. In addition, the staggered grid scheme, which has an advantage over the collocated grid scheme because of its reduced numerical dispersion and enhanced stability, works in first-order wave-equation-based methods. We have developed a Q least-squares reverse time migration method based on the first-order viscoacoustic quasidifferential equations by deriving Q-compensated forward-propagated operators, Q-compensated adjoint operators, and Q-attenuated Born modeling operators. Besides, our method using curvilinear grids is available even when the attenuating medium has surface topography and can conduct Q-compensated migration with density perturbation. The results of numerical tests on two synthetic and a field data sets indicate that our method improves the imaging quality with iterations and produces better imaging results with clearer structures, higher signal-to-noise ratio, higher resolution, and more balanced amplitude by correcting the energy loss and phase distortion caused by Q attenuation. It also suppresses the scattering and diffracted noise caused by the surface topography.

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