Ocean bottom dual-sensor Q-compensated elastic least-squares reverse time migration based on acoustic and separated-viscoelastic coupling equations

The ocean bottom dual-sensor (OBD) observation system places water detectors (pressure sensors) and land detectors on the irregular seabed interface to receive acoustic pressure fields and elastic wavefields, respectively. These data are usually applied to effectively remove ghost waves and ringing interference in the seawater layer, rather than being jointly used for migration. We propose an ocean bottom dual-sensor viscoacoustic and separated-viscoelastic coupled Q-compensated least-squares reverse time migration (OBD-VSV- QLSRTM) in curvilinear coordinates. In this method, to solve the Q-compensated elastic inverse problem, we jointly use the recorded acoustic pressure and elastic multicomponent seismic data from the OBD observation system. A new misfit function in the sense of least-squares inversion is constructed based on viscoacoustic and separated viscoelastic wavefields. Acoustic and separated viscoelastic equations are used to describe the acoustic wavefield in the acoustic medium and the Q-compensated P and S wavefields in the underlying viscoelastic medium, respectively. On the acoustic-viscoelastic interface, we implement a stable governing equation to ensure continuous and steady transmission of Q-compensated stresses in the subseabed and pressure in the seawater. To address the irregular seabed problem, we mesh the acoustic-viscoelastic models onto curvilinear grids and apply coordinate transformations to map the models and equations to a new curvilinear coordinate system. We derive viscoacoustic and separated-viscoelastic coupled adjoint and demigration operators in the curvilinear coordinates, enabling linear acoustic-viscoelastic modeling and stable receiver-side back-propagated wavefield continuation. Numerical examples conducted on two typical acoustic-viscoelastic models demonstrate that our proposed OBD-VSV- QLSRTM in curvilinear coordinates can produce highly accurate P- and S-wave images efficiently.

Steeply dipping structural target oriented viscoacoustic prismatic reverse time migration in frequency domain and its application

AbstractSteeply dipping structural imaging is a great challenge due to its poor illumination. Conventional migration methods are unable to produce an accurate image of complex steeply dipping structures. The prismatic wave can improve the illumination of steeply dipping structures and is often used to improve the imaging results of such structures. Traditional elastic wave theory assumes that seismic waves do not attenuate when propagating through subsurface media. However, during seismic wave propagation, the wave energy decays exponentially due to the absorption and attenuation of the ground layer. Subsurface attenuation leads to amplitude loss and phase distortion of seismic waves, resulting in blurring of migration amplitudes when this attenuation is not taken into account during imaging. To address this issue, a frequency‐domain Q‐compensated prismatic reverse time migration method is proposed, which derives Q‐compensated prismatic wavefield propagation operators. In the proposed frequency‐domain Q‐compensated prismatic reverse time migration, Q attenuation is fully compensated along three propagation paths and two propagation types of prismatic waves. The optimized four‐order mixed 25‐point difference format and LU decomposition method are used to solve the Q‐compensated prismatic wavefield propagation equations with high computational efficiency. Numerical and field data examples demonstrate that the proposed frequency‐domain Q‐compensated prismatic reverse time migration method can compensate for deep attenuation energy and improve the imaging resolution of steeply dipping structures.

Velocity-Adaptive Irregular Point Spread Function Deconvolution Imaging Using X-Shaped Denoising Diffusion Filtering

Elastic full‐waveform inversion based on the double‐cross‐shaped discrete flux‐corrected transport

AbstractMulti‐parameter elastic full‐waveform inversion is a technique that utilizes both P‐ and S‐waves of observed seismic data to produce high‐resolution velocity and density models with accurate amplitude information by minimizing the discrepancy between the predicted and observed multi‐component data. However, due to the nonlinear nature of the multi‐parameter inverse problem, elastic full‐waveform inversion is prone to local minima and ‘cycle‐skipping’. To overcome these challenges, this paper proposes an elastic full‐waveform inversion method that incorporates a double‐cross‐shaped discrete flux‐corrected transport. This method additionally introduces diffusion fluxes in two diagonal directions, which helps to capture low‐frequency information in the observed seismic data and maintain forward modelling stability. Multi‐scale inversion is achieved by gradually decreasing the diffusion flux correction parameter. Numerical experiments on both two typical models and a field data example demonstrate the effectiveness of the proposed elastic full‐waveform inversion method based on the double‐cross‐shaped discrete flux‐corrected transport in generating high‐precision velocity and density models.

Joint Acoustic and Decoupled-Elastic Least-Squares Reverse Time Migration for Simultaneously Using Water-Land Dual-Detector Data

Viscoacoustic least‐squares reverse‐time migration of different‐order free‐surface multiples

AbstractMultiples have longer propagation paths and smaller reflection angles than primaries for the same source–receiver combination, so they cover a larger illumination area. Therefore, multiples can be used to image shadow zones of primaries. Least‐squares reverse‐time migration of multiples can produce high‐quality images with fewer artefacts, high resolution and balanced amplitudes. However, viscoelasticity exists widely in the earth, especially in the deep‐sea environment, and the influence of Q attenuation on multiples is much more serious than primaries due to multiples have longer paths. To compensate for Q attenuation of multiples, Q‐compensated least‐squares reverse‐time migration of different‐order multiples is proposed by deriving viscoacoustic Born modelling operators, adjoint operators and demigration operators for different‐order multiples. Based on inversion theory, this method compensates for Q attenuation along all the propagation paths of multiples. Examples of a simple four‐layer model, a modified attenuating Sigsbee2B model and a field data set suggest that the proposed method can produce better imaging results than Q‐compensated least‐squares reverse‐time migration of primaries and regular least‐squares reverse‐time migration of multiples.

Q-compensated least-squares reverse time migration with velocity-anisotropy correction based on the first-order velocity-pressure equations

Anisotropy and Q attenuation bring great challenges to seismic wave migration. On migrated images, anisotropy creates structural and positioning errors, and Q attenuation leads to weak amplitudes and misplacement of reflectors. A 2D Q-compensated least-squares reverse time migration with velocity-anisotropy correction ( QLSRTM-VA) is proposed through the construction of velocity-anisotropic Q-compensated forward modeling, Q-compensated adjoint, and Q-attenuated demigration operators to simultaneously correct velocity-anisotropy and Q-attenuation in the migration process. The preceding operators are derived using first-order velocity-anisotropic viscoacoustic quasi-differential wave equations with variable densities, which are stable, capable of conveniently dealing with variable density media and are easy to transform between velocity-anisotropic Q-compensation and Q-attenuation versions. As exemplified by two synthetic and field data sets, our QLSRTM-VA method increases the imaging resolution, signal-to-noise ratio, and amplitude preservation in deep regions. Our method is capable of producing better images than viscoacoustic isotropic least-squares reverse time migration (LSRTM) and acoustic anisotropic LSRTM.

Research progress on seismic imaging technology

The 3D conical Radon transform for seismic signal processing

Recently, the attenuation of highly aliased broadband surface waves has received significant attention as their high-frequency and low-speed components render f- k x- k y filters ineffective. As a popular tool widely used in seismic signal processing, the 3D linear Radon ([Formula: see text]) transform does not match the surface wave events in the time domain. This leads to the dispersal of energy over ellipses on the zero-intercept slice, whereas the reflected events over the ellipses are reflected on each intercept slice of the 3D linear Radon transform (LRT) domain, decreasing the resolution in slowness. We have introduced a new type of Radon transform defined on circular cones called 3D conical Radon transform (CRT) for seismic signal processing. Unlike LRT, the CRT maps seismic data to surface integrals on circular cones in the 3D seismic records. Consequently, surface wave events are focused as points on the zero-intercept slice, whereas the reflected events are points on each intercept slice of the CRT domain, which significantly improves the resolution in slowness compared with the LRT. We determine the performance of the CRT for seismic signal processing for random noise attenuation, primary and multiple separations, and surface wave attenuation. Based on a comparison with the LRT, synthetic data and field data sets validate the effectiveness of the CRT method at improving the focusing properties.

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

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. In addition, 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 one field data set 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.

Full-Path Compensated Least-Squares Reverse Time Migration of Joint Primaries and Different-Order Multiples for Deep-Marine Environment

Viscoacoustic reverse time migration of joint primaries and different-order multiples

Compared to primary arrivals, multiples have longer propagation paths and smaller reflection angles, leading to a wider illumination area in the horizontal direction and higher resolution in the vertical direction. Hence, it is better to make full use of the multiples rather than suppressing them. However, seismic attenuation exists widely in the subsurface medium, especially directly below the deep sea bottom. Therefore, to compensate for the attenuation effect during multiple imaging, we have developed a viscoacoustic reverse time migration (RTM) method of different-order multiples. Following the multiple propagation paths, we compensate for the attenuation during source wavefield forward propagation and receiver backward propagation, and we introduce a regularization operator to automatically eliminate the exponential high-frequency noise during the attenuation compensation process. Taking advantage of the full wavefield information, we jointly use the different-order multiples and primaries when implementing viscoacoustic RTM. In numerical examples, we validate the viscoacoustic RTM of different-order multiples in a three-layer attenuation model and an attenuating Sigsbee2B model. Our results suggest that our method can image the models using different-order multiples separately, which suppresses crosstalk artifacts, balances energy, raises resolution, and improves subsalt images dramatically.

Q-compensated reverse time migration in viscoacoustic media including surface topography

Conventional reverse time migration (RTM) may not produce high-quality images in areas with attenuation and severe topography because severe topographic surfaces have a great impact on seismic wave simulation, resulting in strong scattering and diffraction waves, and anelastic properties of the earth affect the kinematics and dynamics of seismic wave propagation. To overcome these problems, we have developed a [Formula: see text]-compensated topographic RTM method. In this method, a new viscoacoustic quasidifferential equation is introduced to simulate forward- and backward-propagated wavefields. The viscoacoustic equation has a lossy term and a dispersion term without memory variables, and it is solved by a hybrid spatial partial derivative scheme. A new stabilization operator is derived and substituted into the [Formula: see text]-compensated viscoacoustic quasidifferential equation to suppress high-frequency noise during the attenuated wavefield compensation. Numerical tests on a sag attenuating topographic model and an attenuating topographic Marmousi2 model demonstrate that our [Formula: see text]-compensated topographic RTM can produce accurate and high-quality images by correcting the anelastic amplitude loss and phase-dispersion effects. Finally, our method is tested on a field data set.

Topographic elastic least‐squares reverse time migration based on vector P‐ and S‐wave equations in the curvilinear coordinates

ABSTRACTElastic least‐squares reverse time migration has been applied to multi‐component seismic data to obtain high‐quality images. However, the final images may suffer from artefacts caused by P‐ and S‐wave crosstalk and severe spurious diffractions caused by complex topographic surface conditions. To suppress these crosstalk artefacts and spurious diffractions, we have developed a topographic separated‐wavefield elastic least‐squares reverse time migration algorithm. In this method, we apply P‐ and S‐wave separated elastic velocity–stress wave equations in the curvilinear coordinates to derive demigration equations and gradient formulas with respect to P‐ and S‐velocity. For the implementation of topographic separated‐wavefield elastic least‐squares reverse time migration, the wavefields, gradient directions and step lengths are all calculated in the curvilinear coordinates. Numerical experiments conducted with the two‐component data synthetized by a three‐topographic‐layer with anomalies model and the Canadian Foothills model are considered to verify our method. The results reveal that compared with the conventional method, our method promises imaging results with higher resolution and has a faster residual convergence speed. Finally, we carry out numerical examples on noisy data, imperfect migration velocity and inaccurate surface elevation to analyse its sensitivity to noise, migration velocity and surface elevation error. The results prove that our method is less sensitive to noise compared with the conventional elastic least‐squares reverse time migration and needs good migration velocities as other least‐squares reverse time migration methods. In addition, when implementing the proposed method, an accurate surface elevation should be obtained by global positioning system to yield high‐quality images.