A compressed data approach for image-domain least-squares migration

We consider the problem of image-domain least-squares migration based on efficiently constructing the Hessian matrix with sparse beam data. Specifically, we use the ultra-wide-band phase space beam summation method, where beams are used as local basis functions to represent scattered data collected at the surface. The beam domain data are sparse. One can identify seismic events with significant contributions so that only beams with non-negligible amplitudes need to be used to image the subsurface. In addition, due to the beams' spectral localization, only beams that pass near an imaging point need to be taken into account. These two properties reduce the computational complexity of computing the Hessian matrix - an essential ingredient for least-squares migration. As a result, we can efficiently construct the Hessian matrix based on analyzing the sparse beam domain data.

Migration deconvolution using domain decomposition

Least-squares migration (LSM) is an effective technique for mitigating blurring effects and migration artifacts generated by the limited data frequency bandwidth, incomplete coverage of geometry, source signature, and unbalanced amplitudes caused by complex wavefield propagation in the subsurface. Migration deconvolution (MD) is an image-domain approach for least-squares migration, which approximates the Hessian operator using a set of precomputed point spread functions (PSFs). We introduce a new workflow by integrating the MD and the domain decomposition (DD) methods. The DD techniques aim to solve large and complex linear systems by splitting problems into smaller parts, facilitating parallel computing, and providing a higher convergence in iterative algorithms. The following proposal suggests that instead of solving the problem in a unique domain, as conventionally performed, we split the problem into subdomains that overlap and solve each of them independently. We accelerate the convergence rate of the conjugate gradient solver by applying the DD methods to retrieve a better reflectivity, which is mainly visible in regions with low amplitudes. Moreover, using the pseudo-Hessian operator, the convergence of the algorithm is accelerated, suggesting that the inverse problem becomes better conditioned. Experiments using the synthetic Pluto model demonstrate that the proposed algorithm dramatically reduces the required number of iterations while providing a considerable enhancement in the image resolution and better continuity of poorly illuminated events.

ADDRESSING THE CROSSTALK ISSUE IN IMAGING USING SEISMIC MULTIPLE WAVEFIELDS

Surface-related multiple wavefields constitute redundant information in conventional migration and can often be difficult to attenuate. However, when used for migration, multiple wavefields can improve subsurface illumination. Unfortunately, the process of imaging using multiples involves the management of crosstalk, which largely restricts its application. Crosstalk causes phantom images formed by spurious correlation of unrelated events in a migration process. These events can be unrelated orders of multiples in the source and receiver wavefields; they can also be one event associated with a reflector in the source wavefield and another event generated by a different reflector in the receiver wavefield. In this paper, we first examine crosstalk by explicitly investigating its generation mechanisms in a migration process and classifying it into different categories based on causality. Following this analysis, crosstalk can be predicted in a migration process and subtracted in the image domain; however, this method is usually difficult to apply due to the complexity of wavefield separation and adaptive subtraction. Furthermore, we present different algorithms to attenuate the crosstalk, including a deconvolution imaging condition, a least-squares migration (LSM) method, and an advanced algorithm combining LSM with a deconvolution imaging condition. We illustrate these different strategies on synthetic examples. A deconvolution imaging condition can attenuate some crosstalk, but it is less effective at suppressing strong coherent crosstalk events. However, the LSM method can fundamentally address the crosstalk issue, and this approach is further optimized when combined with a deconvolution imaging condition.

Accelerating least-squares Kirchhoff time migration using beam methodology

Least-squares migration is an advanced imaging technique capable of producing images with improved spatial resolution, balanced illumination and reduced migration artifacts; however, the prohibitive computational cost poses a great challenge for its practical application. We have incorporated the beam methodology into the implementation of Kirchhoff time modeling/ migration and developed a fast common-offset least-squares Kirchhoff beam time migration (LSKBTM). Different from conventional Kirchhoff time modeling/migration in which the seismic data are modeled/migrated trace by trace, the mapping operation in Kirchhoff beam time modeling/migration is performed in terms of beam components and performed only at sparsely sampled beam centers. Therefore, the computational cost of LSKBTM is significantly reduced in comparison with that of least-square Kirchhoff time migration (LSKTM). In addition, based on the second-order Taylor expansion of the diffraction traveltime, we introduce a quadratic correction term into the inverse/forward local slant stacking, effectively enhancing the computational accuracy of LSKBTM. We have used both 2D synthetic and 3D field data examples to verify the effectiveness of the proposed method. The results show that LSKBTM can produce images comparable to that of LSKTM, but at considerably reduced computational cost.

Elastic least-squares migration for quantitative reflection imaging of fracture compliances

To quantitatively image fractures with high resolution, we have developed an elastic least-squares migration (LSM) algorithm coupled with linear-slip theory, which accurately addresses seismic wave interaction with thin structures. We derive a linearized waveform inversion using the Born approximation to the boundary integral equation for scattered waves, including linear-slip interfaces for P-SV and SH wavefields. Numerical modeling tests assuming a laboratory-scale fracture where a 20 cm long fracture is illuminated by waves with a 50 kHz center frequency show that our LSM successfully estimates fracture compliances. Furthermore, due to the presence of coupling compliances at the fracture, the results using our LSM show better images than those using the conventional LSM estimating the Lamé constants. We also numerically illustrate that our LSM can be successfully applied to dipole acoustic borehole logging data with 3 kHz center frequency for single-well reflection imaging of a 10 m long, dipping fracture embedded in a random background. Finally, we apply LSM to laboratory experimental data, measuring PP reflections from a fluid-filled fracture. We confirm that the estimated fracture compliances correspond well to those estimated by earlier amplitude variation with offset inversion. Furthermore, the LSM resolves the spatially varying fracture compliances due to local filling of water in the fracture. Because the linear-slip theory can be applied to thin structures in a wide range of scales, high-resolution imaging results and estimated fracture compliance distributions will be crucial to further address small-scale properties at fractures, joints, and geologic faults.