Rytov-approximation-based wave-equation traveltime tomography

Most finite-frequency traveltime tomography methods are based on the Born approximation, which requires that the scale of the velocity heterogeneity and the magnitude of the velocity perturbation should be small enough to satisfy the Born approximation. On the contrary, the Rytov approximation works well for large-scale velocity heterogeneity. Typically, the Rytov-approximation-based finite-frequency traveltime sensitivity kernel (Rytov-FFTSK) can be obtained by integrating the phase-delay sensitivity kernels with a normalized weighting function, in which the calculation of sensitivity kernels requires the numerical solution of Green’s function. However, solving the Green’s function explicitly is quite computationally demanding, especially for 3D problems. To avoid explicit calculation of the Green’s function, we show that the Rytov-FFTSK can be obtained by crosscorrelating a forward-propagated incident wavefield and reverse-propagated adjoint wavefield in the time domain. In addition, we find that the action of the Rytov-FFTSK on a model-space vector, e.g., the product of the sensitivity kernel and a vector, can be computed by calculating the inner product of two time-domain fields. Consequently, the Hessian-vector product can be computed in a matrix-free fashion (i.e., first calculate the product of the sensitivity kernel and a model-space vector and then calculate the product of the transposed sensitivity kernel and a data-space vector), without forming the Hessian matrix or the sensitivity kernels explicitly. We solve the traveltime inverse problem with the Gauss-Newton method, in which the Gauss-Newton equation is approximately solved by the conjugate gradient using our matrix-free Hessian-vector product method. An example with a perfect acquisition geometry found that our Rytov-approximation-based traveltime inversion method can produce a high-quality inversion result with a very fast convergence rate. An overthrust synthetic data test demonstrates that large- to intermediate-scale model perturbations can be recovered by diving waves if long-offset acquisition is available.

Finite-frequency traveltime tomography using the Generalized Rytov approximation

SUMMARY Wave-equation-based traveltime tomography has been extensively applied in both global tomography and seismic exploration. Typically, the traveltime Fréchet derivative is obtained using the first-order Born approximation, which is only satisfied for weak velocity perturbations and small phase shifts (i.e. the weak-scattering assumption). Although the small phase-shift restriction can be handled with the Rytov approximation, the weak velocity-perturbation assumption is still a major limitation. The recently developed generalized Rytov approximation (GRA) method can achieve an improved phase accuracy of the forward-scattered wavefield, in the presence of large-scale and strong velocity perturbations. In this paper, we combine GRA with the classical finite-frequency theory and propose a GRA-based traveltime sensitivity kernel (GRA-TSK), which overcomes the weak-scattering limitation of the conventional finite-frequency methods. Numerical examples demonstrate that the accumulated time delay of forward-scattered waves caused by large-scale smooth perturbations can be correctly handled by the GRA-TSK, regardless of the magnitude of the velocity perturbations. Then, we apply the new sensitivity kernel to solve the traveltime inverse problem, and we propose a matrix-free Gauss–Newton method that has a faster convergence rate compared with the gradient-based method. Numerical tests show that, compared with the conventional adjoint traveltime tomography, the proposed GRA-based traveltime tomography can obtain a more accurate model with a faster convergence rate, making it more suited for recovering the large-intermediate scale of the velocity model, even for strong-perturbation and complex subsurface structures.

Gaussian beam velocity tomography based on azimuth-opening angle domain common imaging gathers

Ray-based tomography in the imaging domain, implemented with seismic migration, is currently widely used in industrial applications. However, conventional ray-based tomography has some inherent problems, such as shadow area, multi-path problem and so on, which limit the inversion accuracy. To alleviate these problems, we proposed Gaussian beam velocity tomography (GBT) based on azimuth-opening angle domain common imaging gathers (ADCIGs). According to the first-order Born and Rytov approximations, we derived a linear relationship between travel-time perturbation and velocity perturbation in the imaging domain, by which we construct the explicit expression of the sensitivity kernel function and use a Gaussian beam operator to compute the kernel. Furthermore, by introducing the preconditioned model regularization, a method of GBT under the constraint of a structure-guided filter is derived. Iterative applications of migration and tomography, both based on a Gaussian beam propagator, embody the idea of integrating velocity inversion and imaging. Numerical tests on both synthetic data and field data demonstrate that Gaussian beam propagator-based travel-time tomography in the imaging domain is effective.

Three-dimensional images generated from diffuse ultrasound wave: detections of multiple cracks in concrete structures

The simultaneous detection of multiple defects in concrete structures is a task of pivotal importance for non-destructive testing and evaluation. Diffuse waves experiencing multiple scattering inside media are demonstrated to be sensitive to weak defects. Here, an analytic model is presented for diffuse wave decorrelation associated with sensitivity kernel that describes the time-of-flight distribution in strongly scattering environments. The model is then used for generating three-dimensional images that involve estimating perturbations at each localized position through an iterative, non-linear algorithm. With the consideration of loads and micro-cracks effects on diffuse waves, an application of the approach to a real-size concrete beam shows features that denote the positions and depths of multiple existing cracks. Extension of the approach to other strongly scattering media such as tissues and volcanos is straightforward. This study offers great potential for practical applications such as structural health monitoring, medical image generation, and seismic monitoring.