One-way true-amplitude migration using matrix decomposition

Abstract

To meet the requirement of true-amplitude migration and address the shortcomings of the classic one-way wave equations on the dynamic imaging, one-way true-amplitude wave equations were developed. Migration methods, based on the Taylor or other series approximation theory, are introduced to solve the one-way true-amplitude wave equations. This leads to the main weakness of one-way true-amplitude migration for imaging the complex or strong velocity — contrast media — the limited imaging angles. To deal with this issue, we apply a matrix decomposition method to accurately calculate the square-root operator and impose the boundary conditions of the one-way true-amplitude wave equations. Our migration method and the conventional one-way true-amplitude Fourier finite-difference (FFD) migration method are used by us to test and compare the imaging performance. The impulse responses in a strong velocity-contrast model prove that our migration method works for larger imaging angles than the one-way true-amplitude FFD method. The amplitude calculations in a strong-lateral velocity variation media with one reflector and in the Marmousi model demonstrate that our migration method provides better amplitude-preserving performance and offers higher structural imaging quality than the one-way true-amplitude FFD method. We also use field data to indicate the imaging enhancement and the feasibility of our method compared with the one-way true-amplitude FFD method. Our one-way true-amplitude migration method using matrix decomposition fully exploits the features of one-way true-amplitude wave equations with less approximation, and it is capable of producing more accurate amplitude estimations and potentially wider imaging angles.

Asymptotic Ray Method for the Double Square Root Equation

“…The inverse relations to (14) depend on the choice of parameter σ in (10). In this paper, we consider two options: two-way travel time τ itself and negative depth −z.…”

“…Initial conditions (30) define a ray coinciding with a physical one at any point 𝑥 , 𝑓 𝑥 on the reflector. One can recast them in terms of the slowness vector's components rather than the ray's tangent vector 𝑥 ⃗ using (14). Tending both the source and receiver to the reflection point, we obtain the Exploding Reflector conditions for 𝜏 0:…”

“…x using (14). Tending both the source and receiver to the reflection point, we obtain the Exploding Reflector conditions for τ = 0:…”

“…Alternatively, the DSR equation can be used for upward continuation and modeling seismic data following the "exploding reflector" concept [9]. Later on, a true-amplitude version of the DSR equation was derived from one-way wave equations [10][11][12], and its numerical implementation was discussed in [13,14]. The DSR migration was generalized to a VTI anisotropic case [15] and applied as a tool for migration velocity analysis [16]-a technique for the simultaneous recovery of the velocity model and the scatterer/reflector position.…”

Amplitude-Preserved Wave Equation: An Example to Image the Gas Hydrate System

“…In order to solve the issue of the limited imaging angle, ref. [30] proposed to apply the matrix decomposition theory to calculate one-way true amplitude equations, which achieves a better imaging result compared with the one-way true amplitude equation migration method based on Taylor expansion. The conventional one-way wave equation can only keep the kinematics of two-way wave equation but fails to provide kinetical characteristics.…”