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Model parameterizations in the time domain multi parameter acoustic least squares reverse time migration

Zhang Wei, Gao Jinghuai

Acta Geophysica

2021

Vol. 69, no. 2

441--458

Acoustic least-squares reverse time migration (LSRTM) can retrieve the improved refection images. However, the most existing acoustic LSRTM approaches generally ignore the density variation of the subsurface. The multi-parameter acoustic LSRTM approach in the presence of a density parameter can overcome this weakness. However, diferent model parameterizations in such an acoustic LSRTM approach can lead to diferent migration artifacts and infuence the rate of convergence. In this paper, we mainly investigate and analyze the refectivity images of diferent model parameterizations in the multi-parameter acoustic LSRTM approach, in which the velocity–density parameterization can provide reliable refection images. According to Green’s representation theory, we derive the gradients of the objective function with regard to the multi-parameter refectivity images in detail, in which both the migration image of density in the velocity–density model parameterization and the migration image of impedance in the impedance–velocity model parameterization are free from the low-frequency artifacts. Through numerical examples using the layered and fault models, we have proved that the multiparameter acoustic LSRTM approach with the velocity–density model parameterization can provide the migration images with higher resolution and improved amplitudes. Meanwhile, a correlation-based objective function is less sensitive to amplitude errors than the conventional waveform-matching objective function in the multi-parameter acoustic LSRTM approach.

Reflected wave least squares reverse time migration with angle illumination compensation

Zhou Huamin, Chen Shengchang, Zhou Liming, Ren Haoran, Wu Rushan, Xiao Guoqiang

Acta Geophysica

2019

Vol. 67, no. 6

1551--1561

High-quality seismic data imaging plays an important role in the lithological interpretation of subsurface structures. However, high-quality imaging remains a challenging task. Based on the linear inversion theory of reflected wave equations, this paper proposes reflected wave least squares reverse time migration with angle illumination compensation to better balance the amplitude of seismic imaging. We use the reflected wave migration equation to unify forward and backward propagation, which helps to obtain an image with correct phase and symmetric waveform. Under the assumption that the spectrum of seismic wavefield remains unchanged, the Poynting vector method is used to efficiently calculate the propagation direction of seismic waveform and seismic illumination in the angle domain. During iteration, angle-domain illumination is used as a preconditioner to compensate for the amplitude of the iterated gradient terms based on the angle value. In this manner, we can enhance the imaging energy of steeply inclined structures. To improve the stability of linear inversion, the spatial derivative of the image is used as a regularized constraint term. Numerical tests show that the proposed method can suppress imaging noise as well as improve resolution and amplitude fidelity of the images. Furthermore, the inversed result can be used to estimate underground reflectivity, which is important for the further development of seismic inversion technology.