Tutorial: RTM image enhancement; bad models and mad physics

Least-squares reverse time migration (LSRTM), which aims to match the modeled data with the observed data in an iterative inversion procedure, is very sensitive to the accuracy of the migration velocity model. If the migration velocity model contains errors, the final migration image may be defocused and incoherent. We have used an LSRTM scheme based on the subsurface offset extended imaging condition, least-squares extended reverse time migration (LSERTM), to provide a better solution when large velocity errors exist. By introducing an extra dimension in the image space, LSERTM can fit the observed data even when significant errors are present in the migration velocity model. We further investigate this property and find that after stacking the extended migration images along the subsurface offset axis within the theoretical lateral resolution limit, we can obtain an image with better coherency and fewer migration artifacts. Using multiple numerical examples, we demonstrate that our method provides superior inversion results compared to conventional LSRTM when the bulk velocity errors are as large as 10%.

Least-squares reverse time migration in the presence of velocity errors

Yang

Cheng

et al. 2019

Least-squares extended reverse time migration with randomly sampled space shifts

Yang

Liu

et al. 2020

Because the velocity errors are inevitable in field data application, direct implementation of conventional least-squares reverse time migration (LSRTM) would generate defocused migration images. Extending the model domain has the potential to preserve the data information, and reducing the extended model could provide a final image with more continuous subsurface structures for geologic interpretation. However, the computational cost and the memory requirement would be increased significantly compared to conventional LSRTM. To obtain an inversion image with better quality than conventional LSRTM, while maintaining the same computational cost and memory requirement, we introduce random space shifts in LSRTM. The key point is to perform implicit model extension and immediate model reduction within each iteration of the inversion procedure. To be robust against the random noise during the random sampling process, we formulate the inverse problem based on a correlation objective function. Numerical examples on a simple layered model, the Marmousi model, and the SEAM model demonstrate that even when the bulk velocity errors are up to 10%, we still obtain reasonable results for subsurface geologic interpretation.

Adaptive merging migration

Liu,

Salim,

Chen

et al. 2024

Velocity errors and data noise are inevitable for seismic imaging of field datasets in current production; therefore, it is desirable to improve the seismic images as part of the migration process to mitigate the influence of such errors and noise. To address this, we have developed a new method of adaptive merging migration (AMM). This method can produce migrated sections of equal quality to conventional migration methods given a correct velocity model and noise-free data. Additionally, it can ameliorate the seismic image quality when applied with erroneous migration velocity models or noisy seismic data. AMM employs an efficient recursive Radon transform to generate multiple p-component images, representing migrated sections associated with different local plane slopes. It then adaptively merges the subsections from those p-component images that are less distorted by velocity errors or noise into the whole image. Such merging is implemented by computing adaptive weights followed by a selective stacking. We use three synthetic velocity models and one field dataset to evaluate the AMM performance on isolated Gaussian velocity errors, inaccurate smoothed velocities, velocity errors around high-contrast and short-wavelength interfaces, and noisy seismic data. Numerical tests conducted on both synthetic and field datasets validate that AMM can effectively improve the seismic image quality in the presence of different types of velocity errors and data noise.