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

Acoustic least-squares reverse time migration (LSRTM) can retrieve the improved reflection 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, different model parameterizations in such an acoustic LSRTM approach can lead to different migration artifacts and influence the rate of convergence. In this paper, we mainly investigate and analyze the reflectivity images of different model parameterizations in the multi-parameter acoustic LSRTM approach, in which the velocity–density parameterization can provide reliable reflection images. According to Green’s representation theory, we derive the gradients of the objective function with regard to the multi-parameter reflectivity 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 multi-parameter 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.