星震学是目前为止为数不多能够直接探测恒星内部结构及其演化状态的研究方法和手段之一。同时能够精确确定恒星的基本参数，包括恒星质量、半径、表面重力加速度等。红巨星整体脉动功率谱表现为类太阳震荡。但不同于主序类太阳的是红巨星的脉动模式是能穿透到恒星中心的混合模。它们在恒星包层表现为p模式而在恒星中心表现为g模式。因此，通过对混合模的研究我们能够探知红巨星的整个内部结构。当恒星转动时，脉动频率将发生分裂。因此，通过g模式主导的混合模的频率分裂我们可以研究红巨星中心核的旋转情况。相应地，通过p模式主导的混合模的频率分裂我们可以研究红巨星包层的旋转。通过所有混合模的频率分裂我们可以反演出红巨星内部旋转曲线，研究红巨星内部较差自转。在本项目中，我们将反演红巨星的内部旋转曲线、寻找较差自转变化的规律。为探索新的角动量转移机制提供方向。

Asteroseismology is a powerful tool for directly probing the inner structure and evolutionary status of stars. It can be as well as used to precisely determine stellar fundamental parameters, such stellar mass, radius, and surface gravity. The pulsation of red giants characterizes solar-like oscillations like the main-sequence stars in oscillation power spectra on the whole. But, they are different from the oscillations of main-sequence stars. They are mixed modes which can penetrate into the stellar core. Their oscillation properties characterize as p-modes in p-mode cavity and as g-modes in g-cavity, respectively. These mixed modes can be therefore used to probe the inner structure and states of red giant stars. The degeneracy of oscillation mode will be broke and split as multi-modes, when star rotates. Therefore, the rotational splits of g- and p-dominated mixed mode can be used to constrain the rotation of the core and the envelope, respectively, in red giant stars. Combining the rotational splits of both g- and p-dominated mixed modes, the rotational curves and/or the differential rotations in red giant stars can be inversed. In this project, we will try to inverse the rotational curves of red giant stars and find the law of the differential rotation. It will support the possible directions for finding a new physical mechanism for the achievement of angular momentum transport in red giant stars.