Computing Helioseismic Sensitivity Kernels for the Sun's Large-scale Internal Flows

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Time–distance helioseismology measures travel times of acoustic waves traveling between two different locations on the solar surface. To infer the Sun’s internal flows from such measurements, one needs sensitivity kernels. We recently developed a new method to derive the sensitivity kernels for internal flows based on a global-scale wavefield simulation.

The flow sensitivity kernel at a location (r, θ, φ) in the solar interior can be interpreted as the amount of phase shift, observable on the surface and caused by an infinitesimally small flow perturbation at that location. By simulating wave propagation through infinitesimally small perturbations at many different locations and measuring their effect on travel times, the entire kernel could be mapped out directly. In practice, we cannot simulate infinitesimally small perturbations, and the closest we can get to this scenario is by using flow perturbations that are small relative to the finite wavelength of helioseismic waves, and with speeds that are small compared to the local sound speed to maintain linearity.

We simulated a total of 784 sets of wavefields, each with a flow perturbation volume placed at different locations inside the Sun. We then measured phase shifts from each set of simulation, with different measurement distance as well as different wave traveling directions. These measured phase shifts can be related to the known flow perturbations with the sensitivity kernels, and through solving these linearized equations we are able to infer these sensitivity kernels. Figure 1 shows the sensitivity kernels at 3.0 mHz for a travel distance of 21.6°.