A New Method for Diagnostics of Solar Magnetic Fields and Flows from Time-Distance Analysis

We propose a new method to obtain information on plasma flows and magnetic fields below the visible solar surface using time-distance measurements. The method is based on sine and cosine transforms of propagation times measured as a function of direction. The method allows one to sort out various characteristics of the subsurface medium, the flows, magnetic fields and their nonuniformities, and is less sensitive to the measurement errors. We discuss the parity properties of various contributions to the propagation times with respect to forward and backward directions and show how these properties allow separation of the effects of magnetic field and flows, as well as separation of the horizontal components from the vertical. It is shown that the first harmonics contain information on the direction and absolute value of the velocity, while the second harmonics are sensitive to the orientation and absolute value of horizontal magnetic fields and spatial gradients of the flow velocity. We discuss the effects of discrete mesh on the accuracy of measurements of the propagation time. An advantage of the method is in its intrinsic invariance with respect to the choice of the coordinate frame. The method provides an automatic rule of assigning proper weights to every observation points. We give estimates of the accuracy of the reconstruction of the flow field over distances comparable with the scale of the convection. We also present the "magnetic" corrections to the propagation time in a vertically stratified medium.