A stability estimate for a solution to the problem of determination of two coefficients of a hyperbolic equation

We consider the problem of determination of two coefficients $\sigma(x)$ and $q(x)$ in a hyperbolic equation. Here $\sigma(x)$ is the coefficient of the first derivative with respect to $t$ and $q(x)$ is the coefficient of the solution itself. We suppose that these coefficients are small in some norm and supported in a disk $D$. Oscillations are excited by the impulse function $\delta(t)\delta(x\cdot\nu)$ supported on the straight line $t=0$, $x\cdot\nu=0$. Here $\nu$ is a unit vector playing the role of a parameter of the problem. The acoustic field generated by this source lying outside $D$ is measured at the points of the boundary of $D$ together with the normal derivative on some time interval of a fixed length $T$ for two different values of the parameter $\nu$. We prove that, for a sufficiently large $T$, the given information determines the sought coefficients uniquely. We obtain a stability estimate for a solution to the problem.