**Appendix A. MVSS Beamforming Methodology**

*Appendix A.1. Signal Time Delay Calculation*

The time delay *τ<sup>i</sup>* of each receiver can be calculated by Equation (A1) in a 2D imaging problem where *c* is the background velocity. By adding delayed signals together, the amplitude at the target point can reveal whether the waves were reflected from the target point. As shown in Figure A1, the waves produced by the shot source (*xs*, *zs*) arrive at the scatter point *xf* , *z <sup>f</sup>* and are reflected; then, the reflected wave signals are received by a receiver (*xr*, *zr*). Here, the time difference among the signals at different receivers is caused by the position differences among the receivers and sources. The delay time of each shot-receiver pair includes two parts: *τn*, the time from the source point (*xs*, *zs*) to the target point *xf* , *z <sup>f</sup>* , and *<sup>τ</sup>m*, the time from the target point *xf* , *z <sup>f</sup>* to the receiver (*xr*, *zr*):

$$\tau\_{i} = \tau\_{s} + \tau\_{r} = \frac{\sqrt{\left(\mathbf{x}\_{s} - \mathbf{x}\_{f}\right)^{2} + \left(z\_{s} - z\_{f}\right)^{2}}}{c} + \frac{\sqrt{\left(\mathbf{x}\_{r} - \mathbf{x}\_{f}\right)^{2} + \left(z\_{r} - z\_{f}\right)^{2}}}{c} \tag{A1}$$

**Figure A1.** Time delay calculation.
