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Understanding convection is important in stellar physics, for example as aninput in stellar evolution models. Helioseismic estimates of convective flowamplitudes in deeper regions of the solar interior disagree by orders ofmagnitude among themselves and with simulations. We aim to assess the validityof an existing upper limit of solar convective flow amplitudes at a depth of0.96 solar radii obtained using time-distance helioseismology and severalsimplifying assumptions. We generated synthetic observations for convectiveflow fields from a magnetohydrodynamic simulation (MURaM) using travel-timesensitivity functions and a noise model. We compared the estimates of the flowwith the actual values. For the scales of interest ($\ell<100$), we find thatthe current procedure for obtaining an upper limit gives the correct order ofmagnitude of the flow for the given flow fields. We also show that thisestimate is not an upper limit in a strict sense because it underestimates theflow amplitude at the largest scales by a factor of about two because the scaledependence of the signal-to-noise ratio has to be taken into account. Aftercorrecting for this and after taking the dependence of the measurements ondirection in Fourier space into account, we show that the obtained estimate isindeed an upper limit. We conclude that time-distance helioseismology is ableto correctly estimate the order of magnitude (or an upper limit) of solarconvective flows in the deeper interior when the vertical correlation functionof the different flow components is known and the scale dependence of thesignal-to-noise ratio is taken into account. We suggest that future work shouldinclude information from different target depths to better separate the effectof near-surface flows from those at greater depths. The measurements aresensitive to all three flow directions, which should be taken into account.

Helioseismological determination of the subsurface spatial spectrum of solar convection: Demonstration using numerical simulations