This paper is interesting and very relevant for computational seismologists. Although it does not develop new methods, it contributes a great comparison of different strategies for modeling absorbing boundary conditions. The extensive tests regarding both accuracy and computational performance are very useful and something I have not seen in the literature before. I especially appreciate the honest assessment of unpredictability when it comes to modern FFT libraries.

I really don’t have much to criticize, but I would primarily ask the authors to elaborate a bit more in the discussion on these three points:

1. If I understand it correctly, the error measure considers the wavefield in the entire domain. In many applications, however, one would only be interested in a few measurement points at the surface. Have you done any analysis using such a restricted error criterion, and would you expect a qualitative change of the results?
2. You mention in section 2.1 that by setting the ABL parameter to zero, the same wave equation can be used in the physical domain and in the exterior. Do you distinguish those domains in the implementation? This would potentially affect computational performance considerably (with potential implications on load balancing)?
3. I understand that absorbing boundaries for elastic media are a totally different can of worms, but I would be interested in getting your take on the validity / transferability of the results to VTI acoustic (and maybe elastic) media.

There just a few more small points I noted, which I am listing below.

Line 100:

Do you assume differentiability of the source in time or in time and space? Just wondering about point sources here.

Line 125:

What is the reasoning behind adding the additional point with a pressure of zero? Is it correct that this essentially gives a homogeneous Dirichlet boundary condition? Why don’t you use some first-order condition at the outer boundary instead?

Line 160:

Have you analyzed the effect of the non-differentiability of sigma, i.e., the kink at the transition from the inner to the outer domain? I can imagine this might lead to artificial reflections.

Eq. 11:

Is there any physical intuition behind the exponential decay? I assume artificial reflections can occur similar to DWE if the slope is too steep? Intuitively, I would have assumed that N_ABL also enters into the formula, but it seems the values at the outer boundary will differ depending on the distance only?

Just as a personal preference, I probably would have used other symbols than $\sigma$ and $\mu$ for the ABL-related coefficients, as I would associate those with stress and shear modulus, respectively.

Line 265:

Typo: expressions

Line 288:

Out of curiosity: Is there a reason for not using a more recent version of g++?

Line 397:

Just to double-check: Are you using a free surface condition at the top? I don’t think this is the case, but I somehow would have expected this for the realistic SEG/EAGE model.

Line 445:

Consistency when referring to Fig., Figure, figure.

Line 480:

Typo: Such -> such