This manuscript presents a new algorithm for probabilistic earthquake source inversion based on Hamiltonian Monte Carlo (HMC) sampling of the posterior distribution. The algorithm's efficiency rests on problem-specific adaptations to the base version of HMC, and in particular an iterative linearisation scheme that accelerates the forward problem solution while reducing dependence on the prior.

The manuscript is a please to read and clearly a scientific advancement. Most of my comments are contained in the annotated manuscript. A few more significant, but still minor, ones are listed below:

1) Given that this is a purely synthetic study that could in principle be translated to a broad range of applications, the introduction seems unnecessarily focused on Groningen. This may confuse some readers, and it artificially limits the scope of this work. It may make more sense to centre the introduction around induced seismicity and earthquake moment tensor inversion in general.



2) The reasons for stronger nonlinearity and weaker priors given on page 3 are not so obvious and need more substance. In general, arguing in terms of frequency may have limited meaning because what ultimately counts is the number of wavelengths between source and receiver.



3) While the derivation of the representation theorem for moment tensor sources has educational value, I doubt that this well-known result needs to be repeated in a research paper. My suggestion would be to leave this out and thereby shorten this already rather long manuscript.



4) The conclusion that the proposed algorithm works may be a bit too strong, given that it is only run in a synthetic scenario. So, what is actually shown is that the algorithm satisfies some sort of minimum requirement, which is the delivery of reasonable results under idealised conditions. This is still am important achievement!

This is an interesting study on full waveform inversion of induced seismicity source parameters, using a new approach to calculate the posterior distributions. This manuscript is well written, with nicely presented figures. The structure led the reader through the inversion scheme relatively clearly, and explained the procedure in a way that was very instructive. It seems to be a step forward in joint inversion of source parameters on higher frequency data, and would be a valuable tool in the analysis of induced seismicity.

Not being an expert in the full waveform inversion, some points below may be naive. I am happy to be informed if they are! I did appreciate the time taken to explain the scheme in detail, but this may be too verbose for some with greater knowledge of the specific field.

The majority of induced seismicity microseismic monitoring takes place with relatively dense local arrays, some of which are downhole. The dominant frequency of recorded signals can be larger than the 1-3 Hz data the study limits itself to. This is especially true of downhole data, where high (>~1000 Hz) sampling rates enables events with corner frequencies in excess of 100 Hz to be routinely detected. The paper claims to be more effective at “higher” frequencies, but would still require significant loss of signal through filtering. How badly are the results affected by this loss of signal? How badly does the inversion perform when, say, ~10 Hz data is used?

Without testing any real data, even for a small sample of events from Groningen, it is difficult to justify the conclusion stated in lines ~15 and ~401. It certainly seems to work for this single synthetic event, but maybe the conclusions shouldn’t be overstated. I certainly look forward to the upcoming paper where this is used on Groningen data, but do wish this manuscript included at least a couple of tests of real data to validate the inversion scheme and compare to conventional methods used to locate and invert for focal mechanism.

In the Groninegen velocity model, is anisotropy included? It can make the MT inversion highly degenerate, especially when it comes to inverting for volumetric components, and should be brought up in the introduction.

A couple of small comments and spotted typos:

• Is the semi-colon in the wrong place at the start of line 111?
• Line 179: the references to Figure 1 (a) and (b) appear to be the wrong way round, and (b) is misquoted on line 185. This made Figure 1 more difficult to interpret.
• What fraction (%?) of the MT do you use for MT prior stated on line 331?
• You say on line 412 “significant computing power” to calculate reference seismograms, but how long did SPECFEM take in this case? Would be good to reference in relation to the one minute quoted to run the workflow.