The authors present a novel method for implicit geological modelling based on neural networks. The text is very well-written and organized. I recommend its publication after a clarification of the points presented below, which could also help strenghten the discussion section.

1) The geological operators (fault displacement, overprint, etc.) are mentioned only briefly. I think an appendix would help readers understand the details better by putting all these equations (including those from other works) within a standardized notation.

2) I assume the MLP uses a smooth activation function. Which one? Does the choice of activation have an impact on the final result?

3) Have you considered using Bayesian neural networks? This way probabilistic predictions could be generated from a single model, and the priors on the weights and length scales could help to better control the model smoothness.

4) As the inputs are always in 2D or 3D, have you considered an uniform distribution of directions for the RFF features instead of random sampling? For turning bands this is the recommended method (Emery and Lantéjoul, 2006). Also a "power spectrum" of length scales derived from the grid extents could help reduce the number of hyperparameters. Furthermore, the application of L1 regularization on the weights could help with model interpretability and/or help propagate periodic features far from the data.

5) It seems to me that the average user may find it difficult to adjust the hyperparameters for each field. Is there any recommendation that can be made to help the user choose the values? Any defaults?

6) The examples presented involved some manual interventions such as multiple training phases and fixation of weights. Please discuss how the modelling process could be streamined in future versions of the library.

Minor remarks:

Figure 1 is not cited in the text.

Figure 6: for the sake of clarity it would be good to mention that each field influences the subsequent ones through the displacement functions and etc., pointing to Figure 7.

Lines 210-220: are the points resampled with each training step?

Line 122: verify sentence "...to the Laplace’s equation..."

Line 362: remove "-" 

Line 376: verify "...the monotonicity loss enabled used to encourage..."

Dear editor,

I have reviewed the manuscript "Curlew 1.0: Spatio-temporal implicit geological modelling with neural fields in python" from Kamath et al. and provide detailed comments and suggestions aimed at helping improve the quality of the work. 

Kamath et al. present curlew, a new open-source Python package designed for structural geological reconstructions using measured geological constraints. They use a neural-fields approach which allows for the incorporation of different local and global loss functions. This is a flexible framework for imposing different kinds of geological data constraints. The manuscript also demonstrates how Random Fourier Features (RFFs) can be used both to evaluate model uncertainty and to improve convergence.

The codes related to this work are publicly available in a Zenodo repository. All of the files that were used to produce the diagrams of the manuscript are present in this repository. I tried reproducing the figures by running them in a Jupyter notebook. The Jupyter notebooks included pre-computed outputs, showing that the code had already been run and reproduced the manuscript’s figures. However, rerunning the Jupyter cells yielded results different compared to the original outputs (see attached file). On several occasions the results could alter the interpretation (for example Figure 5d). Therefore, it is unclear whether the random seed was applied correctly. Could this issue be related to the fact that the NumPy and PyTorch operations have not been controlled by the random seed? Additionally, it would be important to assess the extent to which the algorithm’s inherent randomness affects the final geological reconstruction.

A question that arose while reading the manuscript concerns the comparison between curlew and existing structural modeling packages such as Aspen-SKUA, 3D-GeoModeller, Leapfrog and GemPy. The computational benefits of curlew are clear since it is a differentiable and adaptable code that can run in parallel on multi-CPU and GPU systems. However, it would be very insightful if the manuscript elaborated on whether curlew also provides qualitative improvements in geological detail or interpretability due to the flexible incorporation of multiple loss functions. For example, would a model produced with curlew give comparable results to the previously mentioned algorithms? What differences could be expected between the available codes for geological reconstructions?

Another point that could benefit from further discussion is the tuning of the loss-function weighting factors. The authors briefly mention the use of SoftAdapt (Heydari et al., 2019) but also point out that the results are mixed. Because the weights (or hyperparameters) can significantly influence the final reconstruction, additional insight into this challenge would be welcome. For instance, what alternative methods (e.g., Bayesian optimization, gradient-based methods) could be suitable in future improvements of the algorithm and the tuning of the weighting factors?

Finally, I have a few minor remarks regarding the text. I would recommend simplifying some of the sentence structures. In several places the use of long sentences or multiple commas makes the text a bit difficult to follow. Shorter sentences would largely improve the readability. In addition, I noticed a few typographical errors throughout the manuscript. Careful proofreading would be helpful. For example:

• Equation (1) should have v_s instead of v
• Line 48, “do not” instead of “don’t”
• Line 272, there is a noun missing after “from”

Overall, the manuscript presents a very promising and adaptable tool with strong potential for advancing structural reconstructions and I think should be published if the points above are addressed.