This manuscript presents an approach of modeling intrusions more realistically and based on geological conceptual understanding. It is compared with an industry standard, namely radial basis function interpolation. I very much agree that the RBF standard is lacking and creates unrealistic shapes. In reality therefore, people often add fake control points and use this as a hack to create realistic shapes. Hence, there is definitely room for doing something better.

The major problem I have with the manuscript is the conditioning to borehole data. The method proposed, partly based other papers, is not a valid approach. Since the definition of the model is an implicit one, and since the model is now a parametric model, a Bayesian approach is needed, with a prior and a likelihood function/distribution. All other methods will create conditioning artifacts. This is true for all object-based methods (see REF A,B), and is a disadvantage to all object (and implicit) methods. The proposed conditioning using sequential Gaussian simulation of a signed distance function is not a valid approach because the variogram of the signed distance function is not defined, nor inferred anywhere in the manuscript. If the signed distance constraints are too large, then the Gaussian model perturbation implied will make the model shape deviate from the intended shape, hence defeating the purpose.  Also the signed distance function is likely not a Gaussian function, unless, maybe, the signed distance is very small, meaning that the model already constrains well to the data (the easy problem). This is not a realistic assumption.  Additionally, the actual true signed distance is not observed in the borehole data, only the pseudo-signed distance, the latter is not a valid random function (RF), because it depends on the borehole location (see Ref C). That means one cannot use SGS (a RF approach) to do conditioning.

The examples are also not convincing because they appear all to cover the geological shape very well. More rigorous and more challenging test need to be run such as for example, much less data (e.g. 5 boreholes). In exploration/resource definition, this is likely the case, namely, only very few boreholes exist and much more uncertainty around the location of the intrusion is expected. In that case, uncertainty quantification is needed, for example to assess planning of new boreholes. Because of the invalid conditioning, the method will therefore also not properly create uncertainty models.

My recommendation therefore is between major revision or return the manuscript for a longer effort and more in depth effort on conditioning.

Ref A Holden L, Hauge R, Skare Ø, Skorstad A (1998) Modeling of fluvial reservoirs with object models.

Math Geol 30:473–496.

Ref B Skorstad A, Hauge R, Holden L (1999) Well conditioning in a fluvial reservoir model. Math Geol

31:857–872.

Ref C Fouedjio F, Scheidt C, Yang L, Wang Y, Caers J. Conditional simulation of categorical spatial variables using Gibbs sampling of a truncated multivariate normal distribution subject to linear inequality constraints. Stochastic Environmental Research and Risk Assessment. 2021 Feb;35:457-80.

This contribution extends the modelling methodology using structural frames to a new range of geological objects that are intrusive bodies. These geological structures have received very little attention so far in the 3D modelling community and have been mainly addressed with techniques developed for stratigraphic surfaces and fault, ignoring their specificities. However, they are utterly important in a wide range of applications in academia and in the industry as they can be source of metal resources and geothermal energy. Considering the context of energy transition and metal demand, this is a hot topic.

While reusing existing concepts, the proposed method is quite original introduces clever solutions to address the specific problems raised by this new set of objects. The manuscript is very well written and illustrated. The structural geology aspects are well described to allow a reader unaccustomed to intrusions to understand the challenge. Several case studies are presented to illustrate the process and its capabilities are demonstrated on a real and complex case study. Overall, I find this manuscript excellent.

I listed minor suggestions and corrections in the attached document.

A couple of particular comments even if quite minors:

1. there seem to be an issue in equationp10 line 220, probably missing the absolute value symbol?
2. in section 4.3, p15 line 320: the process to edit the stratigraphy to account for the intrusive body shape is not clearly described, but would be very interesting
3. there is a typo in the equation line 288 p 13
4. the colormap for the thickness difference in figure 12 is a bit misleading and would be diffcult for colorblind peoples