the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 31 Mar 2026
SeidarT: An open-source full-waveform seismic and electromagnetic wave propagation modeling toolbox demonstrated in snow and ice
Abstract. We present SeidarT, an open-source, community-driven software package for full-waveform finite-difference time-domain (FDTD) modeling of elastic and electromagnetic wave propagation in heterogeneous, anisotropic, and attenuating media. SeidarT natively incorporates full-tensor anisotropy (all 21 stiffness coefficients), frequency-independent attenuation through a generalized Q formulation, and unified treatment of both seismic and electromagnetic wave physics on a simple Cartesian grid. The software prioritizes accessibility and extensibility by combining the computational efficiency of FORTRAN with the user-friendly scripting capabilities of Python. Model construction leverages an intuitive image-based geometry workflow and JSON project files, eliminating the need for complex mesh generation while allowing flexible specification of arbitrary stiffness or permittivity tensors, material distributions, and boundary conditions. We implement the Convolutional Perfectly Matched Layer (CPML) with explicit tuning strategies adapted for anisotropic media, and provide automatic stability checking via the Courant-Friedrichs-Lévy and wavenumber-bandlimit criteria. The software is validated against analytical solutions for elastic wave propagation and empirically constrained through comparison with ground-penetrating radar and seismic field observations in snow and ice. We document the physical property parameterizations for ice and snow as functions of temperature, pressure, and liquid water content, and provide multiple material homogenization schemes (Hill average, Gassmann substitution, Self-Consistent Approximation) to accommodate variable porosity and fluid saturation regimes. SeidarT is designed to lower economic and technical barriers for scientists, engineers, and students integrating sophisticated wave-physics simulations into workflows spanning cryospheric research, environmental monitoring, subsurface characterization, and civil infrastructure assessment. The open-source development model on GitHub and PyPI encourages community contributions and iterative improvements, positioning SeidarT as a versatile platform for advancing both fundamental understanding and applied geophysical imaging.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-1357', Henry Moore, 26 Apr 2026
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AC1: 'Reply on RC1', Steven Bernsen, 30 Apr 2026
Hi Henry,
Thank you for the constructive feedback and input. I do not have any questions at this time, and I will address your comments.
Steve
Citation: https://doi.org/10.5194/egusphere-2026-1357-AC1 -
AC3: 'Reply on RC1', Steven Bernsen, 22 May 2026
Thank you for reviewing the paper. Suggestions and comments on wording in the attached PDF provide a lot of great feedback and I have no issue with making these changes. A summary of changes is as follows:
- Grammatical, spelling, formatting errors, and redundancy will be addressed.- The rationale behind choosing default values will be made more evident.
- More context will be added behind the EM attenuation and clarification on permittivity and other relative terms will be added.
- The primary focus is on snow and ice while other materials included in the model are much more generalized. I agree that leaving the emphasis on extending the software beyond snow and ice in the Summary/Conclusions makes a lot of sense. I will remove comments in previous sections to keep the scope acute.
Citation: https://doi.org/10.5194/egusphere-2026-1357-AC3
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AC1: 'Reply on RC1', Steven Bernsen, 30 Apr 2026
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RC2: 'Comment on egusphere-2026-1357', Matthias Steiner, 29 Apr 2026
This manuscript presents SeidarT, a novel toolbox for modeling seismic and electromagnetic wave propagation in cryospheric settings. Given its focus on ice and snow scenarios, it is of particular interest to the readership of The Cryosphere. The open-source nature of the project and the sufficiently documented Git repository facilitate community contribution and ease of use.
SeidarT’s workflow, specifically the use of JSON files for parameterization and PNG files for domain definition, is a significant step toward lowering the barrier to entry for numerical modeling. This approach holds great potential for research, but also opens new perspectives in teaching and for citizen science projects.
The manuscript provides a thorough description of SeidarT’s computational framework. This allows potential users to understand exactly how the toolbox handles forward modeling, which (petro-)physical relationships are considered for both seismic and electromagnetic waves, and how the authors have balanced computational efficiency with numerical accuracy.
While SeidarT and the accompanying manuscript are of utmost relevance, the presentation of the toolbox needs to be enhanced prior to publication in The Cryosphere:
Manuscript Preparation
- The manuscript contains numerous citation errors, typos, unreferenced figures, and incomplete sentences that hinder readability.
- The manuscript is currently unbalanced. While the computational framework is described at length, the Validation section is disproportionately brief. An in-depth description of the numerical models and a more robust discussion of results versus theoretical expectations are necessary.
Figures
- Figures lack subplot labels, which makes description provided in the main text of the manuscript hard to follow.
- Some figures seem to be unfinished due to the lack of axis labels, legends etc.
- Several figures are not sufficiently described or interpreted within the main body of the text.
Numerical Studies
- The settings for the synthetic experiments are not sufficiently detailed. These should be supported by graphical illustrations of the experimental design (e.g., layer geometry and source/receiver configurations).
- Information regarding model parameters is not always provided with the required detail or scattered throughout the text. This should be consolidated at the beginning of the relevant sections.
- The authors should explicitly describe the expected physical outcomes of their experiments rather than assuming the reader is familiar with the underlying theoretical considerations or cited literature.
Detailed comments, additional questions and suggestions are provided in the attached commented PDF version of the manuscript.
I hope the review and comments serve as constructive input that is useful to the authors for preparing the manuscript for publication in The Cryosphere.
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AC2: 'Reply on RC2', Steven Bernsen, 30 Apr 2026
Hi Matthias,
Thank you for the constructive feedback and input. I do not have any questions at this time, and I will address your comments.
Steve
Citation: https://doi.org/10.5194/egusphere-2026-1357-AC2 -
AC5: 'Reply on RC2', Steven Bernsen, 22 May 2026
Thank you for the review and constructive feedback. I will revise the manuscript to address your comments as follows.
- Grammatical, spelling, and formatting errors
- Figure 2 is unreferenced and will be removed. Other referencing comments will be addressed.
- We will tidy up figures 4-9 to ensure subplot and axis labels are correct. Figure 5 and 8 legends will be included and more description will be added in the main text where highlighted in the annotated PDF.
- Include graphical representations of the experiments to depict layer geometry and source/receiver configurations where applicable. The ZOP survey, seismic body wave, and seismic surface wave models have table values and model images that we can include in the main text. We will also add more description to the ZOP survey to help the readers understanding.
- We will provide justification and clarification on Table 1 in the main text. This table refers to two layered models used for the seismic body-wave and surface-wave examples. The layer velocities were chosen and tuned to provide clear separation of the phases and to deliberately excite mode conversions. In realistic snow and ice settings, diving waves, low impedance contrasts, and weak Rayleigh modes make these phases more difficult to isolate and visualize.
- We will address comments on numerical studies by adding more context and discussion around the model parameters, the numerical models and their comparison with the theoretical expectations will be added. There are locations that require more definition in the jargon to make it more understandable to the reader so these will be included in the revision.
- Figure 7 used an auto-gain control for display but detail was not provided about what the auto-gain control is. AGC is included in the SeidarT framework and commonly used for visualization so it should be introduced thoroughly in the manuscript. I will add a few details in the main text and figure caption, and include more technical details in an appendix.
- Mitigating numerical effects by changing the CFL or grid spacing can be discussed in more detail. I expect this will be best depicted in a figure and included as a subplot with Figure 8.
- In Figure 9 we used an AIC-based autopicker to identify phase arrivals and noted that both compressional and shear-wave energy propagation are observed. To clarify this, we will add a time-series or section plot of the seismograms, together with the corresponding polarization analysis, to illustrate the picked phases. We will also include the mathematical formulation of the AIC picker and the polarization transformation in an appendix. Because these procedures are auxiliary workflows built around SeidarT rather than core components of the code, we will reference them only briefly in the main text and provide more detail in the appendix.
Citation: https://doi.org/10.5194/egusphere-2026-1357-AC5
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RC3: 'Comment on egusphere-2026-1357', Anonymous Referee #3, 06 May 2026
The manuscript presents SeidarT, an open-source software package for full-waveform finite-difference time-domain (FDTD) modeling of seismic and electromagnetic wave propagation in heterogeneous, anisotropic, and attenuating media. The code integrates a unified treatment of elastic and electromagnetic physics within a single framework.
The topic is relevant to the Solid Earth community, particularly given the increasing demand for accessible, flexible, and reproducible numerical tools. The manuscript is generally well-structured and includes validation against analytical solutions as well as field observations.
However, in its current form, the manuscript reads more as a technical/software description with illustrative examples than as a rigorous validation and benchmarking study. The manuscript claims “computational efficiency,” but no benchmarks are provided. There is no discussion of code performance, scalability, or resource usage. The authors should include benchmark (e.g. runtime vs model size, CPU/GPU usage, memory requirements) and ideally scaling test to support this claim.
One valuable contribution of the software is the image-based geometry workflow (PNG + JSON) for model construction. This approach significantly simplifies model setup compared to traditional mesh-based or script-defined geometries, especially for geometrically complex or highly heterogeneous media. However, the authors should also discuss the potential limitations of raster-based geometries, such as resolution dependence and staircasing effects, and their impact on numerical accuracy. In particular, the relationship between pixel size and model resolution could introduce aliasing effects. It would be very useful to provide a practical guideline, for example, in terms of pixels per wavelength.
Figure 4: In the caption, profile ZOP2 is mentioned, but this profile is not introduced or described in the text, leaving the reader without context. As ZOP2 is not defined, the figure is difficult to interpret.
Figure 8: The left panel lacks a label on the horizontal axis.
Language is generally clear, but occasionally verbose and repetitive. And some sentences are incomplete (see, for instance, lines 483-484) and should be revised for clarity.
Citation: https://doi.org/10.5194/egusphere-2026-1357-RC3 -
AC4: 'Reply on RC3', Steven Bernsen, 22 May 2026
Thank you for your review and constructive feedback. I will revise the manuscript to address you comments as follows.
- We will add a brief discussion on the computational performance including flop count and example OpenMP speedups for representative models.
- We will clarify the scope and contributions of the work in the Introduction and Conclusion. In this manuscript, we are not proposing new numerical discretization. Instead I am implementing well-established staggered-grid FDTD and CPML schemes. The novelty is in the integrated workflow for cryospheric applications including full-tensor anisotropy along with snow and ice homogenization, and the image based geometry an JSON interface in order to lower the barriers to use.
- We will add discussion on the potential limitations of raster-based geometries, such as resolution dependence and staircasing effects, and their impact on numerical accuracy. We will provide practical guidance so that users can choose appropriate image resolution and grid spacing that goes beyond just maintaining numerical stability. Further improvements to geometric representation and local refinement are active areas of development in the code base, and will be documented in future releases. However, these extensions are beyond the scope of the present manuscript.
Citation: https://doi.org/10.5194/egusphere-2026-1357-AC4
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AC4: 'Reply on RC3', Steven Bernsen, 22 May 2026
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- 1
This manuscript presents the new modeling toolbox, SeidarT, for modeling seismic and electromagnetic wave propagation in snow/ice settings. Modeling presented in this manuscript is of particular interest to readers of The Cryosphere in the combined forward modeling approach of seismic and GPR data commonly collected in snow/ice settings. A comprehensive, computationally efficient, and open-source framework is presented with the manuscript, encouraging community use of the forward model. Parameterization and model limitations are well established throughout the manuscript, while also suggesting the possibilities of future research. Results from the forward model contrasted with field data reveal reliable agreement and show promise for interested researchers. Two main comments regarding the manuscript are highlighted below for the consideration of the authors with revisions.
General Comment 1:
In the Introduction, SeidarT is presented as a forward model capable of handling anisotropy in any environment in which seismic/GPR data are collected. Upon reading the rest of the manuscript, many parameters and governing equations are tuned only to the application in snow/ice settings. The Introduction should be tailored to applications in snow/ice environments and not more generally to ensure capabilities are not “over-promised”. While it is acknowledged that such a model could be extended to other applications, the model is not parameterized for such applications, and the manuscript does not present enough case studies for broader applications. Rather than targeting these broader applications, it is suggested that authors simply make this note in the Summary/Conclusions that future work could be done to examine these applications in other fields.
General Comment 2:
Within the governing equations section, further parallels between the seismic and GPR methods could be touched on. Specifically, the attenuation of the EM wave and seismic wave could use additional explanation as to the same amplitude decay governing the propagation in the subsurface. Clarification on the use of the term “permittivity” should also be considered in the GPR section for reader understanding of either the “relative dielectric permittivity” or the “relative permittivity”.
Final Comment:
As a reviewer I see the value of this model and the fit of the manuscript to The Cryosphere journal. Additional minor grammatical and specific queries are provided in the attached “mark-up” version of the manuscript. The suggestions presented above are intended to be constructive, with the aim that they will be useful to the authors.