OSU grant proposal includes developing time-dependent models for the new, modernized NSRS

In my November 2023 GPS World newsletter, I highlighted the announcement made by the National Geodetic Survey (NGS) of the recipients of the National Oceanic and Atmospheric Administration (NOAA) FY 2023 Geospatial Modeling Competition Awards. As stated in the newsletter, NGS awarded the grants for projects that will research emerging problems in the field of geodesy and develop tools and models to advance the modernization of the National Spatial Reference System (NSRS). A significant improvement in the new, modernized NSRS is the time-dependent component being incorporated in the computation of reference epoch coordinates (RECs). That said, developing models that accurately capture the time-dependent component is extremely important to providing reliable, consistent, and accurate RECs. This is not a simple problem to solve. Two of the grantees, Scripps Institution of Oceanography (SIO) and The Ohio State University (OSU) include developing models to address what NGS denotes as the Intra-Frame Deformation Model (IFDM).

This newsletter is going to highlight OSU’s geospatial award and my March newsletter will highlight the SIO proposal.

Summary of the OSU Geospatial Awards. (Image: NGS website)

The time-dependent models for the new, modernized NSRS — that is, Euler pole parameters (EPP) and Intra-Frame Deformation Model (IFDM)] — are discussed in NOAA Technical Report NOS NGS 62, “Blueprint for the Modernized NSRS, Part 1: Geometric Coordinates and Terrestrial Reference Frames” and NOAA Technical Report NOS NGS 67, “Blueprint for the Modernized NSRS, Part 3: Working in the Modernized NSRS.” The EPP2022 and IFDM2022 models will make time-dependent geodetic control useable for most surveyors, engineers, and geospatial users.

So, what are EPP2022 and IFDM2022? What does it mean to users of the new, modernized NSRS? Basically, the EPP model changes the reference frame of the coordinates but not the epoch and the IFDM model changes the epoch of the coordinates but not the reference frame.

As previously mentioned, these models are defined in detail in Blueprint Part 1 and Blueprint Part 3.

For the OSU grant proposal, I had the opportunity to talk with Dr. Demián Gómez, the lead principal investigator (PI) for the OSU grant. Demián has extensive experience in modeling time-dependent coordinates and is the lead author on several papers published in the Journal of Geodesy that address this topic.

Articles by Gómez in the Journal of Geodesy

• Gómez, D., Piñón, D.A., Smalley, R. et al (2015) Reference frame access under the effects of great earthquakes: a least squares collocation approach for non-secular post-seismic evolution. J Geod. https://doi. org/10. 1007/s00190-015-0871-8
• Gómez, D.D., Bevis, M. G. & Caccamise, D.J. Maximizing the consistency between regional and global reference frames utilizing inheritance of seasonal displacement parameters. J Geod 96, 9 (2022). https://doi. org/10. 1007/s00190-022-01594-0
• Gómez, D.D., Figueroa, M. A., Sobrero, F. S. et al. On the determination of coseismic deformation models to improve access to geodetic reference frame conventional epochs in low-density GNSS networks. J Geod 97, 46 (2023). https://doi. org/10. 1007/s00190-023-01734-0

In his latest paper, titled “On the determination of coseismic deformation models to improve access to geodetic reference frame conventional epochs in low-density GNSS networks,” the authors applied their methodology to two earthquakes in Chile: the 2010 Maule and 2015 Illapel earthquakes. The paper describes their methodology for estimating coseismic displacements in areas with low-density continuous GNSS coverage by using geophysical models in a hybrid (dynamic-kinematic) mode. Their methodology provided coseismic estimates on survey GNSS stations with rms (95% confidence interval) residuals of ~ 3 cm for Maule, and ~ 2 cm for Illapel. They also tested their models using InSAR and found that the models correctly predicted the near-field deformation. The authors believe that their methodology to obtain coseismic surface displacement models, based on a spherical layered Earth, for GNSS trajectory prediction models (TPMs) using sparse GNSS data represents a major improvement relative to coseismic models incorporated in TPMs, such as NGS’s Horizontal Time-Dependent Positioning model (HTDP) and Transformations in Four Dimensions (TRANS4D). This is important to users of the new, modernized NSRS because the accuracy of the IFDM2022 model is important to providing accurate RECs in the new, modernized NSRS.

Most individuals in the United States associate earthquakes with California, but earthquakes occur every day in NGS’s area of responsibility. The USGS has a website that lists the location and magnitude of earthquakes.

Plot of earthquakes — 12/21/2023 to 01/20/2024. (Image: USGS website)

The box below highlights the earthquakes in the conterminous United States during a 30-day period. Most of these earthquakes have small magnitudes. The question is, what effects do these earthquakes have on nearby published marks in the NSRS?

Plot of earthquakes in CONUS — 12/21/2023 to 01/20/2024. (Image: USGS website)

The website provides information on both earthquake and non-earthquake events.

Plot of earthquakes in Oklahoma — 12/21/2023 to 01/20/2024. (Image: USGS website)

I was wondering what it meant by non-earthquake events, so I clicked on some of the icons. As indicated on the plot, a quarry blast registered on the USGS system. Again, the question is, do these earthquakes and non-earthquake events affect the coordinates of marks in the ground?

Plot of non-earthquakes in Oklahoma. (Image: USGS website)

Something to note in the plots of Oklahoma is the large number of earthquakes around Oklahoma City during a 30-day period.

Plot of earthquakes north of Oklahoma City. (Image: USGS website)

Notice that there are several CORSs that surround the location of the earthquakes but only one CORS is close to the area. The box below shows a plot of CORS surrounding the area of earthquakes.

Demián’s latest paper describes their methodology for estimating coseismic displacements in areas with low-density continuous GNSS coverage by using geophysical models in a hybrid (dynamic-kinematic) mode. Since many earthquakes occur throughout the United States, it will be interesting to see how well this approach will work in the development of an Intra-Frame Deformation Model.

Earthquake M 4. 3 – 6 km W of Arcadia, Oklahoma. (Image: NGS website)

As previously stated, outside of California, most of these earthquakes have small magnitudes. That said, on August 9, 2020, a magnitude 5.1 earthquake occurred in Sparta, North Carolina. There were reports of damage to roads, water mains, and structures, but what were the effects on nearby published marks in the NSRS?

The box below shows the locations of earthquakes that occurred near Sparta, North Carolina. The plot indicates that there was not just one earthquake in the area, but many that may have affected the coordinates of monuments in the region.

Plot of earthquakes near Sparta, North Carolina. (Image: USGS website)

The image below shows the locations of earthquakes and NGS published geodetic marks in the Sparta region.

Image: Dave Zilkoski

Again, the real issue that needs to be addressed is what effect do these earthquakes and other geophysical activities such as subsidence have on the coordinates of geodetic marks in the region?

OSU’s grant proposal includes merging GNSS and InSAR using deep learning to better estimate the Intra-Frame Deformation Model. Obviously, developing time-dependent models for the new, modernized NSRS is very complex and technical. I contacted Demián and asked him for a list of his major milestones associated with his project.

Based on Demián’s major milestones, I had a few follow-up questions.

1) Reprocess a large dataset for the U.S. and Canada using double and single differences.  This processing will also become the United States’ contribution for the next SIRGAS reprocessing in IGS20.

I asked Demián if he had an estimate of the amount of data he was talking about?

He told me that he did not have an exact number yet because they are still adding data. He said that, at this time, they have 878 stations in the US and Canada which amounts to 4,648,269 station days (i.e., 4. 6M RINEX files, just in the US and Canada). This is the latest number he retrieved from his database but this number increases every day (January 16, 2024).  

2) Development of tools for parallel processing using M-PAGES. This new NGS software has several advantages over double differences and we want to test it and compare it against GAMIT solutions to evaluate its performance.

Demián stated that M-PAGES has several advantages so I asked him to explain what he meant.

He told me that one advantage is that it can process all constellations at once using single differences which allows processing of more stations simultaneously. Another advantage is because single differences produce “lighter” systems of equations (compared to double differences), they can process more stations simultaneously.

3) Develop 3D deformation models that use GNSS and InSAR datasets. These models will be “hybrid” (dynamic and kinematic) to improve the fit to the data without introducing artifacts produced by noise.

[Note: this approach is described in the paper titled “On the determination of coseismic deformation models to improve access to geodetic reference frame conventional epochs in low-density GNSS networks,” J Geod 97, 46 (2023).] 

Demián said “they are in the process of collecting all the GNSS data that they can to process and then they will identify which gaps can be filled with InSAR data.”

I wanted to better understand what Demián meant by “hybrid” model. So, I asked him about his “hybrid” approach and he provided the following explanation:

When we say “kinematic” we refer to a model that does not consider the underlying mechanism to explain the observed effect. A good example are the trajectory models of GNSS stations that describe their motions as a sum of mathematical functions (there are no physics in them). A dynamic model does use the underlying physics to explain the observations. A “hybrid” model is in the middle: it uses a dynamic model but allows some unrealistic model parameters to improve the data fit.

I mentioned to Demián that users would be very interested in the spatiotemporal uncertainties of the intra-frame deformation model. I asked him if, at this time, he had any idea of the size or range of uncertainties.

Demián said “that it will be variable and very dependent on the density of the input data. He said that they are aiming for cm-level uncertainties. Our experience in Argentina tells us that a 5 mm uncertainty level can be achieved on stable regions while about 2 to 3 cm is expected on high deformation areas. We will have to wait and see to understand the model’s performance. ”

I told Demián that the Houston-Galveston, Texas region of the United States is an area of subsidence that would benefit with an accurate Intra-Frame Deformation Model. The Harris-Galveston Subsidence District has a variety of GNSS CORS and PAMS that are not part of NGS’s CORS. My April 2022 GPS World Newsletter, which included the HGSD CORS and PAMS, described the effects of vertical movement on NGS’s modernized 2022 NSRS. I also asked if he was willing to use this data

He had a very simple answer: “Absolutely!”  He said “The more data we incorporate, the better the models will describe reality. Part of the project is related to providing a processing line that can handle large amounts of data. The issue with some data is metadata. Metadata and how we collect it is what really prevents us from reaching that “final mm” uncertainty level we are all looking for. We should be pushing very hard on metadata standardization. In my opinion, the biggest problem is twofold: 1) incorrect antenna identification in RINEX files (due to improper data curation) and 2) lack of a unified/globally accessible database of metadata that is adequately cured.”

4) Develop AI methods to create GNSS time series and identify deformation patterns in InSAR.

Part of the OSU project is to use ML to improve the development of the IFDM.

Excerpt from OSU Proposal on trajectory modeling

Trajectory modeling

For each station, we will obtain KTM parameters, including their uncertainties, for

stations velocities (and acceleration if needed), mechanical and/or geophysical jumps (earthquakes), logarithmic transients after earthquakes (following recommendations from Sobrero et al., 2020), and seasonal coordinate variations.  Other parameters for stations affected by volcanic activity, episodic subsidence, etc will also be added when needed.  We routinely generate these KTMs for thousands of GNSS stations (for the definition of our in-house geodetic RF) using software developed within the Division of Geodetic Science at OSU. Earthquake detection is performed automatically following formulations also developed by the project’s PIs.

Trajectory modeling enhancement using machine learning

We will enhance the capabilities of the KTMs by including a physics-based machine

learning (ML) component to the model that automatically detects, e. g., discontinuities in the time series. Detecting and mitigating the effects of mechanical jumps (those generated by unreported equipment changes and other effects) will increase the overall reliability of the GGPL. ML is well suited for this task and indeed ML algorithms like Random Forests have been explored in a recent work (e. g., Crocetti et al., 2021). We will test a similar approach, as well as more sophisticated convolutional neural networks to automatically detect discontinuities in coordinate trajectories. These ML algorithms will be trained on OSU’s database of trajectory models (~4000 stations). Using this ML algorithm we will also automatically detect other ‘harmful’ residuals in the time series. For example, large residuals can appear right after an earthquake if the postseismic transient does not have the appropriate relaxation time, or if two transients are needed to model the event.  

I find AI and ML fascinating. Basically, machine learning is a field of study in artificial intelligence.

[As a side note: According to Wikipedia, Alan Turing, a mathematician, was the first person to conduct substantial research in the field that he called machine intelligence. Mr. Turing was considered the father of modern computer science. He was famous for his work in decoding the encryption of German Enigma machines during the second world war, and documenting a procedure, known as the Turing Test, that formed the basis for artificial intelligence. Turing was not directly involved with the successful breaking of these more complex codes, but his ideas proved of the greatest importance in this work.]

5) The items above are part of the “Geometric Geodesy Processing Line” that will be deployed at NGS as a “sandbox” framework. We expect to get feedback from NGS on its uses and application as an internal operational reference frame.

The fifth milestone includes developing what Demián calls a “Geometric Geodesy Processing Line (GGPL).” GGPL has three phases, but I am very interested in the first phase. The first phase will begin by analyzing the different components of the GGPL, including the interactions with various geospatial stakeholders, both within and outside of the United States. The plan includes developing a workflow that involves data curation, processing, and analysis to create an operational, fully kinematic reference frame (KRF) for CONUS and Canada. The KRF, once implemented, would at first constitute an experimental or ‘sandbox’ frame executed jointly with NGS’s Geosciences Research Division.

I asked Demián what plans he has for involving users. Especially, how is he going to include surveyors, engineers, photogrammetrists, and spatial data managers?

“My goal is to bring some of the lessons learned in Argentina when we implemented the kinematic reference frame in 2019,” Demián said. Back then, we had discussions with small groups of people in industry to know what their needs were. For example, surveyors will probably need to deal with epoch transformations in a different way than engineers or spatial data managers. The GGPL should facilitate the products that will help these stakeholders. In my experience, the issue is how the data (or model) is accessed so I do not foresee any major issues with users.”

He said that he is open to any suggestions others might have about this.

In phase two, OSU will augment the KRF with locally ‘dynamic’ densifications, which allow

the reference frame to be ‘interpolated’ to locations between the reference stations. Using advanced techniques, such as deep learning, complementary datasets, such as GNSS and InSAR, will be combined and assimilated leading to a kinematic/dynamic reference frame. During phase two, NGS would be assessing the utility and performance of the sandbox GGPL, while OSU works on its dynamic extensions.

In a third phase, the GGPL and the associated KRF and models would undergo any necessary modifications and adaptations, all guided by NGS. By the end of the proposed project, NGS will have a sandbox frame that can implement any new International Terrestrial Reference Frame (ITRF) in a manner that is completely transparent to NSRS users, including all associated models to operate continuously and without interruption.

This newsletter highlighted NGS’s grant to OSU for developing a fully kinematic reference frame for the Continental United States of America and Canada. The primary objectives of this project are to modernize geodetic tools and models and to develop a geodetic workforce for the future. The OSU project will include interactions with various geospatial stakeholders, both within and outside of the United States. In my opinion, it is very important to engage the geospatial user community when developing these new tools so the tools will be useful during the implementation of the new NSRS. A significant improvement in the new, modernized NSRS is the time-dependent component being incorporated in the computation of reference epoch coordinates (RECs). That said, developing models that accurately capture the time-dependent component is extremely important to providing reliable, consistent, and accurate RECs. The goal of the OSU project is to provide an accurate Intra-Frame Deformation Model which will provide reliable, consistent, and accurate reference epoch coordinates (RECs). Throughout the project, OSU would train M.S. and Ph.D. students, and postdocs, providing a source of trained new employees for governmental agencies as well as private industry. Future newsletters will address other NGS recipients of the NOAA FY 23 Geospatial Modeling Competition Awards.