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  • Date:
  • 18 Aug - 20 Aug
  • Location:
  • University West

"Least Squares Approach to Modelling the Geoid"

The workshop is primarily offered only for university students and personnel from public organizations, and the software package is made available only for training of students and scientific works.

After the successful experiences in the determinations and evaluations of precise local geoid models in different countries, as well as the very well met previous International Geoid Schools in September 2010, February-March 2012, August 2014 and September 2016, we will arrange a 3-day workshop based on the KTH Approach.

(KTH is a Swedish abbreviation for Royal Institute of Technology, Stockholm, Sweden).

About the workshop

The school will take place at University West for 3 days from 18 to 20 of August 2020. Arne Bjerhammar, professor at KTH between 1951 and 1983, was the first geodesist to apply analytical continuation in physical geodesy, a method practised in the KTH geoid technique in the software package KTH-GEOLAB.

The KTH approach to geoid determination is unique in the sense that it uses least squares technique in the spectral domain to combine the data in an optimum way by considering the errors of the EGM, the gravity data and the truncation of Stokes’ integral to a cap around the computation point.  Another feature that distinguishes the KTH method from others is the way corrections for topography, atmosphere and ellipsoidal shape of the earth are applied: all corrections are added as separate additive corrections.

This method was successfully applied in the determination of several regional geoid models, for example over Sweden, the Baltic countries, Greece, Iran, Sudan, Zambia, Ethiopia, Tanzania, Serbia, Moldova, part of Turkey, and also tested and compared to other methods, e.g., for instance in the 2009 for the comparison of several up-to-date methods of geoid modelling in Auvergne, France. See also Yildiz et al. (2012). The official geoid models of Sweden and Estonia as well as the NKG2015 geoid model for Scandinavia, Finland and Baltic states (Ågren et al. 2016) all use the LSMSA technique.

Several participants of previous schools have successfully completed their Ph.D. projects using this technique. A description of the method and several examples can be found in Sjöberg and Bagherbandi (2017).

The workshop will be organized with theoretical lectures in the mornings followed by computer exercises in the afternoons, where the software available at KTH will be used.  Computers will be simultaneously available for the exercises.

The workshop is primarily offered only for university students and personnel from public organizations, and the software package is made available only for training of students and scientific works.

Why KTH approach?

Many different methods have been proposed through the years for regional geoid determination by gravimetric data, each based on its own technique and philosophy. Today, all such methods combine long-wavelength Earth Gravity Models (EGMs) with local gravity data, and they mainly differ in the way they combine these data sets. The KTH approach is unique in the sense that it uses least squares technique in the spectral domain to combine the data in an optimum way by considering the errors of the EGM, the gravity data and the truncation of Stokes’ integral to a cap around the computation point.

Another feature that distinguishes the KTH method from others is the way corrections for topography, atmosphere and ellipsoidal shape of the earth are applied: in contrast to other methods, which all apply these corrections both to the gravity anomaly (direct effects) and to the preliminary computed geoid heights (indirect effects), it only corrects the preliminary geoid heights by so-called additive corrections.

Any of the additive corrections can be added afterward at any time when better data are available for its improvement (without the need to repeat all the computations). The method, called Least Squares Modification of Stokes Formula with Additive corrections (LSMSA), is the result of 30 years of research and several M.Sc. and Ph.D. theses at KTH. The LSMSA is an accurate, simple and practical method of determining the geoid.

The theoretical and practical aspects of this method have been developed since 1984 to present mainly by and under the supervision of Prof. Lars E. Sjöberg. (See numerous papers, e.g. in J. of Geodesy.) The method has been successfully applied in the determination of several high-resolution regional geoid models in different areas. Through the LSMSA approach, various data, such as a Global Geopotential Model, gravity anomalies and a high-resolution photogrammetric/SRTM Digital Elevation Model are combined to a gravimetric geoid model, and the method can be (and usually is) designed to match with GPS/levelling data by using the least-squares principle.

Several of the successful applications are reported in M.Sc. and Ph.D. theses at https://www.kth.se/en/fob/publikationer/doktorsavhandlingar-1.929860, but also elsewhere. Notable among these studies are the applications in rough topographic areas and in some developing countries with only limited gravity anomaly data. The results of comparisons clearly show that the LSMSA is advantageous to other methods.

Finally, in the recent test project for the comparison of up-to-date methods of geoid modelling with data from Auvergne area in France, no method provided better results than the LSMSA.  A comparison of remove-compute-restore and LSMS techniques on this data set is also reported in Yildiz et al. (2012; see the reference below).

Practical information

The lecture notes will be prepared on a USB stick, which contains also exercises, data sets and software. Each student will receive a copy of the stick. All lectures are followed by daily computer exercises. The participants should bring their own laptop for the exercises/labs.

This training course provides a good opportunity for the student to familiarize himself with the latest developments in geoid determination, as well as to enhance the international collaboration in gravity field modelling by building contacts to  professionals and students dealing with geoid determination in various countries.

References

  • Ågren J, Strykowski G, Bilker-Koivula M, Omang O, Märdla S, Oja T, Liepiņš I, Paršeliūnas E, Forsberg R, Kaminskis J, Ellmann A, Sjöberg L E, Valsson  (2016)  The NKG2015 gravimetric geoid model for the Nordic-Baltic region.  Presentation at the Int. Symp. GGGH Systems, 19-23 Sept., Thessaloniki, Greece
  • Sjöberg L E (2017) Lecture notes. [With some updates. Will be distributed (only) to registered participants.] (Approx. 75 pages.)
  • Sjöberg L E, Bagherbandi M (2017) Gravity inversion and integration- Theory and Applications in Geodesy and Geophysics. Springer Co. (approx. 400 pages)
  • Yildiz H, Forsberg R, Ågren J, Tscherning C C, Sjöberg L E (2012) Comparison of remove-compute restore and least squares modification of Stokes formula techniques to quasi-geoid determination over the Auvergne test area. Journal of Geodetic Science 2(1): 53-64 (open access)

Workshop on KTH GEOLAB - Preliminary Program

Day 1

Lecture (Morning; 9-12 am)

  • Opening of the school.
  • Lecture 1
    - Basic Physical Geodesy
    - Modification of Stokes’ formula
    Prof. L E Sjöberg

Lecture (Afternoon; 1-4 pm)

  • Geoid Modelling Data
  • Gravity Data Snooping and Gridding
  • Global Geopotential Models (GGMs).
  • Digital Elevation Models (DEMs)
    Prof. Ramin Kiamehr

Day 2

Lecture (Morning; 9-12 am)

  • Lecture 2
    Additive corrections
    Prof. L E Sjöberg

Lecture (Afternoon; 1-4 pm)

  • KTH GEOLAB Software
    Sample Full Project Workshop (Part1)
    Prof. Ramin Kiamehr

Day 3

Lecture (Morning; 9-12 am)

  • LSMSA vs. the RCR-Technique
    Height anomalies
    Prof. L E Sjöberg

Lecture (Afternoon; 1-4 pm)

  • KTH GEOLAB Software
    Sample Full Project Workshop (Part2)
    Prof. Ramin Kiamehr

The Venue

The school will be held at University West, Division of Mathematics, Computer and Surveying Engineering, Gustava Melins gata 2, Trollhättan (see the attached map over Trollhättan). The workshop dinner is planned for Thursday evening on August 20.

Registration

The registration fee is 5500 SEK to be paid due 15 June 2020. Late registration fees of 6500 SEK are accepted after that date. The fee includes lecture notes, preliminary software manual, a USB stick with the LSMSA software package, lunches, coffee/tea at breaks and a social dinner.

Notification of your interest to participate in the workshop:

Please inform one of the contact persons as soon as you know that you are likely to participate.

Details for payment to University West

Within Sweden:
Pay to bankgiro no. 5210-3439

Bank details of foreign payments:
Danske Bank Box 7523 SE-103 92 STOCKHOLM

SWIFT: DABASESX IBAN: SE71 1200 0000 0128 1010 3186
Account no: 1281 0103 186

In both cases, specify IGS2020 and name of participant. Send also emails to the contact persons.

Accommodation

There are many hostels and hotels in Trollhättan (search the web), but unfortunately not many with low prices. For example, best western hotel [www.bestwestern.se/) has single rooms from 550 SEK, double rooms from 650 SEK and triple from 900 SEK.

More information

Contact one of the organizers below for additional questions:

Organizers

The workshop is led by:

Lars E. Sjöberg
Head of Geoid School
Senior Professor
E-mail: lsjo@kth.se
Phone:   +46851010558

Majid Abrehdary
Contact person
Senior Lecturer
majabr@hv.se

Address

Division of Mathematics, Computer and Surveying Engineering
University West
Gustava Melins gata 2
SE- 461 32 Trollhättan
SWEDEN