**1. Introduction**

Special Study Group 4.170 “ Integrated Inverse Gravity Modelling” continued the work of the former identically named SSG 4.141 (1991-1995) (Barzaghi 1995). The now traditional topic belonging to the inverse geodetic problems - Ilk (1992) has given a detailed overview - was slightly enlarged and adapted to new types of geodetic and geophysical techniques and theories which include gravity information. In addition to the classical joint inversion of gravity and seismic data, new combinations have been appeared: gravity data are successfully inverted jointly with stress and strain data, with magnetic and heat flow data, and also coupled to kinematic and rheologic information. The modelled structures under investigation vary widely in dimension, shape and depth, and in scale. A broad spectrum of mathematical and physical models is employed connected with a diversity of solving algorithms for the inversion procedure. The methods are of deterministic and stochastic type or embedded in the frames of information theory and artificial intelligence.

The membership in this group and in the topic of joint inversion was of high interest above all for geophysicists. The maximum number of registered persons (members and associate members – in most cases only a formal difference) was 36. There was also a slight fluctuation from different reasons over the time span. The following list shows the names and distribution over the countries:

Members: Associate Members:

U. Achauer (France) A. Buyanov (Russia)

L. Ballani (Chairman, Germany) R.E. Chavez Segura (Mexico)

R. Barzaghi (Italy) H. ?i?kova (Czech Republic)

O. ?adek (Czech Republic) M. Everaerts (Belgium)

V.N. Glaznev (Russia) A. Geiger (Switzerland)

R. Lehmann (Germany) E.E. Klingele (Switzerland)

Z. Martinec (Czech Republic) O. Legostaeva (Ukraine)

V.O. Mikhailov (Russia) H. Mikada (Japan)

K. Mosegaard (Denmark) I.L. Prutkin (Russia)

I. Nakanishi (Japan) A. Raevsky (Russia)

M.K. Sen (USA) T.V. Romanyuk (Russia)

P. Smilde (Germany) U. Schäfer (Germany)

D. Stromeyer (Germany) V.N. Starostenko (Ukraine)

G. Strykowski (Denmark) I.E. Stepanova (Russia)

G. Toth (Hungary) V.N. Strakhov (Russia)

I. Tziavos (Greece) D.W. Vasco (USA)

Q. Wang (P.R. China)

T. Yegorova (Ukraine)

H. Zeyen (Sweden)

S. Zhao (P.R. China)

**2. Activities**

The main instrument for information and steering the group
were the Circular Letters

(No. 0 up to No. 4). The first letter (No. 0) at the
beginning was a questioning to find out the very different setups, fields,
data and strategies in inversion used. Two meetings to improve the personal
contact within the group could be organized. The first meeting

(28-30 Oct 1996 Walferdange/Luxembourg) was supported
by the fund of the “ Open Partial
Agreement on Major Hazards” offered
by the European Center for Geodynamics and Seismology (E.C.G.S.) in Luxembourg
and Belgium (Prof. Bernard Ducarme), by the Executive Board of the GeoForschungsZentrum
Potsdam (GFZ) and the International Association of Geodesy (IAG). The participants
of the meeting were 20 members of the SSG and 3 guests. 21 papers were
presented followed by intensive discussions. A second shorter meeting took
place during the EGS General Assembly in Vienna/Austria 1997. The mainly
discussed points referred to the structure and the contents of a possible
monograph covering all the topics of the group as well as some open problems
to give an orientation for the future work. A monograph and comparative
tests with data between the algorithms used in the group, as were intended
at the beginning of the time period and were prepared to a certain stage,
could not be finally realized. A home page showing the basic facts of the
group at the internet site of the IAG was created. Some of the members
of the group were engaged in the organization of symposia and partly also
in the edition of proceedings afterwards. Subsequently some significant
meetings, symposia and sub-symposia are listed:

Geodätische Woche (Geodetic Week), Session G12 “ Geodätische Inverse Probleme/Geodetic Inverse Problems” , Stuttgart, Germany, October 7-12, 1996. | |

First Meeting of IAG-SSG 4.170 “ Integrated Inverse Gravity Modelling” , Walferdange, Luxembourg, October 28-30, 1996. | |

EGS XXII General Assembly, Symposium EGS1 “ oint Inversion as a General Problem in Earth Sciences” , Vienna, Austria, 21-25 April 1997. | |

EGS XXIII General Assembly, Symposium EGS3 “ Modelling techniques and joint inversion in Earth sciences” , Nice, France, 20-24, April, 1998. | |

2nd Joint Meeting of the International Gravity Commission and the International Geoid Commision, Session VII - Inverse gravimetric and related problems. Trieste, Italy, September 7-12, 1998, | |

EGS XXIV General Assembly, Symposium G15 “ Topography and bathymetry in geodetic and geophysical applications” , Den Haag, The Netherlands, April 19-23, 1999. | |

EGS XXIV General Assembly, Symposium SE46-02 “ Inversion and interpretation of gravity and magnetic anomalies on all scales, case histories” , Den Haag, The Netherlands, April 19-23, 1999. | |

IUGG General Assembly, Inter-Association Symposium JSA40, “ Solid-Earth Geophysical Data Fusion and Analysis Methods” , Birmingham, UK, July 28, 1999 |

**3. Results and Problems**

As can be seen from the references (see below) a broad spectrum in inverse modelling is covered by the work of the group which can be, of course, summarized in different way. From the aspect of the aims and orientation of the SSG the following lines are important:

ordinary (“ single” ) inversion of gravity, magnetics, seismics and stress | |

joint inversion of gravimetry and seismics or magnetics | |

theoretical and computational aspects of joint inversion | |

geodynamical inverse problems | |

geophysical and geological applications |

Future investigations in the field of integrated inverse gravity modelling should study

the specific assumptions in the different seismic models and codes together with the investigated geophysical situation and the non-uniqueness of single inverse problems | |

the different forms of coupling and correlation in the joint inversion, especially the role of geometry as a common quantity | |

the connection of the mass density with the different geophysical fields and other geo-data, its role in topography, especially the study of the inverse gravimetric problem together with the geoid determination (boundary-value problem) making use of all types of geodetic measurements |

**4. References 1995 - 1999**

A selection only of printed articles, with a few exceptions,
can be given here (in alphabetical order related to the SSG members).
Sobolev, S.V.; **Zeyen, H.**; Granet, M.; **Achauer,
U.**; Bauer, C.; Werling, F.; Altherr, R.; Fuchs, K.: Upper mantle temperatures
and lithosphere-asthenosphere system beneath the French Massif Central
constrained by seismic, gravity, petrologic and thermal observations. Tectonophysics,
vol. 275 (1997) 1-3, 143-164.

**Ballani, L**.: Solving the Inverse Gravimetric Problem:
On the Benefit of Wavelets. in: Sanso, F. (ed.), Geodetic Theory Today.
IAG Symposia 114, Springer -Verlag Berlin etc., 1995, pp. 151-161.

**Ballani, L.**; Greiner-Mai, H.; **Stromeyer, D.**:
Determining the Magnetic Field in the Earth's Deep Mantle by an Inverse
Boundary Value Problem. Scientific Technical Report STR99/12, GeoForschungsZentrum
Potsdam, Potsdam, Germany, 1999, 80 pages.

**Barzaghi, R**.: SSG 4.141 Integrated Inverse Gravity
Modelling. in: Section IV Bulletin, General Theory and Methodology, IAG,
IUGG, No.1, Delft, The Netherlands: The Office of the Netherlands Geodetic
Commission, 1995, pp. 65-67.

Tondi, R.; De Franco, R.; **Barzaghi, R.**: Sequential
integrated inversion of traveltimes and gravity data for 2D structures.
Paper 2nd Joint Meeting of the International Gravity Commission and the
International Geoid Commision, Session VII - Inverse gravimetric and related
problems. September, 7 - 12, 1998, Trieste, Italy. (submitted to IGJ)

**Buyanov, A.F.**; **Glaznev, V.N**.; Mitrofanov,
F.P.; **Raevsky, A.B**.: Three - dimensional modelling of the Lapland
Granulite Belt and adjacent structures of the Baltic Shield from geophysical
data. in: Nor. geol. unders. Special Publ. vol. 7, 1995, pp. 167-178.

**?adek, O**.; **?i?kova, H**.; Yuen,D.A.: Mantle
viscosity inferred by genetic algorithms from the geoid and seismic information.
Phys. Chem. Earth (A), vol. 23 (1998) No. 9/10, 865-872.

Kido, M.; **?adek, O.**: Inferences of viscosity from
the oceanic geoid: indication of a low viscosity zone below the 660-km
discontinuity. Earth Planet. Sci. Lett., vol. 151 (1997), 125-137.

**?i?kova, H**.; **?adek, O**.; Yuen, D.A.; Hua-wei
Zhou: Slope of the geoid spectrum and constraints on mantle viscosity stratification.
Geophys. Res. Lett., vol. 23 (1996) 21, 3063-3066.

Kido, M.; Yuen, D.A**.; ?adek, O**.; Nakakuki, T.:Mantle
viscosity derived by genetic algorithm using oceanic geoid and seismic
tomography for whole-mantle versus blocked-flow situations. Phys. Earth
Planet. Int., vol. 107 (1998) 4, 307-326.

Campos-Enriquez, J.O.; Delgado-Rodriguez, O.; **Chavez-Segura,
R.**;Gomez-Contreras, P.; Flores-Marquez, E.L.; Birch, F.S.: The subsurface
structure of the Chalco sub-basin (Mexico City) inferred from geophysical
data. Geophysics, vol. 62 (1997) 1, 23-35.

**Everaerts, M.**; Poitevin, C.; De Vos, W.; Sterpin,
M.: Integrated geophysical/geological modelling of the western Brabant
Massif and structural implications. Bulletin de la Societe Belge de Geologie,
vol.105 (1996) 1-2, 41-59.

Kahle, H.-G.; **Geiger, A.**; Buerki, B.; Gubler, E.;
Marti, U.; Wirth, B.; Rothacher, M.; Gurtner, W.; Beutler, G.; Bauersima,
I.; Pfiffner, O.A.: Recent crustal movements, geoid and density distribution;
contribution from integrated satellite and terrestrial measurements. In:
Pfiffner, O.A. et al (eds.), Results of NRP 20; Deep Structure of the Swiss
Alps. Birkhaeuser, Basel, Switzerland. 1997, pp. 251-259.

Galichanina, L.D.; **Glaznev, V.N.**; Mitrofanov, F.P.;
Olesen, O.; Henkel, H.: Surface density characteristics of the Baltic shield
and adjacent territories. in: Nor. geol. unders. Special Publ. vol. 7,
1995, pp. 349-354.

**Glaznev, V.N.**; **Raevsky, A.B.**; Skopenko,
G.B.: A three-dimensional integrated density and thermal model of the Fennoscandian
lithosphere.Tectonophysics, vol. 258 (1996) 15-33.

Mints, M.V.; **Glaznev, V.N**.; Raevsky, A.B.: Three-dimensional
geological model of the Earth's upper crust, the Kola ultradeep borehole
and adjacent areas of the Kola Peninsula. Geotectonics, vol. 28 (1995)
6, 457-475.

Ilk, K.H.: Inverse Geodetic Problems. in: Travaux de l’Association Internationale de Géodésie, Paris, vol. 29 (1992) pp. 356 – 391.

Gret, A,; **Klingele, E.**: Application of Artifitial
Neural Networks for Gravity Interpretation in Two Dimension. Geodäsie
und Photogrammetrie ETH-Z. Bericht Nr.279. 1998. ISBN 3-906467-10-4. 88
pages.

**Klingele, E.E.**; Kahle, H.; Seismic Velocity-Density
Relationship: A Critical Review. Paper Symposium EGS1 "Joint inversion
as a general problem in Earth sciences", EGS XXII General Assembly, Vienna,
Austria, April 21-25, 1997.

**Lehmann, R.**: The Integrated Inverse Gravimetric
Problem - a Separated Minimum-Norm-Solution. Paper presented at the First
Meeting of IAG - SSG 4.170 "Integrated Inverse Gravity Modelling", Walferdange,
Luxembourg, October 28-30, 1996.

**Lehmann, R.**: Maximum entropy density determination
for the earth and terrestrial planets. Studia geoghys. et geodaet., vol.
43 (1999) 1, 35-60.

**Martinec, Z.**: Stability investigations of a discrete
downward continuation problem for geoid determination in the Canadian Rocky
Mountains. J. Geod., Vol. 70 (1996) 805-828.

**Martinec, Z.**: Boundary-Value Problems for Gravimetric
Determination of a Precise Geoid. Lecture Notes in Earth Sciences. Springer,
Heidelberg, 1998, 223 pages.

Smolyaninova, E.I.;** Mikhailov, V.O.**; Lyakhovsky,
V.A.: Numerical modelling of regional neotectonic movements in the northern
Black Sea. Tectonophysics, vol. 266 (1996) 1-4, 221-231.

**Mosegaard, K.**; Tarantola,A.: Monte Carlo sampling
of solutions to inverse problems. J. Geophys. Res. vol. 100 (1995) B7,
12431-12447.

Vasin, V.V.; **Prutkin, I.L**; Timerkhanova, L.Yu.
: Retrieval of a Three-Dimensional Relief of Geological Boundary from Gravity
Data. Izvestiya, Physics of the Solid Earth, vol. 32(1996) 901 - 905. (Russ.:
Fizika Zemli, 1996, No.11, 58-62.)

**Prutkin, I.L.**: Determination of the 3D Topography
for a Conductive Half-Space Boundary from Electromagnetic Data. Izvestiya,
Physics of the Solid Earth (Russ.: Fizika Zemli, 1998, No.4, 62-66.).

**Romanyuk, T.V.**: Seismic and density modeling of
the crust and upper mantle along the Quartz traverse. Izvestiya, Physics
of the Solid Earth, vol. 31 (1996) 9, 735-747.

Chunduru, R.K.; **Sen,M.K.**; Stoffa, P.L.: Hybrid
optimization methods for geophysical inversion. Geophysics, vol.62 (1997)
4, 1196-1207.

Zhao Lian She; **Sen, M.K.**; Stoffa, P.L.; Frohlich,
C.: Application of very fast simulated annealing to the determination of
the crustal structure beneath Tibet. Geophys. J. Int., vol.125 (1996) 2,
355-370.

**Sen, M.K.**; Stoffa, P.L.: Bayesian inference, Gibbs'
sampler and uncertainty estimation in geophysical inversion. Geophys. Prosp.,
vol. 44 (1996) 2, 313-350.

**Smilde, P.**: Verwendung und Bewertung von a-priori
Information bei potentiell singulären Inversionsproblemen am Beispiel
der gravimetrischen Bestimmung von Dichteverteilungen (Application and
evaluation of a-priori information in potentially singular inverse problems
demonstrated by the gravimetric determination of density distributions).
DGK: Series C, No. 490, München: Beck, 1998, 90 pages.

**Starostenko, V.I.**; Kozlenko, V.G.; Kostyukevich,
A.S.; Baranova, E.P.; Korenevich, K.A.; Koyfman, L.I.: Structure of the
Earth's Crust in Ukraine at the II and III Geotraverses Intersection according
to Seismogravimetric Modelling Data. Krystalinikum, vol. 22 (1995) 137
- 147.

**Starostenko, V.I.**; **Legostaeva, O.V**.: Calculation
of the Gravity Field from an Inhomogeneous, Arbitrary Truncated Vertical
Rectangular Prism. Izvestiya, Physics of the Solid Earth (Russ.: Fizika
Zemli, 1998, No.12, 31-44).

Buryanov, V.B.; Makarenko, I.B.; **Starostenko V.I.**:
Thickness and structure of the crust of the Black Sea Basin according to
gravity modeling data. Geophys. J., vol. 16 (1997) 5, 603-623.

**Stepanova, I.E.**: The Integral Equation of the Reverse
Potential Problem in Three-Dimensional Case. Dokl. Akad. Nauk, vol. 348
(1996) 2, 252-254. (Russ.)

**Stepanova, I.E.**: On the Numerical Algorithm of
the Solution of the Three-Dimensional Reverse Problem of Potential. Dokl.
Akad. Nauk, vol. 354 (1997) 2, 249-251. (Russ.)

**Stepanova, I.E.**: The Integral Equation of the Three-Dimensional
Structural Inverse Problem. Dokl. Akad. Nauk, vol. 353 (1997) 1, 108-110.
(Russ.)

**Stepanova, I.E.**: Reconstruction of a Gravity Source
in Ore-Type Problems. Izvestiya, Physics of the Solid Earth (Russ.: Fizika
Zemli, 1998, No.11, 86-89).

**Strakhov, V.N.**; **Schäfer, U.**; Strakhov,
A.V.: Neue Lineare Approximationen Linearer Elemente des Gravitationsfeldes
der Erde - Probleme und Perspektiven (New linear approximations of linear
elements of the Earth gravitational field - problems and perspectives).
in: Freeden, W. (ed.), Progress in Geodetic Science, Aachen: Shaker, 1998.
pp. 315-322.

**Strakhov, V.N.**; Strakhov A.V.: On the Regularization
Method of the Least Squares Method (Russ.), Geophysical Journal, vol. 20
(1998) 6, 1-24.

**Strakhov, V.N.**; Strakhov A.V.: On the Construction
of Stable Approximating Solutions of Great and High-dimensional Systems
of Linear Algebraic Equations Originating in Problems of Gravimetry and
Magnetics.(Russ.) Geophysical Journal, vol. 21 (1999) 1, 1-21.

**Stromeyer, D**: Plate boundary forces acting on the
South America Plate derived from stress field inversion. Annales Geophysicae,
vol. 14, Suppl. I, C256, 1996.

**Strykowski, G.**: Dealing with the non-uniqueness
of the solution to the inverse geophysical problems. in: Hansen, P. Ch.
(ed.) Proc. Interdisciplinary Inversion Workshop 4, Danish Technical University,
Lyngby, Denmark, Oct 22, 1997. pp. 67-74.

**Strykowski, G.**: Experiences with a Detailed Estimation
of the Mass Density Contrasts and of the Regional Gravity Field using Geometrical
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845-856.

**Strykowski, G.**: Elements of the Joint Gravimetric-Seismic
Modelling - Coupling the Available Information. in: Bo Holm Jacobsen (ed.),
Proc. Interdisciplinary Inversion Workshop 5, Dept. Earth Sciences, Univ.
Aarhus, Denmark, Sept. 24, 1997. pp. 24-30.

**Strykowski, G.**: Some Technical Details Concerning
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**Strykowski, G.**: Formulation of the mathematical
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of regionally distributed borehole data. In: Segawa, J.; Fujimoto, H.;
Okubo, S. (eds.), Gravity, Geoid and Marine Geodesy. IAG Symposia 117,
Springer-Verlag. New York, 1997. pp. 360-367.

**Strykowski, G.**: Borehole data and stochastic gravimetric
inversion. PhD-thesis, Univ. Copenhagen, Kort & Matrikelstyrelsen,
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**Tziavos, I.N.**; Sideris, M.G.; Suenkel, H.: The
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geoid determination. Reports Finn. Geod. Inst., vol.96 (1996) 2, 99-110.

**Vasco, D.W.**: Regularization and trade-off associated
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**Vasco, D.W.**: Groups, algebras and the non-linearity
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**Vasco, D.W.**; Peterson, J.E.; Majer, E.L.: Nonuniqueness
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**Vasco, D.W.**: A transformation approach to geophysical
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**Wang Qianshen**; Yang Xinshe: Stratified Gravity
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Integrated Inverse Gravity Modelling”
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**Wang Qianshen**; Yang Xinshe: Stratified Gravity
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**Wang Qianshen**; Wu Chuanzhen; Jiang Weiwei: Gravity
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Kong Xiangru; **Wang Qianshen**; Xiong Shaobai: Comprehensive
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**Yegorova, T.P.**; Kozlenko, V.G.; **Starostenko,
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**Yegorova, T.P.**; **Starostenko, V.I**.; Kozlenko,
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**Yegorova, T.P.**; **Starostenko, V.I.**: Gravity
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**Zeyen, H.**; **Achauer, U.**: Joint Inversion
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**Shaorong Zhao**: Detection of the active segment
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**Shaorong Zhao**: Joint inversion of observed gravity
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