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1

Accuracy assessment of high and ultra high-resolution combined GGMs, and recent satellite-only GGMs - Case studies of Poland and Ethiopia

Godah Walyeldeen, Szelachowska Małgorzata, Gedamu Andenet A.

Reports on Geodesy and Geoinformatics

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2024

|

Vol. 117

38--44

EN

The launch of dedicated satellite gravity missions (CHAMP, GRACE, GOCE, and GRACE-FO), as well as the availability of gravity data from satellite altimetry and terrestrial/airborne gravity measurements have led to a growing number of Global Geopotential Models (GGMs) developed. Thus, the evaluation of GGMs is necessary to ensure their accuracy in recovering the Earth's gravity field on local, regional, and global scales. The main objective of this research is to assess the accuracy of recent GGMs over Poland in Central Europe and Ethiopia in East Africa. Combined GGMs of high (degree and order (d/o) 2190) and ultra high-resolution (d/o 5540) as well as five satellite-only GGMs were evaluated using gravity data from absolute gravity measurements and airborne gravity surveys over Poland and Ethiopia, respectively. Based on this evaluation, the estimated accuracy of the high-resolution combined GGM is at the level of 2 mGal. The estimated accuracy for the ultra-high-resolution combined GGM is ~2.5 times lower. The satellite-only GGMs investigated recover the gravity signal at an accuracy level of 10 mGal and 26 mGal, for the areas of Poland and Ethiopia, respectively. When compensating for the omitted gravity signal using a high-resolution combined GGM and the topography model, an accuracy of 2 mGal can be achieved.

2

Application of direct source parameter imaging (direct local wave number) technique to the 2D gravity anomalies for depth determination of some geological structures

Alvandi Ahmad, Toktay Hazel Deniz, Nasri Sara

Acta Geophysica

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2022

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Vol. 70, no 2

659--667

EN

Analytic signal (AS) is a complex quantity defined by two components, amplitude and phase. The intensity of changes in the phase component of the analytic signal is equal to the local wavenumber, which is used to interpret gravity data from the contact, thin dyke, and horizontal cylinder models. However, one of the disadvantages of this method is its sensitivity to noise. This paper introduces an improved local wavenumber (DSPI) based on a direct analytic signal (DAS) that is more accurate in determining the depth of potential features on gravity anomalies. This method was first tried to determine the depth values of noisy and noiseless 2D synthetic model structures. After theoretical approval, the method was examined on two gravity field data from Iran (the Gol-e-Gohar iron ore mine, Kerman) and Canada (Mobrun orebody, near Noranda). The results obtained from the DSPI method have an excellent agreement with the drilling information, Radial amplitude spectrum, and the Euler deconvolution method.

3

Geophysical depth to basement research in the SW sector of the Santa Lucía Basin, southern Uruguay

Corbo-Camargo Fernando, Ramos Julián, Rodríguez Pablo, De los Santos Jorge

Acta Geophysica

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2021

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Vol. 69, no. 4

1287--1296

EN

The Santa Lucía River Basin Trough is located in the southern sector of the Eastern Republic of Uruguay and has an area of almost 6,000 km2 . In this work, the depth to the basement in the SW sector of the Santa Lucia Basin (SLB) was determined, using geophysical methods of exploration. The interest of exploring this geological basin is to determine its depth, recognizing the possible existence of deep aquifers, and the feasibility of hydrothermalism. For this reason were acquired, processed, inverted, and interpreted 10 magnetotelluric (MT) soundings. A 3D inversion based on the ModEM code was performed, and a 2D inversion (NLCG) of the invariant determinant along a profle that crosses the study area was carried out; their comparison yields similar resistivity and structural models results. The resistivity modeling was complemented with a Bouguer anomaly map created from a gravimetric database of 157 stations. Our geophysical results indicate that the Santa Lucia trough deepens toward the E-NE, reaching sedimentary thicknesses that may exceed 950 m. Outside the studied sector, its depth increases according to the gravity minimum, toward the NE of the area. Therefore, sandy or deep fractured episodes could harbor hot springs, whose temperature, considering the normal geothermal gradient of 30 °C/km, would approximately be in the range of 36–40 °C.

4

Applying the Tilt depth and Tilt Euler techniques of gravity data to decipher the basement depth in Sichuan Basin, China

Chen Qing, Dong Yunpeng, Tan Xianfeng, Wang Jiabei, Huang Xiaoyu, Chen Hao

Acta Geophysica

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2021

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Vol. 69, no. 6

2173--2186

EN

The tilt angle (i.e., TDR) provides an efficient way to recognize the horizontal locations of multi-source geological bodies at different depths and inclination angles. The tilt-depth method was initially derived by applying magnetic formulas and used to calculate the depth of magnetic sources. Recently researchers have attempted to extend this method to interpret depths in gravity field data. The tilt-depth method of gravity anomalies (i.e., GTilt-depth) could capture the depth of a buried source effectively, which makes it superior at deciphering the basement relief. Meanwhile, Tilt-Euler deconvolution (i.e., Euler deconvolution of TDR) has been utilized for estimating a source’s position from gridded data automatically, which requires no structural index. However, analytical singularities can be produced when performing inversion with the Tilt-Euler deconvolution owning to the derivatives of TDR being incalculable when the horizontal derivative is zero. The improved Tilt-Euler deconvolution provided an efficient way to eliminate analytical singularities and obtain more stable solutions. The results from the theoretical model show that the GTilt-depth method and improved Tilt-Euler deconvolution could be applied to calculate the buried depths more accurately and effectively. Application of these methods shows that they are able to capture more detailed features, and provide more straightforward and accurate results of depth, than traditional methods. Furthermore, the results obtained from the gravity data in Sichuan Basin show that the basement depth ranges from 3 to 11 km, and 3 to 7 km in the central uplift, which contains a local depression with a depth of 8 km. The basement exhibits a general pattern of “shallow in middle and deep in east and west”, which is consistent with the results revealed by gravityseismic jointly interpreted profile. This research provides a better indication of the basement structure when interpreting the regional geology in Sichuan Basin.

5

Interpretation of gravity anomaly over 2D vertical and horizontal thin sheet with fnite length and width

Biswas Arkoprovo

Acta Geophysica

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2020

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Vol. 68, no. 4

1083--1096

EN

Gravity data are often used for delineation of the lateral and vertical extension of mineralized bodies buried at diferent depths. Various parameters associated with the buried bodies are the primary concern for mineral exploration purposes. Hence, a reliable and efcacious interpretation method is developed for the delineation of gravity anomaly data over the 2D vertical and horizontal sheet with fnite length and width associated with mineralized bodies. The parameters viz. amplitude coefcient (k), location (x0), depth to the top of the body (h), length of the sheet (L), and shape factor (q) for 2D vertical sheet type structure and depth (h) and width (w) of the sheet for 2D horizontal sheet were resolved. Restricting x0 and q has given very reliable results for the 2D vertical sheet, and the w for 2D horizontal sheet shows the problem of equivalence. However, in all cases, the delineated parameters are within the expected uncertainty. The present interpretation method was applied to synthetic and noisy data and three feld examples from the USA, Canada, and Sweden for mineral exploration purposes. It has also been seen that the present study is more reliable in delineating the actual structure associated with mineralized bodies for the 2D vertical and horizontal sheet-type structure. The delineated parameters are in outstanding agreement with the earlier works, borehole information and also updated the actual subsurface structure.

6

An Easy Method for Interpretation of Gravity Anomalies Due to Vertical Finite Lines

Kara I., Hoskan N.

Acta Geophysica

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2016

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Vol. 64, no. 6

2232--2243

EN

A new method is introduced to determine the top and bottom depth of a vertical line using gravity anomalies. For this, gravity at a distance x from the origin and horizontal derivative at that point are utilized. A numerical value is obtained dividing the gravity at point x by horizontal derivative. Then a new equation is obtained dividing the theoretical gravity equation by the derivative equation. In that equation, assigning various values to the depth and length of vertical line, several new numerical values are obtained. Among these values, a curve is obtained for the one that is closest to the first value from attending the depth and length values. The intersection point of these curves obtained by repeating this procedure several times for different points x yield the real depth and length values of the line. The method is tested on two synthetics and field examples. Successful results are obtained in both applications.

7

Structural interpretation of the qingdong area in bohai bay basin from shipborne gravity data

Zhang C., Chen J., Song M., Wang J., Yuan B.

Polish Maritime Research

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2015

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S 1

100--105

EN

The Qingdong area, located in Bohai bay basin, was suspected good exploration prospects. In order to study tectonic features and find out favourable petroleum prospects in the area, the gravity data at a scale of 1:50,000 were interpreted. This paper, through data processing and synthetic interpretation of the high-precision gravity data in the area, discusses characteristics of the gravity field and their geological implications, determines the fault system, analyses features of the main strata, divides structure units and predicts favourable petroleum zones. The results showed that the faults controlled the development of the Mesozoic and Cenozoic strata and the distribution of local structures in this area. The study revealed that the Qingtuozi uplift and the Kendong uplift in the north were formed in Mesozoic, and the Qingdong depression in the middle was the rift basin in Mesozoic and Cenozoic. Thicker strata in Mesozoic and Cenozoic developed in the Dongying depression and the Qingdong depression, so there is abundant hydrocarbon in these two depressions, and then the Guangligang rise-in-sag and the Qingdong rise-in-sag developed in the center in these two depressions are also favorable places for prospecting

8

Determination of Sedimentary Basin Basement Depth : A Space Domain Based Gravity Inversion using Exponential Density Function

Chakravarthi V., Ramamma B.

Acta Geophysica

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2015

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Vol. 63, no. 4

1066--1079

EN

An automatic inversion using ridge regression algorithm is developed in the space domain to analyze the gravity anomalies of sedimentary basins, among which the density contrast decreases with depth following a prescribed exponential function. A stack of vertical prisms having equal widths, whose depths become the unknown parameters to be estimated, describes the geometry of a sedimentary basin above the basement complex. Because no closed form analytical equation can be derivable in the space domain using the exponential density-depth function, a combination of analytical and numerical approaches is used to realize forward gravity modeling. The depth estimates of sedimentbasement interface are initiated and subsequently improved iteratively by minimizing the objective function between the observed and modeled gravity anomalies within the specified convergence criteria. Two gravity anomaly profiles, one synthetic and a real, are interpreted using the proposed technique to demonstrate its applicability.

9

A priori noise and regularization in least squares collocation of gravity anomalies

Jarmołowski W.

Geodesy and Cartography

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2013

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Vol. 62, no. 2

199--216

EN

The paper describes the estimation of covariance parameters in least squares collocation (LSC) by the cross-validation (CV) technique called leave-one-out (LOO). Two parameters of Gauss-Markov third order model (GM3) are estimated together with a priori noise standard deviation, which contributes significantly to the covariance matrix composed of the signal and noise. Numerical tests are performed using large set of Bouguer gravity anomalies located in the central part of the U.S. Around 103 000 gravity stations are available in the selected area. This dataset, together with regular grids generated from EGM2008 geopotential model, give an opportunity to work with various spatial resolutions of the data and heterogeneous variances of the signal and noise. This plays a crucial role in the numerical investigations, because the spatial resolution of the gravity data determines the number of gravity details that we may observe and model. This establishes a relation between the spatial resolution of the data and the resolution of the gravity field model. This relation is inspected in the article and compared to the regularization problem occurring frequently in data modeling.

PL

Artykuł opisuje estymację parametrów kowariancji w kolokacji najmniejszych kwadratów (LSC) przy pomocy techniki kroswalidacji nazywanej leave-one-out (LOO). Wyznaczane są dwa parametry modelu Gaussa-Markova trzeciego rzędu (GM3) wraz z odchyleniem standardowym szumu a priori, które ma znaczny wpływ na macierz kowariancji złożoną z sygnału i szumu. Testy numeryczne przeprowadzono na dużym zbiorze anomalii grawimetrycznych Bouguera z obszaru centralnej części USA. Obszar ten mieści około 103000 pomiarów grawimetrycznych. Dane te wraz z regularnymi siatkami wygenerowanymi z modelu geopotencjalnego EGM2008 pozwalają na pracę z różną rozdzielczością przestrzenną i różnymi wariancjami sygnału i szumu. Odgrywa to kluczową rolę w badaniach numerycznych, ponieważ rozdzielczość przestrzenna danych grawimetrycznych wyznacza liczbę szczegółów pola siły ciężkości, które możemy obserwować i modelować. Oznacza to relację pomiędzy rozdzielczością przestrzenną danych i rozdzielczością modelu pola siły ciężkości. Związek ten jest w artykule analizowany i porównywany z problemem regularyzacji, występującym często w modelowaniu danych przestrzennych.

10

Simultaneous estimation of shape factor and depth of subsurface cavities from rresidual gravity anomalies using feed-forward back-propagation neural networks

Hajian A., Zomorrodian H., Styles P.

Acta Geophysica

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2012

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Vol. 60, no. 4

1043-1075

EN

We develop a new method of using feed-forward back-propagation (FFBP) neural networks to simultaneously estimate shape factor and depth of gravity anomalies. The advantages compared to neural network methods are the following: no pre-assumptions are made on source shape, the FFBP neural network estimates both depth and shape factor of source bodies and, once trained, works well for any new data in the training space, without repeating the initial calculations. The optimum number of neurons in the hidden layer was achieved with a novel multi-start algorithm. The FFBP model after training with suitable data sets and testing with different levels of noisy data is more robust than non-linear least squares minimization methods, especially for data with higher noise levels. The FFBP was tested for two sets of gravity field data over a major container terminal at Freeport, Grand Bahama, and a cavity anomaly at the Medford site, Florida, USA. The estimated parameters of the cavities agree well with the actual values.

11

Validation of GOCE gravity field models over Poland using the EGM2008 and GPS/levelling data

Godah W., Kryński J.

Geoinformation Issues

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2011

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Vol. 3, no. 1(3)

5-17

EN

Since the mid of 2010, global geopotential models based on GOCE mission data became available. The first two releases of GGMs contained four different solutions while in the third release only two solutions have been generated. In the presented study the available GOCE-derived gravity field models were evaluated in terms of height anomalies and gravity anomalies over Poland with the use of the respective functionals calculated from the EGM2008 geopotential model as well as height anomalies at 184 stations of high precision GPS/levelling control traverse. The fit of GOCE gravity field models with the EGM2008 in terms of height anomalies and gravity anomalies measured with a standard deviation is below 10 cm, and 3 mGal, respectively. Their fit with GPS/levelling height anomalies at the stations of GPS/levelling control traverse is at the level of 10 cm. The results obtained indicate some improvement of the consecutive releases of GOCE gravity field models.

PL

Od połowy 2010 roku są udostępnione globalne modele geopotencjału opracowane na podstawie danych z misji GOCE. Pierwsze dwie generacje modeli geopotencjału z misji GOCE zawierały cztery różne rozwiązania podczas gdy trzecia - składała się zaledwie z dwóch rozwiązań. Jakość dostępnych modeli pola siły ciężkości z misji GOCE została w niniejszym opracowaniu oceniona w wyniku porównania obliczonych z nich anomalii wysokości i anomalii grawimetrycznych z odpowiednimi funkcjonałami obliczonymi z modelu geopotencjału EGM2008 oraz z anomaliami wysokości 184 stacji precyzyjnego satelitarno-niwelacyjnego trawersu kontrolnego. Odchylenia standardowe różnic anomalii wysokości i anomalii grawimetrycznych pomiędzy uzyskanymi z opracowanych na podstawie danych z misji GOCE modeli geopotencjału i z modelu EGM2008 wynoszą odpowiednio 10 cm i 3 mGal. Dopasowanie modeli geopotencjału z misji GOCE do anomalii wysokości satelitarno- niwelacyjnego trawersu kontrolnego kształtuje się również na poziomie 10 cm. Uzyskane wyniki wskazują na poprawę w kolejnych generacjach modeli geopotencjału z misji GOCE.

12

Refined astrogravimetric geoid in Poland – Part II

Łyszkowicz A.

Geomatics and Environmental Engineering

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2010

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Vol. 4, no. 2

63-73

EN

Deflections of the vertical were traditionally used for modelling geoid on local and regional scale. First astrogeodetic geoid model for Poland was developed in 1961 while the last was calculated in 2005 in the framework of the project on precise geoid modelling. That model was developed using the improved deflections of the vertical, both astronomic and gravimetric. There are several effects, that were not fully considered, and problems that were not completely solved. They concern quality of archival astrogravimetric data, problem of weighting, the effects of plumb line curvature and elimination of outlying observations. In addition, all those geoid models were determined with the use of simplified astronomical levelling approach. The aim of this study was to improve the astrogravimetric geoid model in Poland by improving the procedure of astrogravimetric geoid modelling and by using improved data. In the part I of this paper (“Geomatics and Environmental Engineering”, Vol. 4, No. 1) theoretical background of astronomic levelling and least squares collocation methods are given. Then the accuracy of the components of the deflections of the vertical was estimated and the weights of astrogeodetic and astrogravimetric deflections of the vertical were determined. After that in the part II the astrogeodetic and astrogravimetric geoid models were determined from improved deflections of the vertical with the use of astronomical levelling. Other astrogeodetic and astrogravimetric geoid models were determined by least squares collocation with additional use of gravity anomalies. All four computed models were compared with the GPS/levelling geoid of the satellite POLREF network. The results obtained indicate that both astrogeodetic and astrogravimetric geoid models determined from the same input data using least squares collocation approach is by factor 5 to 7 more accurate than the ones obtained using classical astronomical levelling.

PL

Tradycyjnie odchylenia pionu są wykorzystywane do wyznaczenia przebiegu geoidy w skali lokalnej lub regionalnej. Pierwszy astrogeodezyjny model geoidy dla obszaru Polski został opracowany w 1961 roku, a ostatni model geoidy opracowano w 2005 roku w ramach grantu zamawianego dotyczącego wyznaczenia precyzyjnego modelu geoidy. Ostatni model geoidy został opracowany na podstawie poprawionych o błędy systematyczne astrogeodezyjnych i astrograwimetrycznych odchyleń pionu. Istnieje szereg czynników, które do końca nie zostały uwzględnione, oraz szereg problemów, których nie wzięto pod uwagę przy opracowywaniu kolejnych modeli geoidy. Problemy te dotyczą jakości danych archiwalnych, zagadnienia wagowania obserwacji, redukcji odchyleń pionu na geoidę, eliminacji obserwacji odstających. Ponadto, wszystkie te modele geoidy były opracowane z użyciem uproszczonej metody, jaką jest metoda niwelacji astronomicznej. Celem niniejszej pracy było opracowanie ulepszonego astrograwimetrycznego modelu geoidy dla obszaru Polski dzięki użyciu udoskonalonych danych i lepszego algorytmu obliczeniowego. W części I publikacji („Geomatics and Environmental Engineering”, t. 4, z. 1) przedstawiono, w dużym skrócie, podstawy teoretyczne niwelacji astronomicznej i kolokacji najmniejszych kwadratów. Następnie oszacowano dokładność składowych odchyleń pionu i określono sposób wagowania obserwacji. W części II opracowano metodą niwelacji astronomicznej dwa modele geoidy: jeden model z poprawionych astrogeodezyjnych danych, a drugi z astrograwimetrycznych danych. Kolejne dwa modele geoidy opracowano metodą kolokacji najmniejszych kwadratów: jeden model z danych astrogeodezyjnych, a drugi z astrogeodezyjnych odchyleń pionu i anomalii grawimetrycznych. Modele te zostały porównane z odstępami geoidy na punktach satelitarnej sieci POLREF. Wyniki porównania wskazują, że modele geoidy opracowane metodą kolokacji są od 5 do 7 razy lepsze niż modele opracowane klasyczną metodą niwelacji astronomicznej.

13

Refined astrogravimetric geoid in Poland – Part I

Łyszkowicz A.

Geomatics and Environmental Engineering

|

2010

|

Vol. 4, no. 1

57-67

EN

Deflections of the vertical were traditionally used for modelling geoid on local and regional scale. First astrogeodetic geoid model for Poland was developed in 1961 while the last was calculated in 2005 in the framework of the project on precise geoid modelling. That model was developed using the improved deflections of the vertical, both astronomic and gravimetric. There are several effects, that were not fully considered, and problems that were not completely solved. They concern quality of archival astrogravimetric data, problem of weighting, the effects of plumb line curvature and elimination of outlying observations. In addition, all those geoid models were determined with the use of simplified astronomical levelling approach. The aim of this study was to improve the astrogravimetric geoid model in Poland by improving the procedure of astrogravimetric geoid modelling and by using improved data. In the part I of this paper theoretical background of astronomic levelling and least squares collocation methods are given. Then the accuracy of the components of the deflections of the vertical was estimated and the weights of astrogeodetic and astrogravimetric deflections of the vertical were determined. After that in the part II (“Geomatics and Environmental Engineering”, Vol. 4, No. 2, in print) the astrogeodetic and astrogravimetric geoid models were determined from improved deflections of the vertical with the use of astronomical levelling. Other astrogeodetic and astrogravimetric geoid models were determined by least squares collocation with additional use of gravity anomalies. All models were compared with the GPS/levelling geoid of the satellite POLREF network. The results obtained indicate that both astrogeodetic and astrogravimetric geoid models determined from the same input data using least squares collocation approach is by factor 5 to 7 more accurate than the ones obtained using classical astronomical levelling.

PL

Tradycyjnie odchylenia pionu są wykorzystywane do wyznaczenia przebiegu geoidy w skali lokalnej lub regionalnej. Pierwszy astrogeodezyjny model geoidy dla obszaru Polski został opracowany w 1961 roku, a ostatni model geoidy opracowano w 2005 roku w ramach grantu zamawianego dotyczącego wyznaczenia precyzyjnego modelu geoidy. Ostatni modelu geoidy został opracowany na podstawie poprawionych o błędy systematyczne astrogeodezyjnych i astrograwimetrycznych odchyleń pionu. Istnieje szereg czynników, które do końca nie zostały uwzględnione, oraz szereg problemów, których nie wzięto pod uwagę przy opracowywaniu kolejnych modeli geoidy. Problemy te dotyczą jakości danych archiwalnych, zagadnienia wagowania obserwacji, redukcji odchyleń pionu na geoidę, eliminacji obserwacji odstających. Ponadto, wszystkie te modele geoidy były opracowane z użyciem uproszczonej metody, jaką jest metoda niwelacji astronomicznej. Celem niniejszej pracy było opracowanie ulepszonego astrograwimetrycznego modelu geoidy dla obszaru Polski dzięki użyciu udoskonalonych danych i lepszego algorytmu obliczeniowego. W części I publikacji przedstawiono, w dużym skrócie, podstawy teoretyczne niwelacji astronomicznej i kolokacji najmniejszych kwadratów. Następnie oszacowano dokładność składowych odchyleń pionu i określono sposób wagowania obserwacji. W części II („Geomatics and Environmental Engineering”, t. 4, z. 2, w druku) opracowano metodą niwelacji astronomicznej dwa modele geoidy, a mianowicie jeden model z poprawionych astrogeodezyjnych danych, a drugi model z astrograwimetrycznych danych. Kolejne dwa modele geoidy opracowano metodą kolokacji najmniejszych kwadratów: jeden model z danych astrogeodezyjnych, a drugi z astrogeodezyjnych odchyleń pionu i anomalii grawimetrycznych. Modele te zostały porównane z odstępami geoidy na punktach satelitarnej sieci POLREF. Wyniki porównania wskazują, że modele geoidy opracowane metodą kolokacji są od 5 do 7 razy lepsze niż modele opracowane klasyczną metodą niwelacji astronomicznej.

14

Badania grawimetryczne ziemnych obiektów hydrotechnicznych

Madej J.

Czasopismo Techniczne. Środowisko

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2008

|

R. 105, z. 3-Ś

59-71

PL

W niniejszym artykule omówiono wyniki badań grawimetrycznych wykonanych na trzech różnych obiektach hydrotechnicznych: zaporach ziemnych w Koronowie na Brdzie, w Wiśle-Czarnej na Wisełce oraz w rejonie zapory wschodniej składowiska "Żelazny Most". Przedstawiono możliwości zastosowania metody mikrograwimetrycznej do badań zapór. Wyniki prac pozwoliły na poznanie zmian w rozkładzie mas i wyodrębnienie w masywie skarp stref rozluźnień. Uzyskane rezultaty potwierdzone zostały metodami badań zagęszczenia gruntu. W artykule przeanalizowano również metodę wyznaczania gęstości objętościowej z pomiarów grawimetrycznych w aspekcie wykorzystania ich do badań zapór ziemnych.

EN

This paper presents results of gravity survey which was made on three kind of hydrotechnic plants - in Koronowo on Brda river and in Wisła-Czarna on Wisełka river and in the area of "Żelazny Most". It is introduced to the possibility using the microgravity method to examinations of dam. Results of works permitted to get to know changes in the schedule of masses, loosen zones and earth dam mass density.

15

Spherical harmonics expansion of the atmospheric gravitational potential based on exponential and power models of atmosphere

Eshagh M.

Artificial Satellites : Journal of Planetary Geodesy

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2008

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Vol. 43, No. 1

25--43

EN

Spherical harmonic formulation of gravitational potential of the atmosphere depends on the analytical model of the atmospheric density which is used. Exponential and power models are two well-known mathematical tools which are used in atmospheric applications. This paper presents simple formulas for the harmonic coefficients of internal and external types of the atmospheric potential based on these models which can be used in most of the gravimetric aspects. It considers the atmospheric effect on the satellite gravity gradiometry data as an example for numerical investigations. The numerical studies on these data show that the maximum atmospheric effect is about 2 mE over Fennoscandia based on both models, and their differences are less than 0.1 mE. The difference between indirect atmospheric effects reaches 2 cm and 0.02 mGal on the geoid and gravity anomaly, respectively in this region.

16

Interpretation of general geophysical patterns in Iran based on GRACE gradient component analysis

Kiamehr R., Eshagh M., Sjöberg L. E.

Acta Geophysica

|

2008

|

Vol. 56, no. 2

440-454

EN

Only with satellites it is possible to cover the entire Earth densely with gravity field related measurements of uniform quality within a short period of time. How-ever, due to the altitude of the satellite orbits, the signals of individual local masses are strongly damped. Based on the approach of Petrovskaya and Vershkov we determine the gravity gradient tensor directly from the spherical harmonic coefficients of the recent EIGEN-GL04C combined model of the GRACE satellite mission. Satellite gradiometry can be used as a complementary tool to gravity and geoid information in interpreting the general geophysical and geodynamical features of the Earth. Due to the high altitude of the satellite, the effects of the topography and the internal masses of the Earth are strongly damped. However, the gradiometer data, which are nothing else than the second order spatial derivatives of the gravity potential, efficiently counteract signal attenuation at the low and medium frequencies. In this article we review the procedure for estimating the gravity gradient components directly from spherical harmonics coefficients. Then we apply this method as a case study for the interpretation of possible geophysical or geodynamical patterns in Iran. We found strong correlations between the cross-components of the gravity gradient tensor and the components of the deflection of vertical, and we show that this result agrees with theory. Also, strong correlations of the gravity anomaly, geoid model and a digital elevation model were found with the diagonal elements of the gradient tensor.

17

Rola pokrywy osadowej w kształtowaniu obrazu anomalii siły ciężkości obszaru lubelskiego

Bojdys G., Grabowska T.

Geologia / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

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1999

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T. 25, z. 1

25-43

PL

W artykule przedstawiono efekty grawitacyjne związane z rozkładem gęstości w obrębie pokrywy osadowej. Bazę obliczeń stanowiły 3D modele gęstościowe kompleksów stratygraficznych (od trzeciorzędu do dewonu), skonstruowane na podstawie map geologiczno-strukturalnych i danych z wierceń. Przeprowadzone obliczenia pozwoliły ocenić udział pokrywy osadowej w kreowaniu anomalii grawimetrycznych o charakterze lokalnym. Wyniki obliczeń zestawione w formie map omówiono na tle ważniejszych dyslokacji lokalizowanych na podstawie danych geologicznych i sejsmicznych. Wskazano również na możliwość istnienia głęboko zakorzenionych NW-SE stref uskokowych w obszarze podniesienia radomsko-kraśnickiego, mogących pozostawać w związku z przebiegiem krawędzi krystalicznego cokołu wschodnioeuropejskiej platformy prekambryjskiej

EN

The paper presents gravity effects from density distribution in the sedimentary cover in the Lublin region. 3D density models of stratigraphic complexes (from Tertiary through Devonian) constructed on the basis of borehole data and geological and structural maps were used in computations. A contribution of the sedimentary cover to generating local gravity anomalies was estimated. The results of computation, given in the form of maps, are discussed taking into account major dislocations determined from geological and seismic data. It is also shown that some deep - seated fault zones with NW-SE course may occur in the Radom-Kraśnik elevation. These zones may be related with the edge of the crystalline base of the East European Precambrian Platform

18

Continuum theory of defects and gravity anomaly

Yamasaki K., Nagahama H.

Acta Geophysica Polonica

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1999

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Vol. 47, nr 3

239-257

EN

Based on the mathematical equivalence between the crack field and the continuous dislocation field, we briefly review continuum theory of defects from the view point of differential geometry. Then we derive a new differential geometric equation of static gravity change for anelastic effect due to the fault (dislocation) density. This equation shows that high gradient of dilatancy caused by the concentration of fault (dislocation) density accompanies high gradient of gravity change near the boundary between positive and negative gravity anomalies. This agrees with the characteristic distribution patterns; the distribution of short-wavelength gravity anomaly, active faults and shallow seismic activities overlap one another in the northeast Japan. Moreover, we discuss: (I) dynamic gravity anomaly related to earthquakes; (II) local gravity anomaly near the edges of an active fault; (III) differential geometric interpretation of gravity anomaly caused by the dislocation density; (IV) differential geometric relationship between gravity anomaly and magnetic anomaly (Poisson's relation).