Elsevier

Computers & Geosciences

Volume 30, Issues 9–10, November–December 2004, Pages 949-957
Computers & Geosciences

Inner and minimum constraint adjustment of marine gravity data

https://doi.org/10.1016/j.cageo.2004.06.004Get rights and content

Abstract

A programme for marine gravity data validation and adjustment is presented—VALDAMA. The aim of the programme is to provide a complete user-friendly system for marine gravity data validation and adjustment that enables the user to define all intervening parameters. The programme is written in standard C and has the possibility of solving for three different types of adjustment: inner constraint, constraint and minimum constraint and allows the user to define the stochastic model. It also has the ability to detect and adjust individual sub-networks, which may occur in regional applications, where track network connectivity fails. VALDAMA uses a parameter file in which the validation parameters, adjustment method and stochastic model are defined. The programme calculates the main statistical parameters and presents the results in spreadsheet format compatible with most common computer office tools. A test case is presented for marine gravity data in the North-East Atlantic Ocean. The complete validation and adjustment of more than 190,000 gravity observations are presented and from an analysis of several adjustment possibilities, it was concluded that inner constraint adjustment may give unpredictable results for global gravity data and that minimum constraint would be the preferred solution.

Introduction

Marine gravity data is one of the fundamental observations for geodetic, geophysical and geological marine applications. Marine gravity data has been used extensively in crustal and mantle structure studies, in gravimetric geoid computation and in providing ground truth for satellite and airborne data. However, its use has been limited in some oceanic areas due to uncertainties in the precision of older data stored in archives. The main source of errors associated with marine gravity observations may be summarized following Wessel and Watts (1988) as instrumental errors of the gravimeter and external influences, positional and navigational errors, and incorrect tie-in to the base station. Gravimeter instrumental errors are mainly characterized by the introduction of a small amplitude noise in the signal (relative gravity value). This type of error is associated with the gravimeter type (cross-coupling), its position in the platform (off-levelling), or changeable weather conditions during observation. These errors, with a random behaviour, are mostly impossible to model and hence not considered in our analysis. Positional errors affect marine missions in two ways: first by giving incorrect geodetic coordinates, affecting all subsequent calculations and, second, by causing an error in azimuth and velocity that affects computation of the Eötvös correction. To obtain a 1 mGal precision in the Eötvös correction the velocity and the azimuth precision must be better than 0.1 m/s and 1°, respectively (Torge, 1989). Marine gravity measurements are relative to some known base station and therefore any incorrect tie-in to that station may lead to a constant offset in all the gravity data of that cruise. Moreover, most marine gravimeters tend to drift with time, introducing systematic errors in the data. The standard way to account for the latter error is to assure correct tie-in in the starting base station and in the ending base station, assuming that the precision of the g-value in these stations is better than the drift of the gravimeter.

The removal of systematic errors (navigation, positioning and tie-in to base station) and the associated random error minimization in marine gravimetric observations has been the subject of several studies (Wessel and Watts, 1988; Motao, 1995; Wenzel, 1992; Adjaout and Sarrailh, 1997; Sevilla and Catalão, 1993). It is believed by most authors that the major source of error is related to navigation and positioning. Even after the removal of systematic errors and the minimization of random errors, a residual error reconnected in the track intersections remains. The residual errors due to positional uncertainty and instrumental precision are inherent and are not removed from the gravimetric database, and therefore it is only possible to keep this error component to a minimum.

This paper presents methods and a standard C language programme for marine gravity data validation and adjustment. The adopted strategy is based on the detection of intersections between tracks, computing the differences between the anomaly estimated at the intersection point from both tracks (cross-over errors (COE)) and finally adjusting these residuals, estimating the best bias for each track. In regional applications or in poorly surveyed areas there is the possibility of losing overall network connectivity. In this programme, an algorithm was implemented with a pivot in which connectivity is ensured through the automatic identification of individual sub-networks and the adjustment is performed individually for each sub-network.

A test case was applied in the North-East Atlantic Ocean between the Azores archipelago and the Iberian Peninsula. In this area the programme was tested and the results of its potentialities are presented. Several tests were made covering almost all possibilities for marine gravity data validation and adjustment.

Section snippets

Pre-processing

A marine gravity survey is composed of a set of tracks. Gravity measurements belonging to the same track share common properties related to the ship, the gravimeter, sea conditions and the positioning system. A sequence of observations within a track is statistically correlated, allowing the detection of possible gross errors by a simple spatial filtering process. This procedure, called pre-processing or track internal validation, detects outliers in the data and flags them for deletion,

The programme

Specific software, VALiDAtion of MArine gravity data (VALDAMA), was written for the validation and adjustment of marine gravity data following the above-described mathematic and stochastic model. The programme was developed within a project of geoid determination in the North-Atlantic Ocean at the Faculty of Sciences, University of Lisbon. The programme is modular and written in standard C, allowing compilation and linkage in any operating system, accepting command-line arguments suitable for

Gravity data set

The original data bank used in this study was the result of a compilation from BGI, NGDC and the Defense Map Agency of the USA (DMA) data banks, and covers an area with the following limits: 35°N<ϕ<45°N, 32°W<λ<6°W. Most of the data were acquired from American, British and French institutions in the period from 1970 to 1990. This data bank was recently improved with a recent gravimetric campaign held in 1997 under the scope of the PDIC/C/Mar project (Fernandes et al., 1998) and the AGMASCO

Discussion and conclusions

There exist several programmes for marine gravity data validation, but most of them were designed for specific institutional purposes and are not in the public domain. The main advantages of VALDAMA over the formal programmes are the possibility of defining all adjustment and validation parameters and its import-export facilities.

This paper has presented the mathematical and stochastic formulation related to the validation and adjustment of marine gravity track data. A programme was presented

References (15)

  • A. Adjaout et al.

    A new gravity map, a new marine geoid around Japan and the detection of the Kuroshio current

    Journal of Geodesy

    (1997)
  • O.B. Andersen et al.

    Global marine gravity field from ERS-1 and Geosat geodetic mission altimetry

    Journal of Geophysical Research

    (1998)
  • Barzaghi, R., Sansò, F., 1983. Sulla stima empirica della funzione di covarianza, Bollettino di Geodesia e Scienze...
  • Catalão, J., Sevilla, M.J., 1999. The effect of high precision bathymetric model on geoid computation. International...
  • Fernandes, M.J., Gidskehaug, A., Solheim, D., Mork, M., Jaccard, P., Catalão, J., 1998. Gravimetric and hydrographic...
  • B. Hofmann-Wellenhof

    Application of sparse matrix techniques to physical geodesy

    Bollettino di Geodesia e Scienze Affini Anno XLI,

    (1982)
  • F.G. Lemoin et al.

    The development of the NASA GSFC and NIMA Joint Geopotential Model

There are more references available in the full text version of this article.

Cited by (5)

View full text