MAPPING OF SEA BOTTOM TOPOGRAPHY OVER

WESTERN OFFSHORE, INDIA USING TOPEX/ERS-1

ALTIMETER DATA{

K.K. MOHANTY and T.J. MAJUMDAR{MWRD/RSAG/RSA, Space Applications Centre (ISRO), 380 053 Ahmedabad, India

P.D. KUNTE

INODC, National Institute of Oceanography, 403 004 Goa, India

and A.K. SRIVASTAVA

R.S. Lab., Keshab Deb Malaviya Institute of Petroleum Exploration (ONGC), 248 195 Dehradun,India

(Received 25 April 1997)

AbstractÐAs bathymetry and geoid are highly correlated in the 50±300 km range, the satellite-derivedgeoid can be used in the mapping of bathymetry. An attempt has been made to assess the accuracy ofpredicting sea bottom topography/bathymetry through a convolution model using satellite altimeterdata over the Indian o�shore region. The study uses TOPEX/POSEIDON as well as ERS-1 altimeterdata, along with National Geophysical Data Centre (NGDC), U.S.A. ship-borne bathymetry data. Thealtimeter range data are corrected for atmospheric and oceanographic e�ects to generate the sea surfaceheight (SSH) over the Indian o�shore. The SSH along repeat altimeter passes over a period of 1 yearare averaged to minimize the contribution due to dynamic sea surface topography in SSH. Cross-overcorrections are applied to account for the orbital error in the altimetric observation. The corrected SSHhas been used as an approximation to the marine geoid. The bathymetry is related with the geoidthrough a convolution model. The one-dimensional response function is computed in the frequencydomain using some of the data tracks for which both bathymetry and geoid data are available. The ac-curacy of the developed model is then assessed by applying it over the rest of the tracks. # 1998 Else-vier Science Ltd. All rights reserved

1. INTRODUCTION

The ship-borne bathymetry data over the Indian

o�shore region is quite sparse. Moreover, it is time-

consuming and erroneous and requires a number of

corrections e.g. Etvos correction due to the ship

movement. Presently, ONGC and Survey of India

have got su�cient coverage of bathymetry data

only up to 200 m isobath along the Indian coast. In

this respect, satellite altimetry has opened up a new

®eld for prediction of bathymetry using the alti-

metric geoidal undulations over a particular sea sur-

face. This geoid based bathymetry model is fast,

reliable and non-hazardous and can be used over

the entire o�shore. Comparison of the ERS-1/

TOPEX predicted bathymetry (using the altimetric

geoid) with available ship-borne data shows satis-

factory results.

A satellite altimeter measures the instantaneous

shape of the ocean at the nadir with a good pre-

cision. Repeated altimetric observations taken at

the same location over a period of time are used to

deduce marine geoidÐan equipotential surface

re¯ecting distribution of mass inside the earth. The

equipotential surface formed by any heterogeneous

mass is related both to its mass distribution and

external shape [1]. Based on our knowledge regard-

ing mass distribution inside the earth, it is related

to the shape of the geoid with the underlying bathy-

metry over a certain range of wavelength (0±

300 km) [2,3]. The most commonly used model to

relate geoid/gravity with bathymetry is a convolu-

tion model. Bathymetry, when convolved with a re-

sponse function, yield geoid or gravity [2,4]. The

response function for the model is generally

obtained either through theoretical simulation or by

comparison of ship-borne and altimetric obser-

vations. The present study attempts to predict

Acta Astronautica Vol. 41, No. 3, pp. 151±154, 1997# 1998 Elsevier Science Ltd. All rights reserved

Printed in Great Britain0094-5765/98 $19.00+0.00PII: S0094-5765(97)00189-6

{Paper IAF-96-B.4.07 presented at the 47th InternationalAstronautical Congress, Beijing, China, 7-11 October1996.

{To whom correspondence should be addressed.

151

bathymetry along a few selected ERS-1/TOPEXtracks in the western o�shore, India.

2. OBJECTIVES

The major objectives of this study are as follows:

1. to predict the ocean bathymetry using along-

track geoidal variation;

2. to develop a methodology for collation of alti-

meter-derived geophysical parameters with ship-

borne geophysical data.

Fig. 1. Combined track plots over western o�shore using ERS-1, TOPEX and ship-borne bathymetrydata.

K. K. Mohanty et al.152

3. DATA SOURCES

1. ERS-1 35 days repeat cycle altimeter data sup-

plied by ESA;

2. TOPEX/POSEIDON 10 days repeat cycle alti-

meter data supplied by JPL, U.S.A.;

3. Bathymetry and gravity data collected by inter-

national ship-cruises, i.e. NGDC, U.S.A. (avail-

able with INODC, NIO).

Figure 1 shows the combined ERS-1/TOPEX/

ship-borne bathymetry tracks over western o�shore

of India.

Fig. 2. Amplitude and phase spectrum of the response function.

Mapping of sea bottom tomography over western o�shore, India 153

4. TEST AREA

Selected tracks in the western o�shore of India,

along which both NGDC ship-borne bathymetryand altimeter-derived sea surface height are avail-able, have been used for modeling and validation.

5. METHODOLOGY

Geoid variation over the area of interest can be

used for prediction of bathymetric anomaly alongthe satellite ascending/descending tracks using amodel given by Mackenzie and Bowin and later by

Dixon et al. The bathymetry and geoid/gravity canbe expressed as di�erent time series. A ®lter f canthen be designed which, when convolved withbathymetry, b, produces a time series resembling

gravity or geoid data g.Thus, in the wave number domain [4]

G�k� � Q�k�:B�k� � n,

where G, Q, B are discrete Fourier transforms of g,f and b, k is the one-dimensional wave number, andn is the noise function.

The tracks along which both bathymetry andgeoid/gravity data are available can be used to gen-erate the response function Q. The response func-tion, has later been used for the adjacent altimeter

tracks for which no bathymetry data is available.For validation of the response function, we consideradjacent pairs of altimeter tracks for both of which

bathymetry and geoid are available. The responsefunction computed using one of the tracks isapplied to the other for predicting the bathymetry

which has subsequently been compared with theactual bathymetry.

6. RESULTS AND DISCUSSION

ERS-1/TOPEX altimeter data have been cor-rected for the atmospheric propagation delay and

dynamic oceanographic variabilities by applyingsuitable atmospheric and oceanographic corrections.Altimeter repeat passes over a period of 1 year are

averaged out to minimize the contribution due todynamic sea surface topography. Rapp's 50�50geoid has been removed from the along track alti-

metric observations to eliminate the deeper earthe�ects [5,6]. Cross-over corrections are applied toaccount for the orbital error in the altimetric obser-vation. The corrected SSH has been used as an ap-

proximation to the marine geoid. NationalGeophysical Data Centre, U.S.A. (NGDC) ship-

borne bathymetry data have been compared withthe altimeter tracks to identify the portions of ship-borne tracks having a separation of less than 5 km

from the altimetric footprints. Figure 1 depicts thebathymetric tracks along with ERS-1 35 days repeatcycle and TOPEX/POSEIDON tracks over the

study area. The amplitude and phase spectra of theresponse function derived for the tracks in the wes-tern o�shore are shown in Figs 2(a) and 2(b), re-

spectively. Figure 3 shows the comparison betweenactual and predicted bathymetry along one of theERS-1 tracks studied.

7. CONCLUSIONS

Satellite altimeter can, thus, be used as an e�-cient tool for interpolation of sparsely availableship-borne bathymetry data. However, presently

available altimeter data is quite sparse in the cross-track direction. With the availability of higher resol-ution altimeter data e.g. ERS-1 168 days repeat

cycle data, the prediction of bathymetry may beimproved. The model has to be modi®ed suitably totake into account sharp variations in subsurface ge-ology in the o�shore region, particularly for tracks

moving away from the coast.

AcknowledgementsÐThe authors acknowledge theEuropean Space Agency (ESA) for providing ERS-1 alti-meter data and Jet Propulsion Laboratory (JPL), U.S.A.for supplying TOPEX/POSEIDON altimeter data for thestudy. The authors are thankful to Dr R.R. Navalgund,Group Director, RSAG and Dr A. Narain, Head,MWRD for their help and encouragements during thecourse of this study. They are also thankful to Shri C.S.Murthy, Head, INODC, NIO and Shri V.N. Misra, C.G.and Former Head, R.S. Lab., KDMIPE (ONGC) for theirhelp in archiving ship-borne geophysical data over thearea of interest.

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Fig. 3. Actual vs predicted bathymetry.

K. K. Mohanty et al.154