Gravity field mapping in the Malaysian exclusive economic zone (EEZ) from a combined GEOS-3 and seasat radar altimeter data base

Gravity field mapping in the Malaysian exclusive economic zone (EEZ) from a combined GEOS-3 and seasat radar altimeter data base

Abd. Majid, A. Kadir
Faculty of Surveying. University Tech. Malaysia.
Locked Bag 791, 80990 Johor Bahru, Johor, Malaysia

Abstract
This work has clearly demonstrated the ability of the satellite radar altimeter data to hold a detailed mapping of the gravity field n the Malaysian Exclusive Economic Zone (EEZ). Gravity anomalies and mean sea surface heights were derived farm a combined Geos-3/SSeasat altimeter data abase. The method of gravity field recovery was based on the theory of the squares collocation. The computations were carried out using OSU81 reference gravity33 model defined by a set of potential coefficients complete to degree and order 180 and th scaled scheming/Rasd covariance model. Satellite track bas was estimated in small 4° x 4° religious to create a bias-free altimeter data set prior to the gravity and production rest.

Fairly good agreement was observed between the predicted point gravity animates and the observed 'ground truth" defined by point (ship) gravity measurements when a sufficiently dense altimeter data set was used. Comparisons along a 300 km gravity profile (free air) at latitudes 6°.2 with the one derived from radar altimetry indicate root-mean-square differences of 5.3 mgal.

Combined GEOS-3 Seasat RADAR altimeter data base
Until recently, the main sources of the altimeter data have been the Geos-3 and Sea sat altimeter satellites. The Geos-3 data was acquired in the time period 1975-1978. While he Sea sat data was limited to the time period June through October 1978. The results to be presented in this study will be based n a combined Geos-3/Sea sat database developed through a series of studies conducted at the Ohio State University, USA. A brief review of these studies can be found in Majid (1987). Figure 1 shows satellite track of Geos-3 and Sea sat in the study area.

The use of altimeter data for determinations of the gravity field in local areas has widely been done in two steps: 1) a cross-over adjustment of the altimeter data. and 2) estimations of gravity field related quantities from the cross-over adjusted altimeter data. The second step will be discussed in section 2.0. The purpose of the adjustment f the altimeter data is to remove blazes due to orbit errors or oceanographic phenomena using the crossing are technique. Details on the global adjustments and editing of Geos-3 and Sea sat data carried out the Ohio State University can be found in Liang (1983). However, further adjustment in local areas are needed to diminish the remaining track errors and to remove any unedited spikes.

For the present study, the Malayalam EEZ is partitioned into ten 3° x 3° equiangular blocks so that cross-over adjustments can be performed in each of these areas. However , in area #5 which is located in the narrowest part of the Straits of Melaka, altimeter tracks are too sparse for any meaningful adjustment. Hence, excluding area #5cross-over adjustments were performed in all the areas shown in Figure 3 to create a bias-free altimeter data set prior to the prediction runs. Although the specific prediction area has a 3° x 3° block size. , the adjustment was carried out in a 4° x 4° block size in order to account for a 0°.5 border area. The statistics resulted from the above adjustment are summarized in Table 1.

Figure.1: Satellite track of Geos-3 (low inclination)and Seasat (high inclination). The 3° X 3° areas numbered # 1,2,3.........10 are the prediction blocks.

Table.1 Altimeter Cross-Over Adjustment Statistics

	PREDICTION AREA (4° x 4°)
	#1 #1	#2	#3	#4	#6	#7	#8	#9	#10
The words are illiegible in the source ---do--- ---do--- ---do--- ---do---	1262 33 63 27 9	1297 31 58 24 16	1386 31 82 26 16	1620 96 193 28 20	1135 27 63 26 15	906 16 28 28 12	1219 21 60 39 22	648 18 22 24 4	1230 21 61 29 16

It is clear from Table 1 that the reot-mean squares (rms) of cross-over differences improved quite substantially after he local adjustments.

Method of gravity field recovery
The primary information from the Geos-3/Seasat missions after editing and adjustment of the altimeter data is a set of time averaged sea-surface heights. Ignoring the effects of the sea surface topography. We can use the altimeter-implied geoids undulations (h) to compute other gravity field related quantities such as gravity anomalies (?g) and components of the deflections of the vertical (§?). The technique that will be used for the gravity anomaly recovery and sea-surface height estimation is least squares collocation as described by Morits (19800. The prediction of the signal and its accuracy estimate is carried out with the following equations.

where
h: column vector of the altimeter-implied undulation:
C_sh:row vector containing covariance (referred to the reference field)
between the quantity being predicted and the given geode undulations:
C_hh:square, symmetric matrix containing the covariance (referred to the reference field) between the geode undulations:
D:error covariance matrix of the observed geoids undulations which was taken to be a diagonal matrix whose elements corresponded to the square of the standard deviations
C_ss expected mean square value (referred to the reference field) of the quantity being predicted:
S_R.h_R: signal being predicted and geoid undulation implied by the reference field.

The reference gravity field model used in computations was the OSU81 potential coefficients set complete to degree and order 180. These coefficients were used to calculate values of h_R and Dg_R on a 0°.25 grid from which interpolations were made to a specific altimeter observation or a p[prediction grid point.

The auto-and cross-covariance functions involving geoid undulation and gravity anomaly with respect to as reference field complete to degree 1810 were evaluated using he subroutine COVA described in Tscherning et at. (1974). The actual covariance function used is the total covariance function which can be described as follows (for details, see Majid, 1987):

K(P.Q) - K_R(P.Q) + D K (P.Q)

where
K(P.Q) covariance function of the disturbing potential:
KR9p.Q) Nth order covariance function:
AK(P.Q) error covariance function implied by the potential coefficient noise model.

The auto and cross-co variances of other gravimetric quantities (i.e., C_hh. C_{D g D g.} etc) can b derived from K(P.Q) according to the law of propagation of covariance and taking into account the well known functional relationship between these quantities with the disturbing potential. In order to save computer time, the co variances are set up in a table at an interval of 0o.05 prior to the actual computations. In the present application, the covariance function will be tailored to a specific area so that it will yield the observed residual undulation variance with this procedure, an approximate local representation of the covariance functions can be achieved.

Prediction Runs and Results
The geographic locations of the prediction areas (no. 1,2,.......,10) that roughly cover he Malaysian EEZ are shown in Figure 1. The gravity field recovery in each of these areas is made don in two steps. Where the first step is a cross-over adjustment as already discussed in section 10 in the second step, geoids undulations and gravity anomalies are estimated from the cross-over adjusted altimeter data using the estimation technique presented in section 2.0. The prediction run was made based on he following prediction choice:

Prediction Block Size	:	3° x 3°
No. of Prediction Sets	:	9(1° x 1°) blocks
Data Boarder	:	0°.5
Data Number	:	300 points (for one matrix inversion)
Grid Interval	:	0°.1
Refrnce Field	:	OSU81 (Nmax =180)
Covariance Field	:	Scaled Tscherning/Rapp
Reference Ellipsold	:	a =6378137, f = 1/258.257

The predicted anomalies and sea-surface heights provide a uniform (0°.1 x 0°.1) data set for almost all ocean areas of he Malaysian EEZ. The accuracy deteriorates The accuracy deteriorates near coastal regions and in areas with sparse altimeter points. To demonstrate this, predicted gravity anomaly maps for area #3 and area #7 are depicted in figure 2 and figure 3 respectively.

Figure 2 shows the gravity anomaly variations in the coastal and off-shore areas of Terengganu and Pahang. The gravity anomaly field over this area indicate a rather smooth field with the exception of several of low (-20 mahls) anomalies. The large data gap centered approximately at j 5°, l =104°.5 clearly hampered a more detailed anomaly recovery in that area. Also clear from this figure is the smoothing effects of the field near and over the land areas since altimeter data simply not available or lacking in these areas.

The second example shown in figure 3 reflects the derived anomaly field in the north-west Sabah offshore area. Two prominent anomaly features scan be distinguish from this figure. The High anomalies region (40 to 80 mgals) stretching from the upper right to lower left hand corners of the plo that reflect the signatures of the islands in this area, namely, Commodore Reef. Mariveles Reef, Swallow Reef, etc. 2) Low anomalies region (-40 to -60 mgals) located to the east of the positive anomalies region which can be associated with the bathymetry of the ocean crust, namely, the Sabah Trough area.

The accuracy estimates computed using equation (2) show standard deviation (m_Dg) values) of about ±8 mgals in areas with good altimeter coverage, but deteriorated ±16 mgals where no altimeter tracks are available. The estimated accuracy also depends on data noise and the scale of magnitude of the covariance's (see Majid, 1987). Tests also were made to compare measured gravity anomalies with those derived from altimetry. Comparison along a 300 km gravity profile at latitude 6°.2 with the one derived from altimetry indicate rms differences of 5.34 mgal (Figure 4)

Figure.2: Predicted total gravity anomalies in area #3. M1,M2...........M9 indicate approximate locations of the known oil and gas fields. (c1=5 mgals)

Figure. 3: Predicted total gravity anormalies in areas #7 (C1=5 mgals)

Figure 4: Comparison of a measured gravity profile at latitude 6°.2 with one derived from altimetry.

Conclusions
We have illustrated the ability of the satellites altimeter data to provide high frequency gravity information in the marines areas. The recovered gravity anomalies can be used fr both geodetic and geophysical purposes. Gravity anomaly maps derived from satellite altimetry can be used to scan large off-shore areas for detecting significant density contrasts within the oceanic outer crust, and thus providing indirect indications of potential hydrocarbon deposits.

Consequently, an altimeter-implied marine gravity data base for he Malaysian EEZ area can be created for various applications.

To improve the gravity anomalies recovery over/near coastal areas we recommend that least squares collocation be used to combine the satellite altimeter data and the gravity anomaly data collected over the coastal areas from land gravity measurements. The anomaly map produced using this technique will be more meaningful from the view point of connecting ocean and land gravity anomaly field for marine geological studies.

References

Liang, C.K. "The adjustment and combination of Geos-3 and Sea sat Altimeter Data", Report No. 346, Dept. of Geodetic Science, the Ohio State University, Columbus, 1983.
Majid Kadir. "The Recovery of High Frequency Gravity Field Information From Satellite Altimeter Data" Internal Report, Dept. of Geodetic Science, The Ohio State University, Columbus, 1987.
Majid Kadir, "The Role of High Degree Coefficients and Satellite Altimeter Data in Gravity Field Approximation of the Malaysian Region'. The Surveyor, institution of Surveyors Malaysia, Vol. 24, No.2. 1989.
Moritz. H., "Advanced Physical Geodesy" Herbet Wichmann Verlag Karlsruhe. West Germany, 1980.
Tscherning. C.C and Rapp. RH., "Closed Covariance expressions for Gravity Anomalies, Geod undulations, and Deflections of the Vertical Imp[lied by Anomaly Degree Variance models", Report No. 208, Department of Geodetic Science. The Ohio State University, Columbus, 1974.