**Report by D.Arabelos, **1999-03-23.

The goal of the following experiments was to study the standard deviation
of depths (in a test-area in the Mediterranean used in earlier investigations)
estimated from
gravity, when the gravity is affected by errors according to the following error models:

(i) EGM96, (ii) GOCE, (iii) GOCE scaled by a constant scale factor and (iv) GOCE scaled linearly.

The method used for the optimum inversion of the gravity data was the least squares collocation inversion
method developed by (Barzaghi et all., 1992; Knudsen 1993; Tscherning et al., 1994).

A two -layers model was used in these experiments. The mean depth of the first layer was 3 km and the
density contrast to the previous layer was 1.6 gr/cm^{3}. The mean depth of the second layer was 18 km
and the density contrast was 0.6 gr/cm^{3}. These values are realistic according to earlier studies in the
same test-area (Arabelos, 1998).

Gravity anomalies were computed from the expansion of the geopotential model EGM96 to degree 200,
adding to the coefficients random errors. This procedure was done using the "Monte-Carlo" simulator
described previously. For each of the four error models mentioned above, 50 gravity 5'x 5' grids were
produced. The inversion was done for each grid selecting model covariance functions to be in
agreement with the empirical covariance functions of the gravity anomalies. For each of the 50 grids
of each of the cases (i)...(iv) the solution (i.e. the depths of the shallow and the deeper layer) was
obtained after three iterations. In this way the differences between "observed" and computed gravity
anomalies (i.e. the response of the two layers) was generally below 0.5 mGal in the case of EGM96
and 0.3 mGal in the case of the test models .

The results of these experiments are shown in Figs.

The code is the following: std is standard deviation egm/goce is the error model, lc is constant scale, ll
is linear scale, 1 is for layer no.1 (shallow) and 2 is for layer no. 2.

Furthermore the standard deviation of the 50 gravity grids was plotted for the 4 error models (see figs:

cemeegmgra.ps & cemeegmgra.jpg

cemegocegra.ps & cemegocegra.jpg

cemegocegralc.ps & cemegocegralc.jpg

cemegocegrall.ps & cemegocegrall.jpg

The following Table shows the variation in standard deviation of the depths estimated from gravity anomalies, with respect to the variation of the standard deviation of the gravity anomalies according the 4 error models.

Depths |

Gravity
(mGal) |
Layer 1
(m) |
Layer 2
(m) | |

EGM96 | 4.5 - 7.5 | 160 - 320 | 300 - 900 |

GOCE | 0.6 - 1.1 | 15 - 75 | 40 - 210 |

GOCE (const. scaling) | 0.4 - 0.9 | 15 - 60 | 30 - 160 |

GOCE (linear scaling) | 1.0 - 1.9 | 30 - 125 | 70 - 290 |

The range of the changes of the standard deviation is larger in the case of the layer 2 because the layer
2 was supposed to have more than two times larger standard deviation comparing to that of layer 1.

From the results of this Table it could be concluded that the EGM96 error model is too pessimistic, the
corresponding for GOCE too optimistic and the scaled GOCE maybe more realistic.

However, in most cases are the results from GOCE up to a factor 10 better
than the results from EGM96. This is significant for depth-estimation in areas'
where the depth estimation from ERS-1 geodetic mission altimeter
data is influenced by sea-surface topography. Here the bathymetry may
be improved, and thereby aid in the hydro-dynamic modelling.

References

Arabelos, D., 1998: On the possibility to estimate ocean bottom topography from marine gravity and satellite altimeter data using collocation. IAG Symposia, Vol. 119, pp. 105-112.

Barzaghi, R., A. Gadino, F. Sanso and C. Zenucchini, 1992: The collocation approach to the inversion of gravity data. Geophysical Prospecting, Vol. 40, pp.429-452.

Knudsen, P., 1993: Integrated inversion of gravity data. Final Report Norsk Hydro R&D Project, KMS, Geodetic Division, Technical Report No. 7, Copenhagen.

Tscherning, C.C., R. Forsberg and P. Knudsen, 1994:First experiments with improvement of depth
information using gravity anomalies in the Mediterranean Sea. "MARE NOSTRUM" GEOMED Rep.
4, pp. 133-145, Thessaloniki.

Next (Conclusion).

Last update 1999-06-22 by cct.