Global Moho Gravity Inversion from GOCE Data: Updates and Convergence Assessment of the GEMMA Model Algorithm
Abstract
:1. Introduction
2. The Inversion Operator
- is the distance between the computational point and the running point inside the masses that can be expressed as [27]:
- is the density contrast between the crust and mantle at point , given the laterally and vertically varying densities of the crust and mantle , i.e.,:
- is the integration domain that in our case is a spherical domain;
- is the infinitesimal area element over the spherical domain;
- G is the universal gravitational constant.
3. The Data Reduction
4. Seismic Data Integration
5. Overall Scheme of the Inversion Algorithm
6. Closed-Loop Test Setup
6.1. The “True” Model
6.2. Tested Scenarios
- s1.
- the a priori density profiles of all geological provinces are assumed to be the same as the “true” ones;
- s2.
- the a priori density profiles of all geological provinces are assumed to be the same as the “true” ones apart from a scale factor (a different value of the scale factor for each geological type was applied, see Table 1);
- s3.
- the a priori density profiles of all geological provinces are assumed to be the same as the “true” ones apart from a scale factor and a bias (a different couple of scale factor and bias for each geological type was applied, see Table 1).
Crustal Type | h | k [kg/m3] | ||||
---|---|---|---|---|---|---|
s1 | s2 | s3 | s1 | s2 | s3 | |
Oceanic | 1.0000 | 0.9987 | 1.0020 | 0.00 | 0.00 | 0.00 |
Mid oceanic ridge | 1.0000 | 1.0013 | 0.9977 | 0.00 | 0.00 | 0.00 |
Extended crust | 1.0000 | 0.9910 | 0.9800 | 0.00 | 0.00 | 31.07 |
Platform | 1.0000 | 1.0068 | 1.0150 | 0.00 | 0.00 | −15.39 |
Shield | 1.0000 | 1.0045 | 1.0100 | 0.00 | 0.00 | −6.26 |
Orogenetic crust | 1.0000 | 1.0090 | 1.0200 | 0.00 | 0.00 | −66.60 |
Igneous provinces | 1.0000 | 0.9955 | 0.9900 | 0.00 | 0.00 | 40.26 |
Basin | 1.0000 | 0.9932 | 0.9850 | 0.00 | 0.00 | 49.39 |
7. Algorithm Convergence
- s2a.
- the Moho undulation at the beginning of the first iteration is equal to 0 everywhere, i.e., ;
- s2b.
- the Moho undulation at the beginning of the first iteration is equal to the “true” one, i.e., .
8. Impact of the Forward Approximations
9. Comparison of the Original and Revised Algorithms
- a global test on the differences between the Moho estimates, i.e.,
- a global test between the differences of the forwarded gravitational signal of the estimated models, i.e.,
- local tests on the Moho differences, by comparing the discrepancy of the two solutions on subsets of grid nodes defined on the basis of the “true” Moho depth. In particular, the subsets are obtained by splitting the “true” Moho depth in 1 km classes. The statistic of the test becomes
- local tests on the Moho differences, by comparing the discrepancy of the two solutions on subsets of grid nodes defined as the geological provinces, i.e.,
10. Conclusions
- the iterative inversion algorithm converges to a unique solution (disregarding differences smaller than the iteration stop criterion) when changing the starting point, e.g., choosing an a priori Moho undulation ranging from zero to the “true” value;
- the Moho depth is retrieved with an accuracy of the order of (in terms of standard deviation), consistently with the solution coming from the original GEMMA algorithm;
- the effect of the linearization is analytically controlled through a suitable data reduction, without the need of a further step in the inversion procedure for the reference Moho refinement, as it happened in the original GEMMA algorithm.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
GEMMA | GOCE Exploitation for Moho Modelling and Applications |
GOCE | Gravity Field and Steady-State Ocean Circulation Explorer |
std | Standard deviation |
PREM | Preliminary reference Earth model |
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Scenario | Mean [km] | Std [km] | Max [km] | Min [km] | Test 1 |
---|---|---|---|---|---|
s1 | 0.22 | 0.66 | 9.95 | −13.25 | 0.33 < 1.96 |
s2 | 0.55 | 1.01 | 10.31 | −12.91 | 0.55 < 1.96 |
s3 | 0.48 | 0.99 | 10.02 | −12.78 | 0.49 < 1.96 |
Scenario | Mean [mE] | Std [mE] | Max [mE] | Min [mE] | Test 2 |
---|---|---|---|---|---|
s1 | −6.47 | 3.58 | 15.71 | −72.01 | 1.80 < 1.96 |
s2 | 0.59 | 3.67 | 22.91 | −63.89 | 0.16 < 1.96 |
s3 | −1.32 | 3.60 | 20.19 | −67.67 | 0.37 < 1.96 |
Scenario | Mean [km] | Std [km] | Max [km] | Min [km] | Test 1 |
---|---|---|---|---|---|
s1 | 0.01 | 0.76 | 12.10 | −8.18 | 0.01 < 1.96 |
s2 | 0.01 | 1.26 | 12.03 | −12.14 | 0.01 < 1.96 |
s3 | 0.06 | 1.23 | 12.18 | −10.24 | 0.05 < 1.96 |
Scenario | Mean [mE] | Std [mE] | Max [mE] | Min [mE] | Test 2 |
---|---|---|---|---|---|
s1 | −6.25 | 3.20 | 13.66 | −24.54 | 1.95 < 1.96 |
s2 | 0.72 | 3.22 | 20.55 | −17.70 | 0.22 < 1.96 |
s3 | −1.15 | 3.21 | 18.28 | −20.03 | 0.36 < 1.96 |
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Rossi, L.; Lu, B.; Reguzzoni, M.; Sampietro, D.; Fadel, I.; van der Meijde, M. Global Moho Gravity Inversion from GOCE Data: Updates and Convergence Assessment of the GEMMA Model Algorithm. Remote Sens. 2022, 14, 5646. https://doi.org/10.3390/rs14225646
Rossi L, Lu B, Reguzzoni M, Sampietro D, Fadel I, van der Meijde M. Global Moho Gravity Inversion from GOCE Data: Updates and Convergence Assessment of the GEMMA Model Algorithm. Remote Sensing. 2022; 14(22):5646. https://doi.org/10.3390/rs14225646
Chicago/Turabian StyleRossi, Lorenzo, Biao Lu, Mirko Reguzzoni, Daniele Sampietro, Islam Fadel, and Mark van der Meijde. 2022. "Global Moho Gravity Inversion from GOCE Data: Updates and Convergence Assessment of the GEMMA Model Algorithm" Remote Sensing 14, no. 22: 5646. https://doi.org/10.3390/rs14225646