Author Contributions
Conceptualization, C.C.-C. and C.O.-A.; data curation, A.T.-A. and C.O.-A.; formal analysis, J.H. and N.V.; funding acquisition, C.C.-C. and A.T.-A. investigation, J.H., A.T.-A. and M.O.-d.-C.; methodology, C.C.-C. and N.V.; project administration, C.O.-A.; resources, M.O.-d.-C. and C.C.-C.; software, N.V., C.C.-C. and J.H.; supervision, C.O.-A.; validation, C.C.-C.; visualization, N.V. and M.O.-d.-C.; writing—original draft preparation, J.H., A.T.-A. and M.O.-d.-C.; writing—review and editing, J.H., C.C.-C., N.V., M.O.-d.-C., C.O.-A. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Differential rectangular prism.
Figure 1.
Differential rectangular prism.
Figure 2.
Schema to numerically compute total magnetic anomaly according to Bhattacharyya [
50].
Figure 2.
Schema to numerically compute total magnetic anomaly according to Bhattacharyya [
50].
Figure 3.
Parallelization scheme for the inversion process by growth of bodies.
Figure 3.
Parallelization scheme for the inversion process by growth of bodies.
Figure 4.
Affinities setup on a Workstation with 2 sockets and 6 cores by socket, with HT enabled. Cores are identified with circles. Curly brackets mean that the virtual cores are handled by the same physical core. The blue numbers indicate the order of assignment of the threads.
Figure 4.
Affinities setup on a Workstation with 2 sockets and 6 cores by socket, with HT enabled. Cores are identified with circles. Curly brackets mean that the virtual cores are handled by the same physical core. The blue numbers indicate the order of assignment of the threads.
Figure 5.
Considered synthetic models used for the computation of field anomalies.
Figure 5.
Considered synthetic models used for the computation of field anomalies.
Figure 6.
Compaction curve relative to sediments in Gulf of Mexico [
36].
Figure 6.
Compaction curve relative to sediments in Gulf of Mexico [
36].
Figure 7.
Interpolated geological horizons from previously interpreted seismic sections.
Figure 7.
Interpolated geological horizons from previously interpreted seismic sections.
Figure 8.
Cross section of three-dimensional model at
Km from the geological horizons shown in
Figure 7. The color for salt (
kg/m
) was modified to green to highlight the salt structure.
Figure 8.
Cross section of three-dimensional model at
Km from the geological horizons shown in
Figure 7. The color for salt (
kg/m
) was modified to green to highlight the salt structure.
Figure 9.
Gravimetric response of the real data-based model.
Figure 9.
Gravimetric response of the real data-based model.
Figure 10.
Air-free gradiometric response for the real data-based model.
Figure 10.
Air-free gradiometric response for the real data-based model.
Figure 11.
Isolated salt body (removed regional field) gradiometric response for the real data-based model.
Figure 11.
Isolated salt body (removed regional field) gradiometric response for the real data-based model.
Figure 12.
Magnetic anomaly corresponding to salt body.
Figure 12.
Magnetic anomaly corresponding to salt body.
Figure 13.
Initial (color map) and inverted (contour lines) gravimetric () response for the T model.
Figure 13.
Initial (color map) and inverted (contour lines) gravimetric () response for the T model.
Figure 14.
Inverted gravimetric T model.
Figure 14.
Inverted gravimetric T model.
Figure 15.
Initial (colour map) and inverted (contour lines) magnetic response for the T model.
Figure 15.
Initial (colour map) and inverted (contour lines) magnetic response for the T model.
Figure 16.
Inverted magnetic T model.
Figure 16.
Inverted magnetic T model.
Figure 17.
Initial (colour map) and inverted (contour lines) gradiometric response for the T model.
Figure 17.
Initial (colour map) and inverted (contour lines) gradiometric response for the T model.
Figure 18.
Inverted gradiometric T model.
Figure 18.
Inverted gradiometric T model.
Figure 19.
Initial (colour map) and inverted (contour lines) gravimetric () response for the S model.
Figure 19.
Initial (colour map) and inverted (contour lines) gravimetric () response for the S model.
Figure 20.
Inverted gravimetric S model.
Figure 20.
Inverted gravimetric S model.
Figure 21.
Initial (colour map) and inverted (contour lines) magnetic response for the S model.
Figure 21.
Initial (colour map) and inverted (contour lines) magnetic response for the S model.
Figure 22.
Inverted magnetic S model.
Figure 22.
Inverted magnetic S model.
Figure 23.
Initial (colour map) and inverted (contour lines) gradiometric response for the S model.
Figure 23.
Initial (colour map) and inverted (contour lines) gradiometric response for the S model.
Figure 24.
Inverted gradiometric S model.
Figure 24.
Inverted gradiometric S model.
Figure 25.
Performance obtained for the inverted the T model. (a) Computing time for gravimetric (red, asterisk), magnetometric (blue, diamond) and gradiometric (green, square) inversions of the T model, respectively, as a function of (even) number of threads. (b) Theoretical ideal speed-up (black, circle) and obtained speed-up for gravimetric (red, asterisk), magnetometric (blue, diamond) and gradiometric (green, square) inversions of the T model.
Figure 25.
Performance obtained for the inverted the T model. (a) Computing time for gravimetric (red, asterisk), magnetometric (blue, diamond) and gradiometric (green, square) inversions of the T model, respectively, as a function of (even) number of threads. (b) Theoretical ideal speed-up (black, circle) and obtained speed-up for gravimetric (red, asterisk), magnetometric (blue, diamond) and gradiometric (green, square) inversions of the T model.
Figure 26.
Performance obtained for the inverted S model. (a) Computing time for gravimetric (red, asterisk), magnetometric (blue, diamond) and gradiometric (green, square) inversions of the S model, respectively, as a function of (even) number of threads. (b) Theoretical ideal speed-up (black, circle) and obtained speed-up for gravimetric (red, asterisk), magnetometric (blue, diamond) and gradiometric (green, square) inversions of the S model.
Figure 26.
Performance obtained for the inverted S model. (a) Computing time for gravimetric (red, asterisk), magnetometric (blue, diamond) and gradiometric (green, square) inversions of the S model, respectively, as a function of (even) number of threads. (b) Theoretical ideal speed-up (black, circle) and obtained speed-up for gravimetric (red, asterisk), magnetometric (blue, diamond) and gradiometric (green, square) inversions of the S model.
Figure 27.
Discrete domain in plant view for the initial model for inversion of real salt structures.
Figure 27.
Discrete domain in plant view for the initial model for inversion of real salt structures.
Figure 28.
Initial (colour map) and inverted (contour lines) gravimetric () response for the salt body.
Figure 28.
Initial (colour map) and inverted (contour lines) gravimetric () response for the salt body.
Figure 29.
Final gravimetric model for the inversion for the salt body. (
a) XZ view. The red dotted line represents the limits of the real model (
Figure 7 and
Figure 8). (
b) XY view. The red dotted line represents the limits of the real model (
Figure 7 and
Figure 8). (
c) Three-dimensional view.
Figure 29.
Final gravimetric model for the inversion for the salt body. (
a) XZ view. The red dotted line represents the limits of the real model (
Figure 7 and
Figure 8). (
b) XY view. The red dotted line represents the limits of the real model (
Figure 7 and
Figure 8). (
c) Three-dimensional view.
Figure 30.
Initial (colour map) and inverted (contour lines) magnetic response for the salt body.
Figure 30.
Initial (colour map) and inverted (contour lines) magnetic response for the salt body.
Figure 31.
Inverted magnetic model for the salt body. (
a) XZ view. The red dotted line represents the limits of the real model (
Figure 7 and
Figure 8). (
b) XY view. The red dotted line represents the limits of the real model (
Figure 7 and
Figure 8). (
c) Three-dimensional view.
Figure 31.
Inverted magnetic model for the salt body. (
a) XZ view. The red dotted line represents the limits of the real model (
Figure 7 and
Figure 8). (
b) XY view. The red dotted line represents the limits of the real model (
Figure 7 and
Figure 8). (
c) Three-dimensional view.
Figure 32.
Initial (colour map) and inverted (contour lines) gradiometric response for the salt body.
Figure 32.
Initial (colour map) and inverted (contour lines) gradiometric response for the salt body.
Figure 33.
Inverted gradiometric model for the salt body.
Figure 33.
Inverted gradiometric model for the salt body.
Figure 34.
Performance obtained for the inverted model for the salt body. (a) Computing time for gravimetric (red, asterisk), magnetometric (blue, diamond) and gradiometric (green, square) inversions of the synthetic real model, respectively, as a function of (even) number of threads. (b) Theoretical ideal speed-up (black, circle) and obtained speed-up for gravimetric (red, asterisk), magnetometric (blue, diamond) and gradiometric (green, square) inversions of the synthetic real model.
Figure 34.
Performance obtained for the inverted model for the salt body. (a) Computing time for gravimetric (red, asterisk), magnetometric (blue, diamond) and gradiometric (green, square) inversions of the synthetic real model, respectively, as a function of (even) number of threads. (b) Theoretical ideal speed-up (black, circle) and obtained speed-up for gravimetric (red, asterisk), magnetometric (blue, diamond) and gradiometric (green, square) inversions of the synthetic real model.
Figure 35.
Behavior of growth algorithm as a function of algorithm.
Figure 35.
Behavior of growth algorithm as a function of algorithm.
Table 1.
Considered parameters to compute field anomalies in T and S models.
Table 1.
Considered parameters to compute field anomalies in T and S models.
(a) For gravity-based anomalies. |
Model | | Depth [km] |
T | 300 | 1 |
S | 300 | 1 |
(b) For magnetic anomalies. |
Model | | FI, FD | MI, MD | Depth [km] |
T | 0.01 | 90°, 0° | 90°, 0° | 1 |
S | 0.01 | 90°, 0° | 90°, 0° | 1 |
Table 2.
Configuration of the gravimetric inversion parameters for the T model.
Table 2.
Configuration of the gravimetric inversion parameters for the T model.
parameter [1] | 2.04 |
Initial maximum density [kg/m] | 300 |
Smoothing coefficient [1] | 8 |
Initial model misfit [mGal] | 116.251 |
Minimum reached misfit [mGal] | 0.373 |
Total iterations | 1314 |
Table 3.
Configuration of the magnetic inversion parameters for the T model.
Table 3.
Configuration of the magnetic inversion parameters for the T model.
Initial maximum magnetization [A/m] | 0.01 |
parameter [1] | 4.04 |
Smoothing coefficient [1] | 8 |
Initial model misfit [nT] | 29,304 |
Minimum reached misfit [nT] | 0.366 |
Total iterations | 1323 |
Table 4.
Configuration of the gradiometric inversion parameters for the T model.
Table 4.
Configuration of the gradiometric inversion parameters for the T model.
parameter | 7.04 | | Initial maximum density [kg/m] | 300 |
Smoothing coefficient [1] | 8 | | Total iterations | 1354 |
initial model misfit [Eo] | 271.326 | | minimum reached misfit [Eo] | 2.102 |
initial model misfit [Eo] | 183.120 | | minimum reached misfit [Eo] | 1.032 |
initial model misfit [Eo] | 581.733 | | minimum reached misfit [Eo] | 4.223 |
Table 5.
Configuration of the gravimetric inversion parameters for the S model.
Table 5.
Configuration of the gravimetric inversion parameters for the S model.
parameter [1] | 2.04 |
Initial maximum density [kg/m] | 300 |
Smoothing coefficient [1] | 8 |
Initial model misfit [mGal] | 84.281 |
Minimum reached misfit [mGal] | 0.273 |
Total iterations | 1299 |
Table 6.
Configuration of the magnetic inversion parameters for the S model.
Table 6.
Configuration of the magnetic inversion parameters for the S model.
Initial maximum magnetization [A/m] | 0.01 |
parameter [1] | 5.04 |
Smoothing coefficient [1] | 8 |
Initial model misfit [nT] | 18.645 |
Minimum reached misfit [nT] | 0.276 |
Total iterations | 1212 |
Table 7.
Configuration of the gradiometric inversion parameters for the S model.
Table 7.
Configuration of the gradiometric inversion parameters for the S model.
parameter | 7.04 | | Initial maximum density [kg/m] | 300 |
Smoothing coefficient [1] | 8 | | Total iterations | 1146 |
initial model misfit [Eo] | 200.341 | | minimum reached misfit [Eo] | 2.583 |
initial model misfit [Eo] | 113.830 | | minimum reached misfit [Eo] | 1.771 |
initial model misfit [Eo] | 370.240 | | minimum reached misfit [Eo] | 5.043 |
Table 8.
Configuration of the gravimetric inversion parameters for the salt body.
Table 8.
Configuration of the gravimetric inversion parameters for the salt body.
parameter [1] | 2.04 |
Initial maximum density [kg/m] | 2200 |
Smoothing coefficient [1] | 8 |
Initial model misfit [mGal] | 28.411 |
Minimum reached misfit [mGal] | 0.061 |
Total iterations | 31,677 |
Table 9.
Configuration of the magnetic inversion parameters for the salt body.
Table 9.
Configuration of the magnetic inversion parameters for the salt body.
Initial maximum magnetization [A/m] | −0.00036 |
parameter [1] | 8.04 |
Smoothing coefficient [1] | 8 |
Initial model misfit [nT] | 10.547 |
Minimum reached misfit [nT] | 0.111 |
Total iterations | 33,878 |
Table 10.
Configuration of the gradiometric inversion parameters for the salt body.
Table 10.
Configuration of the gradiometric inversion parameters for the salt body.
parameter | 8.04 | | Initial maximum density [kg/m] | 2200 |
Smoothing coefficient [1] | 8 | | Total iterations | 30,611 |
initial model misfit [Eo] | 20.607 | | minimum reached misfit [Eo] | 0.451 |
initial model misfit [Eo] | 16.446 | | minimum reached misfit [Eo] | 0.180 |
initial model misfit [Eo] | 50.209 | | minimum reached misfit [Eo] | 0.624 |