Model fusion and its use in earth sciences
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Model Fusion and its Use in Earth Sciences. R. Romero, O. Ochoa, A. A. Velasco, and V. Kreinovich. Need to Combine Data from Different Sources-1. In science and engineering, data are generated by different sources For example in geophysics there are many sources of data for Earth models:

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Model Fusion and its Use in Earth Sciences

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Model fusion and its use in earth sciences

Model Fusion and its Use in Earth Sciences

R. Romero, O. Ochoa,

A. A. Velasco, and V. Kreinovich

Joint Annual Meeting

NSF Division of Human Resource Development


Need to combine data from different sources 1

Need to Combine Data from Different Sources-1

  • In science and engineering, data are generated by different sources

  • For example in geophysics there are many sources of data for Earth models:

    • first-arrival passive seismic data

    • first-arrival active seismic data

    • gravity data

    • surface waves

Joint Annual Meeting NSF Division of Human Resource Development


Need to combine data from different sources 2

Need to Combine Data from Different Sources-2

  • Datasets from different sources provide complementary information

    • Different geophysical datasets contain different information on Earth structure

Joint Annual Meeting NSF Division of Human Resource Development


Need to combine data from different sources 3

Need to Combine Data from Different Sources-3

  • In general, some datasets provide better accuracy and/or spatial resolution in some areas

    • gravity measurements have (relatively) low spatial resolution

    • a seismic data point comes from a narrow trajectory of a seismic signal. Thus, spatial resolution is higher

Joint Annual Meeting NSF Division of Human Resource Development


Joint inversion an ideal solution 1

Joint Inversion: An Ideal Solution-1

  • Currently

    • Datasets are processed separately

    • No efficient algorithm to process all datasets simultaneously

  • Ideally

    • All datasets are used for a single model

Joint Annual Meeting NSF Division of Human Resource Development


Joint inversion an ideal solution 2

Joint Inversion: An Ideal Solution-2

  • Designing such a joint inversion technique presents an important theoretical and practical challenge

Joint Annual Meeting NSF Division of Human Resource Development


Proposed solution model fusion 1

Proposed Solution: Model Fusion-1

  • Joint inversion methods still being developed

  • Solution: fuse models from different datasets

  • Simplest case: data fusion, probabilistic uncertainty

    • several estimates of the same quantity

Joint Annual Meeting NSF Division of Human Resource Development


Proposed solution model fusion 2

Proposed Solution: Model Fusion-2

  • each estimation error is normally distributed with 0 mean and known standard deviation

  • Least squares: find that minimizes

solution:

Joint Annual Meeting NSF Division of Human Resource Development


Additional problem different resolution 1

Additional Problem: Different Resolution-1

  • Different models have different spatial resolution

    • Seismic data leads to higher spatial resolution estimates of the desnsity at different locations

    • Gravity data leads to lower spatial resolution estimates of the same densities

Joint Annual Meeting NSF Division of Human Resource Development


Additional problem different resolution 2

Additional Problem: Different Resolution-2

  • Towards precise formulation:

    • High spatial resolution estimates correspond to small spatial cells

    • Low spatial resolution estimate is affected by several neighboring spatial cells

Joint Annual Meeting NSF Division of Human Resource Development


Towards formulation of a problem 1

Towards Formulation of a Problem-1

  • What is given:

    • High spatial resolution estimates

      of the values in several small cells

    • Low spatial resolution estimates for the weighted averages

Joint Annual Meeting NSF Division of Human Resource Development


Towards formulation of a problem 2

Towards Formulation of a Problem-2

  • Objective: based on the estimates and , a more accurate estimate for must be provided

  • Geophysical example: represents the density.

Joint Annual Meeting NSF Division of Human Resource Development


Model fusion probabilistic uncertainty 1

Model Fusion: Probabilistic Uncertainty-1

  • Taking into account several different types of approximate equalities

    • Each high spatial resolution value is approximately equal to the actual value with a known accuracy :

Joint Annual Meeting NSF Division of Human Resource Development


Model fusion probabilistic uncertainty 2

Model Fusion: Probabilistic Uncertainty-2

  • Each low spatial resolution value is approximately equal to the weighted average, with a known accuracy :

  • Prior knowledge of the values is approximately equal to with accuracy

    :

Joint Annual Meeting NSF Division of Human Resource Development


Model fusion probabilistic uncertainty 3

Model Fusion: Probabilistic Uncertainty-3

  • Each lower spatial resolution value is approximately equal to the value within each of the smaller cells:

Joint Annual Meeting NSF Division of Human Resource Development


Model fusion least squares approach

Model Fusion: Least Squares Approach

  • Using the Least Squares technique, calculate the desired combined value of by minimizing the corresponding sum of weighted squared differences

Joint Annual Meeting NSF Division of Human Resource Development


Example

Example

+

Joint Annual Meeting NSF Division of Human Resource Development


Conclusion and future work

Conclusion and Future Work

  • A fast practical alternative to joint inversion of multiple datasets was presented

  • Future work planned is to apply this algorithm with a actual gravity and seismic datasets (Summer ‘10)

Joint Annual Meeting NSF Division of Human Resource Development


Further questions

Further Questions

  • Omar Ochoa – [email protected]

  • VladikKreinovich – [email protected]

  • Aaron Velasco – [email protected]

  • Rodrigo Romero – [email protected]

Joint Annual Meeting NSF Division of Human Resource Development


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