Method of forming a model representative of the distribution of a physical quantity in an underground zone, free of the effect of correlated noises contained in exploration data
First Claim
1. A method of estimating, from data obtained by exploration of a zone of a heterogeneous medium, a model representative of a distribution, in the zone, of at least one physical quantity, the model being free of a presence of correlated noises that may be contained in the data, comprising:
- a) acquiring measurements giving information about physical characteristics of the zone by following a predetermined experimental protocol;
b) specifying a noise modelling operator which associates, with a model of each physical quantity, synthetic data that constitute a response of the model, the measurements and the synthetic data belonging to a data space;
c) selecting, for each correlated noise referenced by a subscript j ranging from 1 to J, a noise modelling operator which associates a correlated noise with a noise-generating function belonging to a predetermined space of the noise-generating functions (Bj);
d) specifying a norm or of a semi-norm in the data space;
e) specifying a semi-norm in the space of the noise-generating functions for which each noise modelling operator establishes substantially an isometric relation between the space of noise-generating functions and the data space;
f) defining a cost function quantifying a difference between the measurements on one hand and a superposition of a model response and of the correlated noise associated with the noise-generating function on the other hand; and
g) adjusting the model and of the noise-generating functions by minimizing the cost function, by means of an algorithmic method taking advantage of isometry of properties of the noise modelling operators.
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Abstract
The invention is a method of estimating, from data obtained by exploration of a zone of a heterogeneous medium, a model representative of a distribution, in the zone, of at least one physical quantity, the model being free of a presence of correlated noises that may be contained in the data which has application to determining the distribution in an underground zone of acoustic impedance, propagation velocities and permeabilities, etc. The method includes acquiring measurements giving information about physical characteristics of the zone; specifying a noise modelling operator which associates, with a model of each physical quantity, synthetic data that constitute a response of the model; selecting a noise modelling operator which associates a correlated noise with a noise-generating function belonging to a predetermined space of the noise-generating functions; specifying a norm or of a semi-norm in the data space; specifying a semi-norm in the space of the noise-generating functions; defining a cost function; and adjusting the model and of the noise-generating functions.
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Citations
37 Claims
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1. A method of estimating, from data obtained by exploration of a zone of a heterogeneous medium, a model representative of a distribution, in the zone, of at least one physical quantity, the model being free of a presence of correlated noises that may be contained in the data, comprising:
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a) acquiring measurements giving information about physical characteristics of the zone by following a predetermined experimental protocol; b) specifying a noise modelling operator which associates, with a model of each physical quantity, synthetic data that constitute a response of the model, the measurements and the synthetic data belonging to a data space; c) selecting, for each correlated noise referenced by a subscript j ranging from 1 to J, a noise modelling operator which associates a correlated noise with a noise-generating function belonging to a predetermined space of the noise-generating functions (Bj); d) specifying a norm or of a semi-norm in the data space; e) specifying a semi-norm in the space of the noise-generating functions for which each noise modelling operator establishes substantially an isometric relation between the space of noise-generating functions and the data space; f) defining a cost function quantifying a difference between the measurements on one hand and a superposition of a model response and of the correlated noise associated with the noise-generating function on the other hand; and g) adjusting the model and of the noise-generating functions by minimizing the cost function, by means of an algorithmic method taking advantage of isometry of properties of the noise modelling operators. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37)
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Specification