# US 8,571,842 B2 · Method of determining parameter from sparse measurement data

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- Number: US 8,571,842 B2
- Document ID: US8571842B2
- Status: Granted
- Kind: B2
- Application number: 12/819,313
- Filed: 2010-06-21
- Published: 2011-12-22
- Granted: 2013-10-29
- Earliest claimed: 2010-06-21
- Assignees: Schlumberger Technology Corporation
- Applicants: Khaled Hadj-Sassi; Jean-Marc Donadille
- Inventors: Khaled Hadj-Sassi; Jean-Marc Donadille
- Web page: https://patentgrep.com/patent/US8571842B2

## CPC

- G06F 17/11: for solving equations {, e.g. nonlinear equations, general mathematical optimization problems (optimization specially adapted for a specific administrative, business or logistic context G06Q10/04)}
- G01V 20/00: Geomodelling in general
- G01V 2210/169: Sparse arrays
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02)

## Abstract

A method of simultaneously determining multiple parameters or a parameter distribution characterizing material properties of a volume under investigation using an inversion process of sparse measurements is described including the step of defining an initial model of the volume and modifying the initial model by matching the multiple parameters or parameter distribution with the measurements using alternatingly an iterative inversion method and a probabilistic inversion method, and determining the multiple parameters or parameter distribution after one or more iterations of the alternating inversions.

## Claims

### Claim 1

A method of simultaneously determining multiple parameters or a parameter distribution characterizing material properties of a volume of a subterranean formation under investigation using an inversion process of sparse measurements, the method comprising:
performing a potential field survey of the volume of the subterranean formation using sensors located around or within the volume;
defining a model of said volume and modifying said model by matching said multiple parameters or parameter distribution characterizing material properties with said measurements of the effects of the potential field using alternatingly an iterative inversion method and a probabilistic inversion method; and
determining said multiple parameters or parameter distribution characterizing material properties after one or more iterations of said alternating inversions wherein a pseudo-converged model obtained after one or more iterations of an inversion is transformed and the transformed model of the inversion is used as an input model for a successive inversion.

### Claim 2 (depends on 1)

The method of claim 1, wherein after a probabilistic inversion, a most probable model of the probabilistic inversion is transformed and used as a starting model for the iterative inversion.

### Claim 3 (depends on 2)

The method of claim 2, wherein the most probable model is selected as the model having the maximum probability.

### Claim 4 (depends on 1)

The method of claim 1, wherein a first switching condition is associated with the iterative inversion method to switch to the probabilistic inversion method and a second switching condition is associated with said probabilistic inversion method to switch to said iterative inversion method.

### Claim 5 (depends on 1)

The method of claim 1, wherein the iterations are terminated when a first termination condition is satisfied after the iterative inversion method and a second termination condition is satisfied after the probabilistic inversion method within one iteration of the alternating iterations.

### Claim 6 (depends on 1)

The method of claim 1, wherein the number of iterations of said alternating inversions exceeds 4.

### Claim 7 (depends on 1)

The method of claim 1, wherein the number of iterations of said alternating inversions exceeds 9.

### Claim 8 (depends on 1)

The method of claim 1, wherein the alternating inversions continue until both the iterative inversion method and the probabilistic inversion method converge.