Constrained MWNI Data Reconstruction for Aliased Geophysical Signals

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Solution Overview

Problem

The Minimum Weighted Norm Interpolation (MWNI) algorithm struggles to effectively handle spatially aliased data in geophysical applications, leading to poor reconstruction of subsurface structures due to data gaps and irregularities, as existing methods either degrade the interpolation results or fail to accurately interpolate missing data.

Innovation Solution

The approach involves computing an initial, regularly interpolated model with no data gaps and using the resulting spectral weights as constraints in a constrained minimum weighted norm interpolation process, which reduces aliasing artifacts by converting the model into a frequency domain and computing unknown spectral weights using Fourier transforms, allowing for improved data regularization.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Manufacturing precision

If traditional MWNI algorithm is used to interpolate missing data, then data regularization is achieved, but spatially aliased data cannot be properly processed leading to poor reconstruction of steeply dipping structures

Engineering Contradiction:

Improvedata reconstruction accuracyVSAvoidhandling of spatially aliased data

Core Design Contradiction:

Manufacturing precisionVSReliability

Solution Approach 1:

The method performs preliminary interpolation of missing data using a simplified model before applying the full MWNI algorithm. This preliminary action creates an initial regularized dataset that enables subsequent processing of spatially aliased data, resolving the contradiction by preparing the data in advance to make it suitable for accurate reconstruction.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent introduces an intermediate step that computes spectral weights from the preliminary interpolated model and uses these weights to constrain the final MWNI solution. This intermediary mechanism bridges the gap between handling aliased data and achieving accurate reconstruction, allowing both objectives to be satisfied simultaneously.

Inventive Principle:

Principle #24Intermediary (Mediator)

2Object-affected harmful factors

If filtering is applied to remove aliased energy before MWNI interpolation, then data aliasing is reduced, but interpolation results are degraded especially for steeply dipping structures

Engineering Contradiction:

Improvealiasing artifactsVSAvoidinterpolation result quality

Core Design Contradiction:

Object-affected harmful factorsVSManufacturing precision

Solution Approach 1:

Instead of removing aliased energy through filtering, the method converts the harmful aliasing into useful information by using it to compute spectral weights. These weights are then used to constrain the interpolation, transforming what was previously a harmful artifact into a beneficial constraint that improves both aliasing reduction and interpolation accuracy.

Inventive Principle:

Principle #22Blessing in disguise (Convert harm into benefit)

Solution Approach 2:

The patent changes the parameter being processed from time-domain signal filtering to frequency-domain spectral weight computation. By transforming the approach from removing aliased energy to utilizing it for weight computation, the method simultaneously reduces aliasing artifacts and preserves interpolation quality for steeply dipping structures.

Inventive Principle:

Principle #35Parameter changes

3Reliability

If bootstrapping method with lower-frequency solution is used to constrain higher-frequency solution, then data aliasing is attempted to be handled, but low-frequency signals that are difficult to record cannot be recovered

Engineering Contradiction:

Improvehandling of aliased frequency rangesVSAvoidlow-frequency signal recovery

Core Design Contradiction:

ReliabilityVSLoss of information

Solution Approach 1:

The patent inverts the traditional bootstrapping approach by not assuming low-frequency signals exist in the data. Instead, it computes spectral weights across all frequencies including those where low-frequency signals are absent, using the preliminary interpolated model to provide constraints where actual low-frequency data is missing. This reversal allows handling of aliased frequencies without relying on unavailable low-frequency information.

Inventive Principle:

Principle #13The other way round (Inversion)

Data Source

PatentUS9158016B2Multi-dimensional data reconstruction constrained by a regularly interpolated model

Publication Date: 2015.10.13 CONOCOPHILLIPS CO

AI summary

A process for overcoming aliasing using a minimum weighted norm interpolation (MWNI) technique may include computing an initial, regularly interpolated model with no data gaps and computing a plurality of initial spectral weights using the initial, regularly interpolated model. The initial, regularly interpolated model is used to compute the spectral weights as initial constraints in a least-squares solution methodology. The initial spectral weights are used as initial constraints in a constrained minimum weighted norm interpolation data reconstruction. The process may further include converting the initial, regularly interpolated model into a frequency domain and computing unknown spectral weights from frequency data at each frequency slice of the initial, regularly interpolated model using Fourier transform. The process results in reducing aliasing artifacts and improving data regularization.