Method for improving convergence in gradient-based iterative inversion of seismic data ( 101 ), especially advantageous for full wavefield inversion The method comprises decomposing the gradient into two (or more) components ( 103 ), typically the migration component and the tomographic component, then weighting the components to compensate for unequal frequency content in the data ( 104 ), then recombining the weighted components ( 105 ), and using the recombined gradient to update ( 106 ) the physical properties model ( 102 )

Tomographically Enhanced Full Wavefield Inversion

Method for reducing artifacts in a subsurface physical properties model (120) inferred by iterative inversion (140) of geophysical data (130), wherein the artifacts are associated with some approximation (110) made during the iterative inversion. In the method, some aspect of the approximation is changed (160) as the inversion is iterated such that the artifacts do not increase by coherent addition.

Artifact reduction in iterative inversion of geophysical data

Method for multi-parameter inversion using elastic inversion. This method decomposes data into offset/angle groups and performs inversion on them in sequential order. This method can significantly speed up convergence of the iterative inversion process, and is therefore most advantageous when used for full waveform inversion (FWI). The present inventive approach draws upon relationships between reflection energy and reflection angle, or equivalently, offset dependence in elastic FWI. The invention uses recognition that the amplitudes of small angle (near offset) reflections are largely determined by acoustic impedance alone (1), independent for the most part of Vp/Vs. Large angle (middle and far offset) reflections are affected by Ip, Vp/Vs (2) and other earth parameters such as density (3) and anisotropy. Therefore, the present inventive method decomposes data into angle or offset groups in performing multi-parameter FWI to reduce crosstalk between the different model parameters being determined in the inversion.

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Multi-parameter inversion through offset dependent elastic fwi

An extended subspace method for inverting geophysical data to infer models for two or more subsurface physical properties, using gradients of an objective function as basis vectors for forming model updates. The extended set of basis vectors provides explicit mixing between gradient components corresponding to different medium parameters, for example P-wave velocity and an anisotropy parameter. In a preferred embodiment, off-diagonal elements of the mixing matrix may be scaled to adjust the degree of mixing between gradient components. Coefficients of the basis vector expansion are determined in a way that explicitly accounts for leakage or crosstalk between different physical parameters. The same extended subspace approach may be used to make further improvement to the model updates by incorporating well constraints, where well log data are available.

Extended Subspace Method for Cross-Talk Mitigation in Multi-Parameter Inversion

There is provided a method for subsurface exploration. The method comprises generating a geophysical representation of a portion of the volume of the Earth from a seismic measurement. The method comprises: providing, from said seismic measurement, a measured seismic data set obtained from said portion of the volume of the Earth, the measured seismic data set comprising measured time-domain values of at least one physical parameter measured at a plurality of discrete data points; generating, using a subsurface model of a portion of the Earth, at least one modelled seismic data set comprising modelled time-domain values of at least one physical parameter at the same plurality of discrete data points; applying a time-domain window to said modelled time-domain values of said modelled seismic data set to generate a windowed modelled seismic data set; performing a Fourier transform on said windowed modelled seismic data set to obtain windowed modelled values taken at one or more selected frequencies, said windowed modelled values comprising amplitude and phase components; applying a time-domain window to said measured time-domain values of said measured seismic data set to generate a windowed measured seismic data set; performing a Fourier transform on said windowed seismic measured data set to obtain windowed measured values taken at one or more selected frequencies, said windowed measured values comprising amplitude and phase components; calculating, from the phase component of said windowed measured values and the phase component of said windowed modelled values, the unwrapped phase residual at said one or more selected frequencies, the unwrapped phase residual of a discrete data point comprising the mismatch between the phase of the windowed measured values and the windowed modelled values of the at least one physical parameter for that discrete data point; generating an unwrapped phase residual data set at said one or more selected frequencies and for said at least one physical parameter; minimising the value of the unwrapped phase residual data set to produce an updated subsurface model; and providing an updated model for subsurface exploration.

Method of, and apparatus for, full waveform inversion

Method for speeding up iterative inversion of seismic data ( 106 ) to obtain a subsurface model ( 102 ), using local cost function optimization. The frequency spectrum of the updated model at each iteration is controlled to match a known or estimated frequency spectrum for the subsurface region, preferably the average amplitude spectrum of the subsurface P-impedance. The controlling is done either by applying a spectral-shaping filter to the source wavelet ( 303 ) and to the data ( 302 ) or by applying the filter, which may vary with time, to the gradient of the cost function ( 403 ). The source wavelet's amplitude spectrum (before filtering) should satisfy D(f)=fI p (f)W(f), where f is frequency, D(f) is the average amplitude spectrum of the seismic data, and I p (f) is the average amplitude spectrum for P-impedance in the subsurface region ( 306,402 ) or an approximation thereof.

Convergence rate of full wavefield inversion using spectral shaping

Wavelet estimation method, particularly advantageous for full wavefield inversion ("FWI") of seismic data, that makes use of both the primary and multiple reflections in the data. The inventive method uses an FWI algorithm to generate a subsurface model from primary reflections (101) in a shallow layer before first arrival of multiple reflections (101). The model is then used to simulate multiples (102). The wavelet is subsequently modified (104) such that the simulated multiples closely match the true recorded multiples (103). The simulated multiples may then be subtracted from the measured data (105) thereby creating a deeper top layer of data substantially free of multiples, and the method may then be repeated to extend the subsurface model to a greater depth (106).

Ke Wang

Papers

Convergence rate of full wavefield inversion using spectral shaping

Multi-parameter inversion through offset dependent elastic fwi

Method of Wavelet Estimation and Multiple Prediction In Full Wavefield Inversion