Sequential Inversion Approach Research Articles

Characterization of a carbonate reservoir using elastic full‐waveform inversion of vertical seismic profile data

ABSTRACTTwo‐dimensional elastic full waveform inversion was applied to two lines extracted from a spiral three‐dimensional vertical seismic profile data acquired in an oilfield offshore, Abu Dhabi, in the United Arab Emirates. The lines were selected to be parallel and perpendicular to the plane defined by the deviated borehole. The purpose of the inversion was to derive high‐resolution elastic properties of the subsurface. After pre‐processing, the data were band‐pass filtered with a minimum frequency of 3.5 Hz and a maximum frequency of 30 Hz. A sequential inversion approach was used to mitigate non‐linearity. The pre‐processing of the data consisted in the removal of bad traces, followed by amplitude and phase corrections. High‐resolution P‐ and S‐wave velocity models that show good correlations with the available sonic logs were obtained. The results of the inversion suggest that the oilfield consists of a stack of layers with varying lithology, porosity and possibly fluid content.

A multiscale approach to full-waveform inversion using a sequence of time-domain misfit functions

Most of the approaches designed to avoid cycle skipping in full-waveform inversion (FWI) involve calculating a sequence of inversions in a multiscale fashion. We have adopted an alternative strategy, which is inverting a sequence of different misfit functions in the time domain. This is an implicit multiscale approach in the sense that the used misfit functions are sensitive to different wavelengths, but all of the inversion steps use the same modeling algorithm and the same model grid. In the first and third inversion steps, the transmitted (early arrivals) and reflected (late arrivals) components of the wavefield envelopes are respectively fitted. The second step promotes a smooth transition between the first and third steps, by using the envelope of the complete waveform. Because fitting just the envelope of the reflected waves has a minor effect on the misfit function of the whole data set, the phases of the reflected waves are mostly fitted in the fourth step, which is based on the waveform misfit function preserving only the late arrivals. The third and fourth steps are of crucial importance to fit the reflected events. We test the sequential inversion approach with the Marmousi model using data sets with different frequencies, obtaining better estimates of the velocity field than those obtained with the classic FWI. The solutions obtained with classic FWI and sequential inversion approach degrade with a progressively higher peak frequency data set, but the classic FWI solution degrades more rapidly.

Estimation of geoacoustic model parameters from modal amplitude information

This paper analyzes an approach for estimating geoacoustic model parameters from information contained in normal modes of a broadband signal. Propagating modes are resolved by time-warping deconvolved signals from light bulb sound sources deployed at short ranges in shallow water. Amplitudes of the resolved modes contain information about sediment sound attenuation through the modal attenuation coefficient. However, the coefficient also depends on the sediment sound speed and density. A sequential inversion approach was developed that enables effective use of modal amplitudes to estimate sound attenuation in sediments. The inversion is based on a sequential Bayesian approach applied to features of resolved modal data that are highly sensitive to specific geoacoustic model parameters. Travel times of modal frequency components are inverted first for sediment sound speed and sediment layer thickness, and these estimates are used in subsequent stages. The effects of errors in estimates from previous stages a...

Sequential inversion of modal data for sound attenuation in sediment at the New Jersey Shelf.

This paper presents a method for estimating bottom geoacoustic properties especially the sediment attenuation from information contained in normal modes of a broadband signal. Propagating modes are resolved using the time-warping technique applied to signals from light bulb sound sources deployed at ranges of 5 and 7 km in the Shallow Water '06 experiment. A sequential inversion approach is designed that uses specific features of the acoustic data that are highly sensitive to specific geoacoustic model parameters. The first feature is the modal group speed, which is inverted for seabed sound speed, density, and sediment thickness. The second feature is the modal depth function for inverting receiver depths. The third feature is related to the modal coefficient spectra, and this is inverted for source depth and sediment attenuation. In each subsequent stage, estimates from the previous stage(s) are used as known values. The sequential inversion is stable and generates estimates for the geoacoustic model parameters that agree very well with results from other experiments carried out in the same region. Notably, the inversion obtains an estimated attenuation of 0.078 dB/λ in the band 120-180 Hz for the de-watered marine sediment characteristic of the continental shelf at the site.

Estimation of low frequency sound attenuation in marine sediments

This paper presents a method for estimating low frequency sound attenuation from information contained in normal modes of a broadband signal. Propagating modes are resolved using the time-warping technique applied to signals from light bulb sound sources deployed at relatively short ranges of 5 and 7 km in the Shallow Water ’06 experiment. A sequential inversion approach is designed that uses specific features of the acoustic data that are highly sensitive to specific geoacoustic model parameters. The first feature is the modal group velocity which is inverted for sediment sound speed and sediment layer thickness. The second feature is the modal amplitude function which is inverted for water depth and receiver depths. The third feature is related to the modal amplitude spectrum and is inverted for source depth and sound attenuation. In each subsequent stage, estimates from the previous stage(s) are used as known values. The sequential inversion is stable and generates geoacoustic model parameter estimates that agree very well with results from other experiments carried out in the same region. Notably, the inversion obtains an estimated value of 0.08 dB/λ in the band 120–180 Hz for the de-watered marine sediment characteristic of the continental shelf at the site.

A new parameterization for frequency-domain elastic full waveform inversion for VTI media

Abstract To improve full waveform inversion (FWI) results for 2-D vertical transverse isotropic (VTI) media, we propose a new parameterization scheme that is based on Lame constants. In the new parameterization approach, elastic constants of C11, C13, C33, and C44 are replaced with Lame constants and newly introduced parameters of ξ1 and ξ2 for anisotropic properties. Multi-parametric inversion for elastic VTI media has been conducted using a two-step sequential inversion strategy, in which primary parameters (that are well inverted) are inverted first, and secondary parameters are inverted using the inverted primary parameters. In the conventional VTI parameterization approach, C33 and C44 are regarded as the primary parameters, whereas in the new parameterization approach, Lame constants are primary parameters. The new parameterization scheme is distinguished from the conventional VTI parameterization approach in scattering patterns of partial derivative wavefields with respect to primary parameters. Scattering patterns of Lame constants are similar to those of the isotropic case. Because Lame constants are well inverted in the isotropic case, they may also be well inverted in the new parameterization. On the other hand, we do not expect any direct improvements for anisotropic properties because ξ1 and ξ2 produce the same scattering patterns as those of C11 and C13. Gradient directions for a two-layered model show that we can improve the resolution of gradient direction for μ (one of the primary parameters). Although ξ1 and ξ2 of the new parameterization retain characteristics of C11 and C13 in the conventional parameterization, improved primary parameters (Lame constants) affect anisotropic parameters positively. Consequently, inversion results for all of the parameters can be improved. Numerical examples indicate that the new parameterization scheme provides more reliable inversion results than the conventional and sequential inversion approaches. In addition, the new parameterization approach exhibits higher degrees of computational efficiency than the sequential inversion approach because it involves simultaneous inversion of all parameters and does not require an additional inversion stage. Our new parameterization scheme can therefore overcome the intrinsic disadvantages of elastic inversion for VTI media. In applying the new parameterization to real seismic data, it is necessary to increase its applicability to noisy and low-frequency missing data and it also needs to be extended to 3-D case.

Feasibility of Sequential and Coupled Inversion of Time Domain Reflectometry Data to Infer Soil Hydraulic Parameters under Falling Head Infiltration

Accurate estimation of soil hydraulic properties is a prerequisite for efficient soil and water management. On a small scale, time domain reflectometry (TDR) measurements obtained during an infiltration event can be used for estimating soil hydraulic properties either using a sequential or a coupled inversion approach. In the traditional sequential approach, the TDR measurements are inverted into water content averages based on travel time analysis and subsequently used for calibrating a hydrologic model. Travel time analysis has been reported to be subjective and difficult to use for analyzing TDR measurements obtained during infiltration. In this paper, we extend the sequential inversion approach by using water content profiles (WCPs) obtained via inverse modeling of TDR measurements and introduce a coupled inversion approach which directly uses the TDR measurements for constraining the inversion for hydraulic properties without first inverting them into WCPs or averages. By comparing the feasibility of these approaches to infer three Mualem-van Genuchten (MVG) hydraulic parameters (α, n, Ks) from TDR measurements obtained under falling head infiltration, we concluded that the coupled approach is more practical and less uncertain than the sequential approach. In particular, the coupled inversion approach allows to simultaneously monitor ponding depth and water infiltration, which avoids the laborious task of manually measuring the ponding depths and can thus enable rapid estimation of the soil hydraulic parameters for multiple locations through automatic measurements of ponded infiltration for multiple rings through TDR multiplexing.

Simultaneous multifrequency inversion of full-waveform seismic data

We present a simultaneous multifrequency inversion approach for seismic data interpretation. This algorithm inverts all frequency data components simultaneously. A data-weighting scheme balances the contributions from different frequency data components so the inversion process does not become dominated by high-frequency data components, which produce a velocity image with many artifacts. A Gauss-Newton minimization approach achieves a high convergence rate and an accurate reconstructed velocity image. By introducing a modified adjoint formulation, we can calculate the Jacobian matrix efficiently, allowing the material properties in the perfectly matched layers (PMLs) to be updated automatically during the inversion process. This feature ensures the correct behavior of the inversion and implies that the algorithm is appropriate for realistic applications where a priori information of the background medium is unavailable. Two different regularization schemes, an [Formula: see text]-norm and a weighted [Formula: see text]-norm function, are used in this algorithm for smooth profiles and profiles with sharp boundaries, respectively. The regularization parameter is determined automatically and adaptively by the so-called multiplicative regularization technique. To test the algorithm, we implement the inversion to reconstruct the Marmousi velocity model using synthetic data generated by the finite-difference time-domain code. These numerical simulation results indicate that this inversion algorithm is robust in terms of starting model and noise suppression. Under some circumstances, it is more robust than a traditional sequential inversion approach.

Inversion of controlled-source seismic tomography and gravity data with the self-adaptive wavelet parametrization of velocities and interfaces

A self-adaptive automated parametrization approach is suggested for the sequential inversion of controlled-source seismic tomography and gravity data. The velocities and interfaces are parametrized by their Haar wavelet expansion coefficients. Only those coefficients that are well constrained by the data, as measured by the number of rays that cross the corresponding wavelet function support area and their angular coverage, are inverted for, others are set to zero. This approach results in a reasonable distribution of resolution throughout the model even in cases of irregular ray coverage and does overcome the trade-off between different types of model parameters. A modified sequential inversion approach is suggested to join the traveltimes and gravity anomalies inversion. An algorithm is developed that inverts for smooth velocity and density variations inside the seismic layer, the position of its bottom interface as well as for optimal values of the velocity-to-density regression coefficients. The algorithm makes use of direct (diving), reflected and head (critically refracted) wave traveltimes. The algorithm workflow is demonstrated on a synthetic data example.