1-D elastic waveform inversion: A divide‐and‐conquer approach

Geophysics ◽  
1998 ◽  
Vol 63 (5) ◽  
pp. 1670-1684 ◽  
Author(s):  
Ganyuan Xia ◽  
Mrinal K. Sen ◽  
Paul L. Stoffa
Keyword(s):  
Seismic Velocity ◽  
Waveform Inversion ◽  
P Wave ◽  
Divide And Conquer ◽  
Rock Properties ◽  
Inversion Method ◽  
Earth Model ◽  
Model Parameters ◽  
Waveform Data ◽  
True Model

Subsurface rock properties are manifested in seismic records as variations in traveltimes, amplitudes, and waveforms. It is commonly acknowledged that traveltimes are sensitive to the long wavelength part of the velocity, whereas amplitudes are sensitive to the short wavelength part of the velocity. The inherent sensitivity of seismic velocity at different wavelengths suggests an approach that decomposes the waveform data into traveltime and amplitude components. Therefore we propose a divide‐and‐conquer approach to the elastic waveform inversion problem. We first estimate the smoothly varying background velocity from the traveltime and the rapidly changing perturbations from the amplitude by amplitude variation with offset (AVO) inversion based on linearized reflection coefficient. Then we combine the perturbation with the background to obtain a starting model to be used in the final waveform inversion that models all converted waves and internal multiples assuming a 1-D earth model. For estimating the background velocity, we use the flatness of events as the objective criterion, and simulated annealing as a search tool. Three different model parameterization schemes (constant velocity blocks, splines, and arctangent models) are compared, with the arctangent having the most flexibility and least artifacts. Having obtained the background velocities, we analyze the AVO effects to estimate the perturbations to the background, for which we use a linearized inversion method. The combination of the perturbation and background should be sufficiently close to the true model so that the inverse problem becomes quasi‐linear. A full elastic waveform inversion is used to fine‐tune the combined model to obtain P-wave and S-wave velocity and density, again using either a nonlinear optimization method or an iterative linearized solution. Application of the inversion algorithm to synthetic data from an 84-layer model was able to predict the full reflectivity data and recover the true model parameters. Application to one seismic line in the Carolina Trough area found a thin gas zone which produces strong Bottom Simulating Reflectors (BSRs).

scholarly journals Variational Bayesian inversion of seismic attributes jointly for geologic facies and petrophysical rock properties

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. MR213-MR233 ◽  
Author(s):  
Muhammad Atif Nawaz ◽  
Andrew Curtis ◽  
Mohammad Sadegh Shahraeeni ◽  
Constantin Gerea
Keyword(s):  
Gaussian Mixture ◽  
Seismic Attributes ◽  
Joint Estimation ◽  
Training Data ◽  
P Wave ◽  
Rock Properties ◽  
Inversion Method ◽  
Computationally Efficient ◽  
S Wave ◽  
Well Data

Seismic attributes (derived quantities) such as P-wave and S-wave impedances and P-wave to S-wave velocity ratios may be used to classify subsurface volume of rock into geologic facies (distinct lithology-fluid classes) using pattern recognition methods. Seismic attributes may also be used to estimate subsurface petrophysical rock properties such as porosity, mineral composition, and pore-fluid saturations. Both of these estimation processes are conventionally carried out independent of each other and involve considerable uncertainties, which may be reduced significantly by a joint estimation process. We have developed an efficient probabilistic inversion method for joint estimation of geologic facies and petrophysical rock properties. Seismic attributes and petrophysical properties are jointly modeled using a Gaussian mixture distribution whose parameters are initialized by unsupervised learning using well-log data. Rock-physics models may be used in our method to augment the training data if the existing well data are limited; however, this is not required if sufficient well data are available. The inverse problem is solved using the Bayesian paradigm that models uncertainties in the form of probability distributions. Probabilistic inference is performed using variational optimization, which is a computationally efficient deterministic alternative to the commonly used sampling-based stochastic inference methods. With the help of a real data application from the North Sea, we find that our method is computationally efficient, honors expected spatial correlations of geologic facies, allows reliable detection of convergence, and provides full probabilistic results without stochastic sampling of the posterior distribution.

Simultaneous inversion of prestack seismic data for rock properties using simulated annealing

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1877-1885 ◽  
Author(s):  
Xin‐Quan Ma
Keyword(s):  
Simulated Annealing ◽  
Seismic Data ◽  
Low Frequency ◽  
Optimization Procedure ◽  
P Wave ◽  
Rock Properties ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Simultaneous Inversion ◽  
Reflection Seismic

A new prestack inversion algorithm has been developed to simultaneously estimate acoustic and shear impedances from P‐wave reflection seismic data. The algorithm uses a global optimization procedure in the form of simulated annealing. The goal of optimization is to find a global minimum of the objective function, which includes the misfit between synthetic and observed prestack seismic data. During the iterative inversion process, the acoustic and shear impedance models are randomly perturbed, and the synthetic seismic data are calculated and compared with the observed seismic data. To increase stability, constraints have been built into the inversion algorithm, using the low‐frequency impedance and background Vs/Vp models. The inversion method has been successfully applied to synthetic and field data examples to produce acoustic and shear impedances comparable to log data of similar bandwidth. The estimated acoustic and shear impedances can be combined to derive other elastic parameters, which may be used for identifying of lithology and fluid content of reservoirs.

Elastic reflection traveltime inversion with decoupled wave equation

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. R463-R474 ◽  
Author(s):  
Guanchao Wang ◽  
Shangxu Wang ◽  
Jianyong Song ◽  
Chunhui Dong ◽  
Mingqiang Zhang
Keyword(s):  
Wave Equation ◽  
Wave Velocity ◽  
Waveform Inversion ◽  
P Wave ◽  
Model Parameters ◽  
Local Minima ◽  
S Wave ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Elastic Reflection

Elastic full-waveform inversion (FWI) updates high-resolution model parameters by minimizing the residuals of multicomponent seismic records between the field and model data. FWI suffers from the potential to converge to local minima and more serious nonlinearity than acoustic FWI mainly due to the absence of low frequencies in seismograms and the extended model domain (P- and S-velocities). Reflection waveform inversion can relax the nonlinearity by relying on the tomographic components, which can be used to update the low-wavenumber components of the model. Hence, we have developed an elastic reflection traveltime inversion (ERTI) approach to update the low-wavenumber component of the velocity models for the P- and S-waves. In our ERTI algorithm, we took the P- and S-wave impedance perturbations as elastic reflectivity to generate reflections and a weighted crosscorrelation as the misfit function. Moreover, considering the higher wavenumbers (lower velocity value) of the S-wave velocity compared with the P-wave case, optimizing the low-wavenumber components for the S-wave velocity is even more crucial in preventing the elastic FWI from converging to local minima. We have evaluated an equivalent decoupled velocity-stress wave equation to ERTI to reduce the coupling effects of different wave modes and to improve the inversion result of ERTI, especially for the S-wave velocity. The subsequent application on the Sigsbee2A model demonstrates that our ERTI method with the decoupled wave equation can efficiently update the low-wavenumber parts of the model and improve the precision of the S-wave velocity.

scholarly journals A Bayesian 3-D linear gravity inversion for complex density distributions: application to the Puysegur subduction system

2020 ◽  
Vol 223 (3) ◽  
pp. 1899-1918
Author(s):  
Erin Hightower ◽  
Michael Gurnis ◽  
Harm Van Avendonk
Keyword(s):  
Subduction Zones ◽  
Structural Changes ◽  
Seismic Velocity ◽  
Equality Constraints ◽  
Moho Depth ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Model Parameters ◽  
Density Distributions ◽  
Complex Density

SUMMARY We have developed a linear 3-D gravity inversion method capable of modelling complex geological regions such as subduction margins. Our procedure inverts satellite gravity to determine the best-fitting differential densities of spatially discretized subsurface prisms in a least-squares sense. We use a Bayesian approach to incorporate both data error and prior constraints based on seismic reflection and refraction data. Based on these data, Gaussian priors are applied to the appropriate model parameters as absolute equality constraints. To stabilize the inversion and provide relative equality constraints on the parameters, we utilize a combination of first and second order Tikhonov regularization, which enforces smoothness in the horizontal direction between seismically constrained regions, while allowing for sharper contacts in the vertical. We apply this method to the nascent Puysegur Trench, south of New Zealand, where oceanic lithosphere of the Australian Plate has underthrust Puysegur Ridge and Solander Basin on the Pacific Plate since the Miocene. These models provide insight into the density contrasts, Moho depth, and crustal thickness in the region. The final model has a mean standard deviation on the model parameters of about 17 kg m–3, and a mean absolute error on the predicted gravity of about 3.9 mGal, demonstrating the success of this method for even complex density distributions like those present at subduction zones. The posterior density distribution versus seismic velocity is diagnostic of compositional and structural changes and shows a thin sliver of oceanic crust emplaced between the nascent thrust and the strike slip Puysegur Fault. However, the northern end of the Puysegur Ridge, at the Snares Zone, is predominantly buoyant continental crust, despite its subsidence with respect to the rest of the ridge. These features highlight the mechanical changes unfolding during subduction initiation.

A Procedure for the Extraction of Multiple Body Wave Traveltimes From Seismological Waveform Data

1991 ◽  
Vol 02 (01) ◽  
pp. 276-283 ◽  
Author(s):  
GÖTZ H.R. BOKELMANN ◽  
PAUL G. SILVER
Keyword(s):  
Travel Time ◽  
Seismic Velocity ◽  
Body Wave ◽  
Path Model ◽  
Nonlinear Dependence ◽  
Model Parameters ◽  
Time Inversion ◽  
Waveform Data ◽  
Short Period ◽  
Period Data

A scheme for extracting multiple phase body wave traveltimes is presented which is most applicable to teleseismic broadband and short period data from permanent and portable instruments. The method specifically allows for the nonlinear dependence of waveforms on travel time by performing a nonlinear search over a reduced set of “projected model parameters”. This reduced set is found by splitting the method into two parts, the nonlinear dependence of waveforms on traveltime perturbations (particularly strong for broadband and short period data) and the linearizable dependence of travel time perturbations on variations in seismic velocity. By use of generalized inverse, the traveltime perturbations can be adequately characterized by a reduced number of linear combinations of model parameters. Consequently, the nonlinear search is performed over an optimally compact model space. The technique can consider simultaneously a large number of body wave phases creating a systematic methodology for extracting large numbers of traveltimes from single source-receiver pairs. The resulting path model may or may not be of physical significance; the primary goal is the extraction of travel times that may be subsequently used for a more comprehensive travel time inversion.

Exploiting surface consistency for surface-wave characterization and mitigation — Part 1: Theory and 2D examples

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. V21-V37 ◽  
Author(s):  
Christine E. Krohn ◽  
Partha S. Routh
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Single Mode ◽  
Complex Surface ◽  
Companion Paper ◽  
Inversion Method ◽  
Earth Model ◽  
Model Parameters ◽  
Quality Factors ◽  
Near Surface

We have developed a new tomographic inversion method that is able to determine the properties of complex surface waves, which are multimodal and heterogeneous. These properties can be used to generate a detailed near-surface earth model or to predict and remove the surface waves, while protecting reflection signals even with aliased data. The inversion assumes plane-wave physics and generates surface-consistent model parameters as a function of frequency. In this paper, we validate our method with 2D models and data. In a companion paper, we demonstrate its application to 3D data. Inversion for a single mode is linear, but the linearity does not hold at higher frequencies, where multiple modes interfere. However, single-mode inversion results can be used to create a starting model for the subsequent nonlinear multimode tomography. The resulting velocity-frequency grid has greater resolution compared with a beam-forming method. The dispersion curves can be used as input to a subsequent standard 1D surface-wave inversion to generate a velocity-depth model. The tomographic method also determines a grid of attenuation quality factors and variations in the source amplitude and bandwidth, which correlate with the near-surface elevation changes. The amplitude and phase properties can be used together to predict the surface-wave waveforms, which can then be adaptively subtracted from the data on a trace-to-trace basis.

Long-Wavelength Earth Model via Accelerated Full-Waveform Inversion

2021 ◽  
Author(s):  
Solvi Thrastarson ◽  
Dirk-Philip van Herwaarden ◽  
Lion Krischer ◽  
Martin van Driel ◽  
Christian Boehm ◽  
...  
Keyword(s):  
Waveform Inversion ◽  
Large Data ◽  
Earth Model ◽  
Full Waveform Inversion ◽  
Waveform Data ◽  
Long Wavelength ◽  
Computational Overhead ◽  
Full Dataset ◽  
Full Waveform ◽  
Seismic Waveform

<p>As the volume of available seismic waveform data increases, the responsibility to use the data in an effective way emerges. This requires computational efficiency as well as maximizing the exploitation of the information associated with the data.</p><p>In this contribution, we present a long-wavelength Earth model, created by using the data recorded from over a thousand earthquakes, starting from a simple one-dimensional background (PREM). The model is constructed with an accelerated full-waveform inversion (FWI) method which can seamlessly include large data volumes with a significantly reduced computational overhead. Although we present a long-wavelength model, the approach has the potential to go to much higher frequencies, while maintaining a reasonable cost.</p><p>Our approach combines two novel FWI variants. (1) The dynamic mini-batch approach which uses adaptively defined subsets of the full dataset in each iteration, detaching the direct scaling of inversion cost from the number of earthquakes included. (2) Wavefield-adapted meshes which utilize the azimuthal smoothness of the wavefield to design meshes optimized for each individual source location. Using wavefield adapted meshes can drastically reduce the cost of both forward and adjoint simulations as well as it makes the scaling of the computing cost to modelled frequencies more favourable.</p>

Two-dimensional shallow soil profiling using time-domain waveform inversion

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. EN27-EN41 ◽  
Author(s):  
Mohamed Amrouche ◽  
Hiroaki Yamanaka
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Modal Identification ◽  
Reference Station ◽  
Staggered Grid ◽  
Inversion Method ◽  
Waveform Data ◽  
Near Surface ◽  
Soil Model ◽  
Shallow Soils

Near-surface characterization has now gained significance among exploration geophysicists, and many methods are being proposed to retrieve the 2D structures of shallow soils. Because most of these methods are based on the modal inversion of the surface waves, they can only be applied to laterally homogeneous or smoothly heterogeneous soil models. We have developed a time-domain waveform inversion method for 2D near-surface exploration that offers an alternative approach to existing surface-wave techniques for layered soils with a flat surface. Our method directly fits the input Rayleigh waveforms to retrieve the 2D soil structure without need of any modal identification, allowing the inversion of soil models that can be challenging with modal-inversion-based approaches. In our method, the forward problem formulated in the time domain is based on a 2.5D staggered-grid finite-difference scheme to simulate the P-SV wavefield; soil modeling was achieved by dividing soil layers into specific number of blocks with discontinuous interfaces. The inversion strategy depends on attributing suitable values for the interface depth and S-wave velocity for each block to reconstruct a numerical soil model that fit the input waveforms. Because we cannot know the source signature during data acquisition, source deconvolution by a reference station is applied to observed and calculated waveforms to make a waveform inversion free of the source signature. Numerical experiments revealed that our method was able to sufficiently reconstruct soil structures with strong lateral velocity gradient or soils with a blind layer in noisy environments, using a single source and reasonable number of receivers. We also applied this method to real waveform data, and we succeeded in obtaining good correlation between the inverted 2D soil model and the existing borehole data.

Joint inversion of Rayleigh-wave dispersion and P-wave refraction data for laterally varying layered models

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. EN49-EN59 ◽  
Author(s):  
Daniele Boiero ◽  
Laura Valentina Socco
Keyword(s):  
Rayleigh Wave ◽  
Joint Inversion ◽  
A Priori ◽  
P Wave ◽  
Inversion Method ◽  
Model Parameters ◽  
Data Set ◽  
Wave Refraction ◽  
Velocity Models ◽  
Refraction Data

We implemented a joint inversion method to build P- and S-wave velocity models from Rayleigh-wave and P-wave refraction data, specifically designed to deal with laterally varying layered environments. A priori information available over the site and any physical law to link model parameters can be also incorporated. We tested and applied the algorithm behind the method. The results from a field data set revealed advantages with respect to individual surface-wave analysis (SWA) and body wave tomography (BWT). The algorithm imposed internal consistency for all the model parameters relaxing the required a priori assumptions (i.e., Poisson’s ratio level of confidence in SWA) and the inherent limitations of the two methods (i.e., velocity decreases for BWT).

scholarly journals Delineation of Upper Crustal Structure Beneath the Island of Lombok, Indonesia, Using Ambient Seismic Noise Tomography

2021 ◽  
Vol 9 ◽  
Author(s):  
Achmad F. N. Sarjan ◽  
Zulfakriza Zulfakriza ◽  
Andri D. Nugraha ◽  
Shindy Rosalia ◽  
Shengji Wei ◽  
...  
Keyword(s):  
Group Velocity ◽  
Ambient Noise ◽  
Velocity Structure ◽  
Seismic Velocity ◽  
Inversion Method ◽  
Good Resolution ◽  
Ambient Noise Tomography ◽  
Fast Marching ◽  
Waveform Data ◽  
Short Period

We have successfully conducted the first ambient noise tomography on the island of Lombok, Indonesia using local waveform data observed at 20 temporary stations. Ambient noise tomography was used to delineate the seismic velocity structure in the upper crust. The waveform data were recorded from August 3rd to September 9th, 2018, using short-period and broadband sensors. There are 185 Rayleigh waves retrieved from cross-correlating the vertical components of the seismograms. We used frequency-time analysis (FTAN) to acquire the interstation group velocity from the dispersion curves. Group velocity was obtained for the period range of 1 s to 6 s. The group velocity maps were generated using the subspace inversion method and Fast Marching Method (FMM) to trace ray-paths of the surface waves through a heterogeneous medium. To extract the shear wave velocity (Vs) from the Rayleigh wave group velocity maps, we utilize the Neighborhood Algorithm (NA) method. The 2-D tomographic maps provide good resolution in the center and eastern parts of Lombok. The tomograms show prominent features with a low shear velocity that appears up to 4 km depth beneath Rinjani Volcano, Northern Lombok, and Eastern Lombok. We suggest these low velocity anomalies are associated with Quaternary volcanic products, including the Holocene pyroclastic deposits of Samalas Volcano (the ancient Rinjani Volcano) which erupted in 1257. The northeast of Rinjani Volcano is characterized by higher Vs, and we suggest this may be due to the presence of igneous intrusive rock at depth.

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