Conventional Inversion Schemes Research Articles

Inversion of Deep-Water Velocity Using the Munk Formula and the Seabed Reflection Traveltime: An Inversion Scheme That Takes the Complex Seabed Topography Into Account

The sound speed of seawater is not constant. It varies with season, day time, depth and range. This variation was not considered in marine seismic data processing and imaging before deep-water seismic acquisition became a routine activity. As a result, non-ignorable errors may be contained in the final migrated-image of deep-water seismic data. To eliminate such errors, we propose here a scheme for inverting the seawater velocity under the condition that the seabed has a complex topography. In this scheme, the seabed topography is represented by step grids constrained by measured water depth data, and the sound profile is assumed to be the one satisfying the Munk formula. Thus, only the parameters appearing in the Munk formula need to be inverted. This is quite different from the conventional inversion schemes that take the velocity as the inversion target. We use the conjugate gradient method to minimize the objective function given as the sum of squares of traveltime differences. Tests on synthetic common-shot data set show that our scheme presented here works as expected. Applications to real marine data set further validates the reasonability and feasibility of our scheme under complex seabed topography. To investigate the reliability of our inversion scheme, we migrate the real 2D data set using the Kirchhoff migration with the inverted Munk profile as the velocity model. The corresponding results show that the seawater velocity obtained by our inversion scheme improves the imaging quality of underwater structures.

A Reconstruction Scheme Using an Average Conductivity Element for Pitting Corrosion Defects in Steam Generator Tubes From Eddy Current Testing Signals

Pitting corrosion is a typical defect in steam generator tubes of nuclear power plants (NPPs) which may cause leak of coolant water in the first circulation loop of an NPP. Different from a crack, the pitting defect has small hole-like geometrical feature, which makes the conventional inversion scheme for crack profile reconstruction using eddy current testing (ECT) signals unsuitable. In this article, a numerical scheme to reconstruct the pitting corrosion defect from ECT signals is proposed and validated, including a new efficient ECT signal forward solver and an iterative inversion algorithm. For efficient calculation of the ECT signals due to a pitting hole, defect model based on a finite element of average conductivity is proposed. The model is validated by comparing its results with those of the conventional finite element method and boundary element method (FEM-BEM) hybrid code of $A$ – $\phi $ formulation using a detailed mesh for a flat-bottom hole. To reconstruct the defect profile such as the depth and diameter, the particle swarm optimization algorithm was adopted to solve the inversion problem iteratively. Finally, ECT experiments were conducted for test piece tubes with artificial pitting defects of different sizes and the defect profile parameters were reconstructed from the measured ECT signals with the proposed numerical schemes. Both the depths and the diameters of the artificial pitting defects, i.e., flat-bottom holes, were properly reconstructed referring to the true defect sizes.

A nonlinear multiscale inversion approach for ambient noise tomography

SUMMARYAmbient noise tomography (ANT) has been considerably used in the last decade in both academic and industrial research. In this work, we propose an innovative technique for ANT based on nonlinear multiscale inversions. Our method relies on a progressive increase in the model parametrization to reduce the nonlinearity of the inverse problem. The developed method is compared with conventional inversion schemes (linear and nonlinear), using different regularization techniques and two different network configurations. The inversion is tested on 22 different synthetic models including classical checkerboard tests. Furthermore, we performed the inversion using real data from a campaign in 2018 at Cumbre Vieja volcano (Canary Islands). The results obtained on both network configurations show an improvement compared to conventional linear and nonlinear inversion schemes, especially when the ray path density is low. This technique does not require expensive computational resources, making it convenient for small-scale industrial applications, especially in the framework of geothermal exploration.

Inversion without Explicit Jacobian Calculations in Electrical Impedance Tomography

Electrical impedance tomography (EIT) is the inverse problem of finding the internal conductivity distribution of a medium given boundary electrical measurements performed via an electrode array onto its surface. Conventional inversion schemes adopt Tikhonov regularized Newton-type methods. Following a transport back-transport approach, we develop in this work an adjoint approach which allows reducing computational burden in enabling inversion without explicit Jacobian calculation. Forward and back-projection operators are defined from potential gradients, along with their efficient implementation. These derivations allow the transparent use of inversion algorithms. We first check the implementation of operators. We then evaluate how reconstructions perform on simulated noisy data using a preconditioned conjugate gradient. We eventually practice our inversion framework on experimental data acquired in vitro from a saline phantom.

DC-Electrical Resistivity Imaging for embankment dike investigation: A 3D extended normalisation approach

Levee, dike and earth embankment dam structures are difficult to assess because of their length and complexity. Managers often include geophysical investigations in the overall dike condition assessment and the DC-Electrical Resistivity Imaging (ERI) method is particularly applicable owing to its cost-effectiveness and its potential sensitivity to internal erosion. However, due to the truly 3D nature of embankment dikes, implementing inline longitudinal tomographies along with conventional 2D inversion is likely to yield image artefacts. 3D effects from external causes (geometry, water reservoir) can be predicted and therefore we present a new approach based on redefining the normalisation principle to derive apparent resistivities from the measured data. The aim is to provide a set of pre-processed apparent resistivities that are not contaminated by external 3D effects and that yield more reliable results when processed within a 2D conventional inversion scheme. The presented approach is successfully applied to synthetic and real data sets, proving superior to the conventional 2D approach, although data acquisition approach is the same thus keeping the same cost-effectiveness.

Geoacoustic inversion based on both acoustic pressure and particle velocity

Conventional inversion schemes for environmental assessment depend on an objective function that exploits amplitude or phase information of acoustic pressure data alone. This work investigates the potential of vector sensors for geoacoustic inversion by defining an objective function that also takes into account acoustic particle motion. Calculations are performed on synthetic broadband data for a shallow water environment (South Elba) with an optimization scheme based on different metaheuristics. Differences in the inversion process, including sensitivity of the cost function to environmental parameters and convergence speed of the optimization algorithm, are presented by comparing inversion results for a sparse pressure-only array and a vector sensor array.

Recursive travel-time inversion: A tool for real-time seismic tomography

Abstract A new recursive inverse scheme is applied to a currently popular problem named seismic travel-time tomography, in order to enhance the efficiency and reliability in obtaining a new velocity model if a small number of new data are added to a large data set in the past. In comparison with conventional inverse schemes in seismic tomography, either least-squares or iterative types, this scheme does not require large amounts of matrix-type computations but utilizes the amount of modification in model parameters responsible for each new data set. We also introduce the computation of a collocation travel time (i.e., from a given station to every grid point) for the reference velocity model inverted by the data for all the past events, using a ray tracing scheme called the Huygens’ method (Saito, 2001), suitable to computations prior to a new event. Combining the above information already stored with the recursive inverse scheme, we can obtain a new or updated velocity model immediately after a new event takes place, because a temporal interval between two events is usually very long in a given local area. Since the model is revised at each recursive step, we perform ray tracings with the updated reference model to get more accurate ray paths and travel times than the conventional inversion schemes that use all the ray tracings for the same reference model. We first showed the validity and stability of the proposed method with synthetic data. We then applied the new approach to the P-wave travel-time data recorded in the Hidaka, south-central Hokkaido, Japan, region, and compared our result with other previous results. Our result shares the overall feature with the previous ones. In addition, a new low-velocity zone is detected in the east of the Hidaka mountains at the depth of 10 km, corresponding to the collision zone of two arcs, due to the use of the updated reference velocity model at each recursive step. We also confirmed that the order of data does not affect the final result, so that the present approach is shown as an appropriate tool for so-called real-time seismic tomography: a updated velocity model is immediately obtained at each time that a new event takes place, in order to monitor temporal variations of model parameters such as velocity structure on the real-time basis.

An inversion scheme to model subsurface fracture systems using shear wave splitting polarization and delay time observations simultaneously

SUMMARY Shear wave splitting polarization (p) and delay time (Δt) observations are used to invert for fracture orientation and intensity of fracturing, simultaneously. By addressing the different levels of uncertainty involved in measurements of these two parameters, as well as their dissimilar relationships to fracture configuration, we have developed an inversion algorithm which reduces the primary double-response inversion to two connected single-response ones. We show that its inherent non-linearity complicates this problem, which therefore requires a more sophisticated attack than conventional inversion schemes. It will be shown that the construction of residue function contours in the model plane and the generation of surrogate data by simulation process are essential to this approach. We illustrate the capabilities of this technique by inverting shear wave splitting data from The Geysers geothermal reservoir in California. In principle the method should be useful for characterizing fractured reservoirs, whether geothermal or hydrocarbon.