On Quadratic Wasserstein Metric with Squaring Scaling for Seismic Velocity Inversion

The quadraticWasserstein metric has shown its power in comparing prob-ability densities.It is successfully applied in waveform inversion by generating ob-jective functions robust to cycle skipping and insensitive to data noise.As an alter-native approach that converts seismic signals to probability densities,the squaring scaling method has good convexity and thus is worth exploring.In this work,we apply the quadratic Wasserstein metric with squaring scaling to regional seismic to-mography.However,there may be interference between different seismic phases in a broad time window.The squaring scaling distorts the signal by magnifying the unbalance of the mass of different seismic phases and also breaks the linear super-position property.As a result,illegal mass transportation between different seismic phases will occur when comparing signals using the quadratic Wasserstein metric.Furthermore,it gives inaccurate Fr´echet derivative,which in turn affects the inver-sion results.By combining the prior seismic knowledge of clear seismic phase sep-aration and carefully designing the normalization method,we overcome the above problems.Therefore,we develop a robust and efficient inversion method based on optimal transport theory to reveal subsurface velocity structures.Several numerical experiments are conducted to verify our method.

Crustal velocity structure of central Gansu Province from regional seismic waveform inversion using firework algorithm

The firework algorithm（FWA） is a novel swarm intelligence-based method recently proposed for the optimization of multi-parameter, nonlinear functions. Numerical waveform inversion experiments using a synthetic model show that the FWA performs well in both solution quality and efficiency. We apply the FWA in this study to crustal velocity structure inversion using regional seismic waveform data of central Gansu on the northeastern margin of the Qinghai-Tibet plateau. Seismograms recorded from the moment magnitude（MW） 5.4 Minxian earthquake enable obtaining an average crustal velocity model for this region. We initially carried out a series of FWA robustness tests in regional waveform inversion at the same earthquake and station positions across the study region,inverting two velocity structure models, with and without a low-velocity crustal layer; the accuracy of our average inversion results and their standard deviations reveal the advantages of the FWA for the inversion of regional seismic waveforms. We applied the FWA across our study area using three component waveform data recorded by nine broadband permanent seismic stations with epicentral distances ranging between 146 and 437 km. These inversion results show that the average thickness of the crust in this region is 46.75 km, while thicknesses of the sedimentary layer, and the upper, middle, and lower crust are 3.15,15.69, 13.08, and 14.83 km, respectively. Results also show that the P-wave velocities of these layers and the upper mantle are 4.47, 6.07, 6.12, 6.87, and 8.18 km/s,respectively.

Integrative method in lithofacies characteristics and 3D velocity volume of the Permian igneous rocks in H area, Tarim Basin

This paper introduces horizon control, seismic control, logging control and facies control methods through the application of the least squares fitting of logging curves, seismic inversion and facies-controlled techniques. Based on the microgeology and thin section analyses, the lithology, lithofacies and periods of the Permian igneous rocks are described in detail. The seismic inversion and facies-controlled techniques were used to find the distribution characteristics of the igneous rocks and the 3D velocity volume. The least squares fitting of the logging curves overcome the problem that the work area is short of density logging data. Through analysis of thin sections, the lithofacies can be classified into eruption airfall subfacies, eruption pyroclastic flow subfacies and eruption facies.

Applying accurate gradients of seismic wave reflection coefficients (SWRC) to the inversion of seismic wave velocities

Through solving the Zoeppritz's partial derivative equations, we have obtained accurate partial derivatives of reflected coefficients of seismic wave with respect to Pand S-wave velocities.With those partial derivatives, a multi-angle inversion is developed for seismic wave velocities.Numerical examples of different formation models show that if the number of iterations goes over 10, the relative error of inversion results is less than 1%, whether or not there is interference among the reflection waves.When we only have the reflected seismograms of P-wave, and only invert for velocities of P-wave, the multi-angle inversion is able to obtain a high computation precision.When we have the reflected seismograms of both P-wave and VS-wave, and simultaneously invert for the velocities of P-wave and VS-wave, the computation precisions of VS-wave velocities improves gradually with the increase of the number of angles, but the computation precision of P-wave velocities becomes worse.No matter whether the reflected seismic waves from the different reflection interface are coherent or non-coherent, this method is able to achieve a higher computation precision.Because it is based on the accurate solution of the gradient of SWRCs without any additional restriction, the multi-angle inversion method can be applied to seismic inversion of total angles.By removing the difficulties caused by simplified Zoeppritz formulas that the conventional AVO technology struggles with, the multiangle inversion method extended the application range of AVO technology and improved the computation precision and speed of inversion of seismic wave velocities.