TY - JOUR
T1 - The exponentiated phase measurement, and objective-function hybridization for adjoint waveform tomography
AU - Yuan, Yanhua O.
AU - Bozdaǧ, Ebru
AU - Ciardelli, Caio
AU - Gao, Fuchun
AU - Simons, F. J.
N1 - Funding Information:
This paper grew out of early discussions with Jeannot Trampert on combining different phase measurements in adjoint tomography. We thank Ryan Modrak and Jeroen Tromp for fruitful discussions. We also thank Ridvan Orsvuran for computing the global kernels. The open-source spectral-element software package SPECFEM and the automated window-selection package FLEXWIN are freely available from the Computational Infrastructure for Geodynamics (www.geodynamics.org). We gratefully acknowledge the computational resources provided by the Princeton Institute for Computational Science & Engineering (PICSciE). CC thanks the Fundac¸ão de Amparo à Pesquisa do Estado de São Paulo (FAPESP 2018/04918-6) for providing the financial support for his PhD studies, and FJS thanks the U.S. National Science Foundation (EAR 1736046), the King Abdullah University of Science and Technology (OSR-2016-CRG5-2970-01) and TOTAL EP Research and Technology for financial support, as well as the Institute for Advanced Study in Princeton for a quiet yet stimulating work environment during 2018–2019. The authors thank the Global Seismographic Network (GSN) for making data available. We would like to thank the editor, Dr Martin Schimmel, and two anonymous reviewers for their careful reading and constructive suggestions, which have helped improve the manuscript. Our computer codes are available from https://github.com/yanhuay/seisEP.
Publisher Copyright:
© The Author(s) 2020. Published by Oxford University Press on behalf of The Royal Astronomical Society.
PY - 2020/1/29
Y1 - 2020/1/29
N2 - Seismic tomography has arrived at the threshold of the era of big data. However, how to extract information optimally from every available time-series remains a challenge; one that is directly related to the objective function chosen as a distance metric between observed and synthetic data. Time-domain cross-correlation and frequency-dependent multitaper traveltime measurements are generally tied to window selection algorithms in order to balance the amplitude differences between seismic phases. Even then, such measurements naturally favour the dominant signals within the chosen windows. Hence, it is difficult to select all usable portions of seismograms with any sort of optimality. As a consequence, information ends up being lost, in particular from scattered waves. In contrast, measurements based on instantaneous phase allow extracting information uniformly over the seismic records without requiring their segmentation. And yet, measuring instantaneous phase, like any other phase measurement, is impeded by phasewrapping. In this paper,we address this limitation by using a complex-valued phase representation that we call 'exponentiated phase'. We demonstrate that the exponentiated phase is a good substitute for instantaneous-phase measurements. To assimilate as much information as possible from every seismogram while tackling the non-linearity of inversion problems, we discuss a flexible hybrid approach to combine various objective functions in adjoint seismic tomography. We focus on those based on the exponentiated phase, to take into account relatively small-magnitude scattered waves; on multitaper measurements of selected surface waves; and on cross-correlation measurements on specific windows to select distinct body-wave arrivals. Guided by synthetic experiments, we discuss how exponentiated-phase, multitaper and cross-correlation measurements, and their hybridization, affect tomographic results. Despite their use of multiple measurements, the computational cost to evaluate gradient kernels for the objective functions is scarcely affected, allowing for issues with data quality and measurement challenges to be simultaneously addressed efficiently.
AB - Seismic tomography has arrived at the threshold of the era of big data. However, how to extract information optimally from every available time-series remains a challenge; one that is directly related to the objective function chosen as a distance metric between observed and synthetic data. Time-domain cross-correlation and frequency-dependent multitaper traveltime measurements are generally tied to window selection algorithms in order to balance the amplitude differences between seismic phases. Even then, such measurements naturally favour the dominant signals within the chosen windows. Hence, it is difficult to select all usable portions of seismograms with any sort of optimality. As a consequence, information ends up being lost, in particular from scattered waves. In contrast, measurements based on instantaneous phase allow extracting information uniformly over the seismic records without requiring their segmentation. And yet, measuring instantaneous phase, like any other phase measurement, is impeded by phasewrapping. In this paper,we address this limitation by using a complex-valued phase representation that we call 'exponentiated phase'. We demonstrate that the exponentiated phase is a good substitute for instantaneous-phase measurements. To assimilate as much information as possible from every seismogram while tackling the non-linearity of inversion problems, we discuss a flexible hybrid approach to combine various objective functions in adjoint seismic tomography. We focus on those based on the exponentiated phase, to take into account relatively small-magnitude scattered waves; on multitaper measurements of selected surface waves; and on cross-correlation measurements on specific windows to select distinct body-wave arrivals. Guided by synthetic experiments, we discuss how exponentiated-phase, multitaper and cross-correlation measurements, and their hybridization, affect tomographic results. Despite their use of multiple measurements, the computational cost to evaluate gradient kernels for the objective functions is scarcely affected, allowing for issues with data quality and measurement challenges to be simultaneously addressed efficiently.
KW - Inverse theory
KW - Seismic tomography
KW - Time-series analysis
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U2 - 10.1093/gji/ggaa063
DO - 10.1093/gji/ggaa063
M3 - Article
AN - SCOPUS:85082065698
SN - 0956-540X
VL - 221
SP - 1145
EP - 1164
JO - Geophysical Journal International
JF - Geophysical Journal International
IS - 2
ER -