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Filtering Unevenly Spaced Geophysical Time Series as an Ill-Posed Problem.

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Title: Filtering Unevenly Spaced Geophysical Time Series as an Ill-Posed Problem.
Authors: Ji, Kunpu1 (AUTHOR), Zhang, Lin1 (AUTHOR), Wang, Fengwei1 (AUTHOR) wangfw-foster@tongji.edu.cn
Source: Surveys in Geophysics. Feb2026, Vol. 47 Issue 1, p23-59. 37p.
Subject Terms: *Irregular sampling (Signal processing), *Time series analysis, *Interpolation, *Signal reconstruction, *Signal processing, *Global Positioning System, *Least squares
Abstract: Irregularly sampled geophysical time series are common in practice due to data gaps caused by sensor outages, environmental disturbances, or quality control procedures. Conventional digital filters, such as Fourier filters, require complete time series data and therefore cannot be directly applied to unevenly spaced noisy data without prior interpolation. In this study, we demonstrate that filtering unevenly spaced time series using Fourier filtering is inherently an ill-posed problem, manifested as rank deficiency in the associated parametric model. Building on this insight, we propose a minimum norm least squares Fourier filtering (MFF) that processes unevenly spaced time series without the need for preliminary data interpolation. Additionally, the prior covariance matrix of the time series is incorporated to further improve the filtering performance. We first apply the proposed method to extract deformation signals from daily position time series of 27 global navigation satellite system (GNSS) monitoring stations across the mainland China spanning from 1999 to 2024. The performance of MFF is compared with conventional Fourier filtering (CFF) with interpolation. The results demonstrate that MFF outperforms CFF, especially when prior precision is considered, as evidenced by a smaller fitting error of the extracted signals. Simulations confirm that signals recovered by MFF are closer to the true signals, with root mean square error (RMSE) reductions of 12.3 to 19.4% across the 27 stations, depending on the percentage of missing data. Incorporating formal errors provides an additional average RMSE reduction of 2.9%. Finally, we apply MFF to retrieve mass change signals from monthly gravity recovery and climate experiment (GRACE) and GRACE-FO gravity field solutions. The results agree with those from GNSS time series and show that MFF outperforms CFF in extracting components within desired frequency bands. [ABSTRACT FROM AUTHOR]
Database: Energy & Power Source
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  Availability: 0
Header DbId: enr
DbLabel: Energy & Power Source
An: 192011109
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Label: Title
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  Data: Filtering Unevenly Spaced Geophysical Time Series as an Ill-Posed Problem.
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  Data: <searchLink fieldCode="AR" term="%22Ji%2C+Kunpu%22">Ji, Kunpu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhang%2C+Lin%22">Zhang, Lin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wang%2C+Fengwei%22">Wang, Fengwei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wangfw-foster@tongji.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Surveys+in+Geophysics%22">Surveys in Geophysics</searchLink>. Feb2026, Vol. 47 Issue 1, p23-59. 37p.
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  Data: *<searchLink fieldCode="DE" term="%22Irregular+sampling+%28Signal+processing%29%22">Irregular sampling (Signal processing)</searchLink><br />*<searchLink fieldCode="DE" term="%22Time+series+analysis%22">Time series analysis</searchLink><br />*<searchLink fieldCode="DE" term="%22Interpolation%22">Interpolation</searchLink><br />*<searchLink fieldCode="DE" term="%22Signal+reconstruction%22">Signal reconstruction</searchLink><br />*<searchLink fieldCode="DE" term="%22Signal+processing%22">Signal processing</searchLink><br />*<searchLink fieldCode="DE" term="%22Global+Positioning+System%22">Global Positioning System</searchLink><br />*<searchLink fieldCode="DE" term="%22Least+squares%22">Least squares</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Irregularly sampled geophysical time series are common in practice due to data gaps caused by sensor outages, environmental disturbances, or quality control procedures. Conventional digital filters, such as Fourier filters, require complete time series data and therefore cannot be directly applied to unevenly spaced noisy data without prior interpolation. In this study, we demonstrate that filtering unevenly spaced time series using Fourier filtering is inherently an ill-posed problem, manifested as rank deficiency in the associated parametric model. Building on this insight, we propose a minimum norm least squares Fourier filtering (MFF) that processes unevenly spaced time series without the need for preliminary data interpolation. Additionally, the prior covariance matrix of the time series is incorporated to further improve the filtering performance. We first apply the proposed method to extract deformation signals from daily position time series of 27 global navigation satellite system (GNSS) monitoring stations across the mainland China spanning from 1999 to 2024. The performance of MFF is compared with conventional Fourier filtering (CFF) with interpolation. The results demonstrate that MFF outperforms CFF, especially when prior precision is considered, as evidenced by a smaller fitting error of the extracted signals. Simulations confirm that signals recovered by MFF are closer to the true signals, with root mean square error (RMSE) reductions of 12.3 to 19.4% across the 27 stations, depending on the percentage of missing data. Incorporating formal errors provides an additional average RMSE reduction of 2.9%. Finally, we apply MFF to retrieve mass change signals from monthly gravity recovery and climate experiment (GRACE) and GRACE-FO gravity field solutions. The results agree with those from GNSS time series and show that MFF outperforms CFF in extracting components within desired frequency bands. [ABSTRACT FROM AUTHOR]
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=enr&AN=192011109
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s10712-025-09924-5
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 37
        StartPage: 23
    Subjects:
      – SubjectFull: Irregular sampling (Signal processing)
        Type: general
      – SubjectFull: Time series analysis
        Type: general
      – SubjectFull: Interpolation
        Type: general
      – SubjectFull: Signal reconstruction
        Type: general
      – SubjectFull: Signal processing
        Type: general
      – SubjectFull: Global Positioning System
        Type: general
      – SubjectFull: Least squares
        Type: general
    Titles:
      – TitleFull: Filtering Unevenly Spaced Geophysical Time Series as an Ill-Posed Problem.
        Type: main
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          Name:
            NameFull: Ji, Kunpu
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            NameFull: Zhang, Lin
      – PersonEntity:
          Name:
            NameFull: Wang, Fengwei
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          Dates:
            – D: 01
              M: 02
              Text: Feb2026
              Type: published
              Y: 2026
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              Value: 01693298
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              Value: 47
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              Value: 1
          Titles:
            – TitleFull: Surveys in Geophysics
              Type: main
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