InSAR Detection of Slow Ground Deformation: Taking Advantage of Sentinel-1 Time Series Length in Reducing Error Sources
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis manuscript proposes a novel SBAS deformation inversion strategy that leverages long temporal baselines and short perpendicular baselines to mitigate atmospheric effects and unwrapping errors, thereby improving the minimum detectable deformation velocity. While the approach presents some degree of innovation, several aspects of the current presentation lack clarity and need to be addressed:
- Lines 124–127: The authors state that for C-band data under single-look conditions, when coherence is 0.1, the deformation standard deviation is 6 mm. They further infer that deformation below 6 mm cannot be detected, while deformation above 6 mm can. This conclusion is misleading. For example, in extreme cases where coherence approaches zero, the deformation standard deviation could be even larger, but the phase becomes completely meaningless. Hence, it is incorrect to claim that deformation greater than a certain threshold is detectable. This assumption, which appears multiple times in the manuscript, is flawed and requires proper justification.
- Lines 179–180: The manuscript claims that the proposed LSTPB method reduces the sensitivity of SBAS to atmospheric phase screens. However, the explanation is fragmented and difficult to follow. The authors should provide a more coherent theoretical rationale explaining why and how LSTPB effectively suppresses atmospheric effects.
- Lines 209–211: The statement that “robust SBAS should use differential interferograms where the atmospheric phase screen is greater than δα” is unclear. What is the basis for this statement, and how should it be interpreted? This sentence, in its current form, is confusing and should be clarified or better supported.
- Section 4: The authors argue that LSTPB can reduce the impact of phase unwrapping errors. However, longer time intervals typically lead to denser fringes and more severe unwrapping issues. Therefore, the authors need to explain the theoretical mechanism by which LSTPB reduces unwrapping errors. This point currently lacks adequate justification.
Author Response
Major Comments:
Comment 1: Lines 124–127: The authors state that for C-band data under single-look conditions, when coherence is 0.1, the deformation standard deviation is 6 mm. They further infer that deformation below 6 mm cannot be detected, while deformation above 6 mm can. This conclusion is misleading. For example, in extreme cases where coherence approaches zero, the deformation standard deviation could be even larger, but the phase becomes completely meaningless. Hence, it is incorrect to claim that deformation greater than a certain threshold is detectable. This assumption, which appears multiple times in the manuscript, is flawed and requires proper justification.
Response 1: We thank the reviewer for this insight and have revised the text to explain our rationale. We state that for all cases, long-term coherence is required for the method, i.e., not coherence approaching zero, and have modified lines 124 to 127 to reflect this. We have also revised line 127 to add clarity as to what is intended to be InSAR measurement error for only decorrelation:
“Neglecting sources of noise, including inherent noise and thermal noise of the SAR sensor, coherence determines the smallest measurement that can be achieved by an interferogram.”
Comment 2: Lines 179–180: The manuscript claims that the proposed LSTPB method reduces the sensitivity of SBAS to atmospheric phase screens. However, the explanation is fragmented and difficult to follow. The authors should provide a more coherent theoretical rationale explaining why and how LSTPB effectively suppresses atmospheric effects.
Response 2: We have added the following text to Section 3 that describes our analyses framework (lines 176 to 185):
“Below, we first determine the minimum detectable phase measurement with regards to only the tropospheric phase delay error. This is accomplished by evaluating the signal-to-noise ratio required for a robust SBAS solution by determining the total error introduced by the tropospheric phase delay in a set of interferograms. We then demonstrate, using real-world total tropospheric phase delay from the GNSS Zenith Total Delay, that LTSPB interferograms are capable of measuring differential phases that exceed this source of noise and achieve velocity detection thresholds of 2 mm yr-1 to 3 mm yr-1. Then we show, via simulation of tropospheric phase delay error, that the LTSPB interferograms do exceed the tropospheric phase delay error and provide robust SBAS-derived time series solutions.”
Comment 3: Lines 209–211: The statement that “robust SBAS should use differential interferograms where the atmospheric phase screen is greater than δα” is unclear. What is the basis for this statement, and how should it be interpreted? This sentence, in its current form, is confusing and should be clarified or better supported.
Response 3: We thank the reviewer for this comment but we believe there may be some misattribution of this comment to the sentence. The sentence is “Considering the signal-to-noise ratio (Equation 4), a robust SBAS time series solution should use differential phase measurements that are greater than . “
Comment 4: Section 4: The authors argue that LSTPB can reduce the impact of phase unwrapping errors. However, longer time intervals typically lead to denser fringes and more severe unwrapping issues. Therefore, the authors need to explain the theoretical mechanism by which LSTPB reduces unwrapping errors. This point currently lacks adequate justification.
Response 4: This is correct for fast deformation rates. However, the LTSPBP method is ideal for slow to medium deformation rates, which is why the manuscript emphasizes the possible velocity detection threshold of LTSPB. We have added “The LTSPB strategy excels at measuring slow rates of deformation.” to the introduction of the Discussion section (line 446).
Reviewer 2 Report
Comments and Suggestions for AuthorsDear authors, thank you for your manuscript. It concerns improving the SBAS-InSAR results by incorporating image pairs with long temporal, but very short perpendicular baseline.
The article is sometimes difficult to understand.
I appreciate the discussion, where the limits of the proposed method are discussed together with the proposed procedures to overcome the limits.
I also appreciate the analysis and derivation of the APS errors.
However, a basic question I did not understand from the manuscript: why to use SBAS technique, if aiming and long-term coherent scatterers and having a long-term dataset? Why PSInSAR should not be used in this case, which allows to detect even slower displacements?
Figure 1: do you distinguish temporal and spatial coherence? In the text, you usually refer to temporal coherence, but I suppose in this figure it is the spatial one.
Moreover, in the methodology description, it is not clear if you use only the LTSPB interferograms, or if you combine them with SBAS. This is clear only much later in the result description.
Section 2: "coherence phase noise" - should i t be "coherence and phase noise"?
Section 3.1: APS estimation from interferograms (SBAS): is the APS estimated for each interferogram independently, or is that then adapted to correspond to each image? If for each image, formulas (5,6) do not apply. Moreover, in the derivation of APS estimation effects, could you please distinguish bias and noise? I think that errors in APS estimation cause rather noise (in the final time series) than bias.
Minor issues:
- there is a mistake in dates in Figure 1 description
- lines 72-74 to be re-formulated
- line 83: "5m" -> "<5m" ?
- line 89: backscatters -> scatterers?
- line 91: phase noise due to long-term coherence (reformulate)
- lines 93-94: LTSPB is only useful in areas covered by PS
- lines 115-116: coherence determines the smallest measurement (??)
- lines 121-122: what does it mean to create interferograms with PS method?
- lines 139-140: temporal coherence noise is Gaussian and zero mean; please reformulate. temporal coherence does not have zero mean
- table 1 seems to be too wide for the page
- line 257: zero mean normal distribution temporal coherence
- line 376: wrong date
- line 376: Permanent -> Persistent
Author Response
Major Comments:
Comment 1: Why to use SBAS technique, if aiming and long-term coherent scatterers and having a long-term dataset?
Response 1: We suggest including SB interferograms if a study also requires investigating transient events that might be aliased over by the long-temporal baselines. The aim of LTSPB is to measure slow probably monotonic deformation. The following text has been added to the Introduction (line 127 to 128):
“It is also possible to use LTSPB interferograms with Distributed Scatters if there are sufficient long-term coherence scatters (see Appendix B).”
Text has also been added to the Methods Section (only mention of complementing LSTPSB with full SB interferograms) to further clarify this (line 389):
“It should be noted that the LTSPB method does not require SB interferograms when observing slow deformation rates”
Comment 2: Why PSInSAR should not be used in this case, which allows to detect even slower displacements?
Response 2: PS-InSAR is still constrained by InSAR measurement error. PS and SB have been combined in the Multi-temporal method (Hooper 2008) and take advantage of the high resolution/low error pixels and spatial coverage. Our method is not similar to PS interferometric pair selection, and we have added text clarifying this (lines 124 to 128).
Comment 3: Figure 1: do you distinguish temporal and spatial coherence? In the text, you usually refer to temporal coherence, but I suppose in this figure it is the spatial one.
Response 3: We thank the reviewer for highlighting this oversight. While the figure does not mention temporal coherence, there is text surrounding the figure that does so incorrectly. We mean “coherence due to temporal baseline”. This has been fixed throughout the manuscript.
Comment 4: Moreover, in the methodology description, it is not clear if you use only the LTSPB interferograms, or if you combine them with SBAS. This is clear only much later in the result description.
Response 4: We have added the following text to the Methodology to emphasize that SB interferograms are not needed (line 389):
“It should be noted that the LTSPB method does not require SB interferograms when observing slow deformation rates. “
Comment 5: Section 2: "coherence phase noise" - should it be "coherence and phase noise"?
Response 5: Coherence phase noise is correct. To emphasize this, we have added to the Introductory paragraph that the phase noise is associated with decorrelation.
Comment 6: Section 3.1: APS estimation from interferograms (SBAS): is the APS estimated for each interferogram independently, or is that then adapted to correspond to each image? If for each image, formulas (5,6) do not apply. Moreover, in the derivation of APS estimation effects, could you please distinguish bias and noise? I think that errors in APS estimation cause rather noise (in the final time series) than bias.
Response 6: We thank the reviewer for this comment. We state in line 190:
“… the phase delay difference in two-pass interferometry is called the Atmospheric Phase Screen (APS). “
Equations 6 and 7 represent the total propagated APS error from the set of interferograms used in an SBAS solution. It should be considered a component of the formal error as opposed to the RMS error from the least squares solution. We modified line 209 to reflect this.
When we refer to bias, we refer to the SBAS-estimated time series. We do agree that the APS affects the variance, or noise, of the time series. However, outliers introduced by the APS do create a bias in the estimated velocity because the SBAS least squares formulation solves the incremental displacement between acquisitions. Please refer to Appendix D, Figure D1b and D1c. There is no introduced deformation but the velocity field has a bias of 3 mm/yr due to APS. In the text, we have added a reference to Appendix D.
Minor comments:
Comment 1: There is a mistake in dates in Figure 1 description
Response: Fixed
Comment 2: lines 72-74 to be re-formulated
Response: Fixed. Has been rewritten for clarity.
Comment 3: line 83: "5m" -> "<5m" ?
Response 3: Fixed
Comment 4: line 89: backscatters -> scatterers?
Response 4: Fixed
Comment 5: line 91: phase noise due to long-term coherence (reformulate)
Response 5: We have added the following text: “, i.e., decorrelation,”
Comment 6: lines 93-94: LTSPB is only useful in areas covered by PS
Response 6: This is true but we only address the robustness of the LTSPB time series estimation compared to that of SB. We also introduce using LSTPB using DS in Appendix B of the manuscript. We’ve added text to the Introduction to make this clear (lines 127 to 128).
Comment 7: lines 115-116: coherence determines the smallest measurement (??)
Response: Fixed. In this Section of the manuscript, we only consider the phase noise due to temporal baseline decorrelation and have modified the text in line 130 to explicitly state this: “That is, the patch of pixels will not be able to resolve a phase difference of 6 mm or lower, even if there are no other sources of error.“
Comment 8: lines 121-122: what does it mean to create interferograms with PS method?
Response 8: Fixed. We have added text that emphasizes the multi-temporal PS approach to disambiguate from the PS method of one primary to several secondary (lines 124 to 128).
Comment 9:lines 139-140: temporal coherence noise is Gaussian and zero mean; please reformulate. temporal coherence does not have zero mean
Response 9: Fixed.
Comment 10: table 1 seems to be too wide for the page
Response 10: We hope that this is addressed during the final formatting of the article.
Comment 11: line 257: zero mean normal distribution temporal coherence
Response 11: Fixed
Comment 12: line 376: wrong date
Response: Fixed
Comment 13: line 376: Permanent -> Persistent
Response 13: Fixed
Reviewer 3 Report
Comments and Suggestions for AuthorsThe paper is very well written and presents a comprehensive and insightful study on the use of LTSPB interferograms for mitigating common sources of error in InSAR analysis, particularly tropospheric delays and phase unwrapping errors. The authors clearly articulate the motivation behind the work and provide a well-structured methodology that is easy to follow and technically sound.
One of the major strengths of this work is its clarity in demonstrating how LTSPB interferograms can significantly improve the reliability and accuracy of InSAR measurements. The discussion on error sources is thorough, and the way the authors connect theoretical concepts with practical implementation is commendable. The results are compelling and well supported by figures and analysis, and the conclusions are appropriately grounded in the data presented.
Figure 1: There is a minor inconsistency in the caption for part (d), where the perpendicular baseline is listed as 1.5 m, while the figure itself mentions 2 m. Please update one of these to maintain consistency.
Additionally, in line 77, I recommend including a reference to phase triplet error. Since it is an important concept in understanding phase inconsistencies across interferogram networks, a citation here would enhance the technical robustness of the discussion and provide helpful context for readers less familiar with the term.
Overall, this is a strong and well-executed paper that makes a valuable contribution to the field. With minor corrections, it will be well suited for publication.
Author Response
Minor comments
Comment 1: Figure 1: There is a minor inconsistency in the caption for part (d), where the perpendicular baseline is listed as 1.5 m, while the figure itself mentions 2 m. Please update one of these to maintain consistency.
Response 1: Accepted
Comment 2: Additionally, in line 77, I recommend including a reference to phase triplet error. Since it is an important concept in understanding phase inconsistencies across interferogram networks, a citation here would enhance the technical robustness of the discussion and provide helpful context for readers less familiar with the term.
Response 2: Fixed. We have added citations that provide good overviews of this problem ( Agram & Simons, 2015; Zheng et al 2022).
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsOverall, the authors did not adequately address the issues raised in my previous review. The responses are overly brief and lack clarity and structure. A proper reply should start with a clear and concise answer to each question, followed by a detailed list of corresponding revisions made in the manuscript. Specific concerns are as follows:
- Regarding Question 1, the authors stated that “coherence determines the smallest measurement that can be achieved by an interferogram.” What exactly is meant by "smallest measurement"? Does it refer to measurement resolution? In fact, the measurement resolution of InSAR is determined by parameters such as baseline length and wavelength. Coherence mainly affects the measurement accuracy. This needs to be clarified.
- Regarding Question 2, it is unnecessary to simply add a description of subsequent processing steps. The authors should instead explain, based on theoretical principles, why the method reduces sensitivity to atmospheric phase delays.
- Regarding Question 4, it remains unclear why the LSTPB method is able to reduce phase unwrapping errors in cases of slow or moderate deformation rates. The underlying mechanism should be explained more clearly.
Author Response
Comment 1: Regarding Question 1, the authors stated that “coherence determines the smallest measurement that can be achieved by an interferogram.” What exactly is meant by "smallest measurement"? Does it refer to measurement resolution? In fact, the measurement resolution of InSAR is determined by parameters such as baseline length and wavelength. Coherence mainly affects the measurement accuracy. This needs to be clarified.
Response 1: The reviewer is correct. Throughout the manuscript, what we describe as a detectable measurement, i.e., above measurement uncertainty, is in fact the accuracy of InSAR measurements. Decorrelation (baseline, uncorrelated, and correlated coherence) is a source of phase noise. Disregarding all other sources of error (tropospheric, sensor, dem) coherence will determine the smallest detectable differential phase, i.e., the measurement that exceeds the phase noise due to coherence. We have modified Section 2 to use the correct nomenclature.
Comment 2: Regarding Question 2, it is unnecessary to simply add a description of subsequent processing steps. The authors should instead explain, based on theoretical principles, why the method reduces sensitivity to atmospheric phase delays.
Response 2: We thank the reviewer for the comment but disagree. The reviewer may have overlooked lines 226 to 227 in the manuscript that describes that there is no general analytical description of tropospheric phase delay that accounts for varying 2D turbulence, vertical stratification, etc. Therefore, there is no general comparison between LTSPB measurements and APS noise. We do not describe processing steps but instead establish the efficacy of the LTSPB method for providing robust SBAS solutions from a least squares perspective by increasing the signal-to-noise ratio. The manuscript describes the signal-to-noise ratio as the expected value of the squared norm of the observed differential phases vector over the total error, in this case, only due to APS. The manuscript then describes what is the propagated total error of the APS for a set of interferograms. This allows for a quantitative comparison between LTSPB differential phase and total APS error from the set of interferograms. Unfortunately, deriving an analytical expression that quantifies the total APS is intractable and, if one were to derive such an expression, it would not prove to be useful in the general sense because of the extremes of parameter values in the real world. Instead, we show statistically that LTSPB interferograms increase the signal-to-noise ratio using real data from GNSS Zenith Total Delay from regions that represent end members of tropospheric phase delay characteristics. We then prove this via simulated interferograms and subsequent SBAS estimated time series.
Comment 3: Regarding Question 4, it remains unclear why the LSTPB method is able to reduce phase unwrapping errors in cases of slow or moderate deformation rates. The underlying mechanism should be explained more clearly.
Response 3: Like comment #2 we treat the analysis of unwrapping errors and LTSPB interferograms with respect to the least squares framework for SBAS time series estimation. The manuscript states that unwrapping errors are outlier errors and previous studies have treated this error source in the same manner (cited in text; see Fattahi et al., 2015; Xu et al., 2020). Least squares minimizes the sum of squared residuals, and unwrapping errors present as large outliers of N2π radians. That is, they have a significant influence on the SBAS solution if the differential phases observed are much smaller, which is always the case. LTSPB observed differential phases are larger than SB, and, thus, do not remove unwrapping errors (outliers) but minimize their influence on the SBAS solution.
