Imaging the Earth Using Time‐Domain Surface‐Wave Measurements: Evaluation and Correction of the Finite‐Frequency Phase Shift. Issue 5 (12th May 2022)

• Record Type: Journal Article
• Authors: Xu, Yihe; Lebedev, Sergei; Meier, Thomas
• Is Part Of: Journal of geophysical research. Volume 127:Issue 5(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-05-12
• Subjects: surface wave -- phase shift -- phase velocity measurement -- noise interferometry; Geomagnetism -- Periodicals; Geochemistry -- Periodicals; Geophysics -- Periodicals; Earth sciences -- Periodicals; 551.1
• DOI: 10.1029/2021JB023701
• Languages: English
• ISSNs: 2169-9313

Abstract

Abstract: Surface waves propagating from earthquakes, active sources or within the ambient noise wavefield are widely used to image Earth structure at various scales, from centimeters to hundreds of kilometers. The accuracy of surface‐wave, phase‐velocity measurements is essential for the accuracy of the Earth models they constrain. Here, we identify a finite‐frequency phase shift in the phase travel time that causes systematic errors in time‐domain, phase‐velocity measurements. The phase shift arises from the approximation of monochromatic surface waves with narrow‐band filtered surface waves. We derive an explicit formula of the finite‐frequency phase shift and present a numerical method for its evaluation and for the correction of the measurements. Applications to high‐frequency and long‐period examples show that the phase shift is typically around π/60‐π/16 for the common settings of ambient‐noise imaging studies, which translates to 0.2%–0.8% phase‐velocity measurement errors. The finite‐frequency phase shift depends on the (a) second derivative of the wavenumber with respect to frequency; (b) width of the narrow‐band filter; (c) epicentral or interstation distance; and (d) center frequency of the filter. In conversion to phase velocity, the last two factors cancel out. Frequency‐domain methods for phase‐velocity measurements have the advantage of not producing the finite‐frequency phase shift. Both time‐ and frequency‐domain measurements, however, can be impacted by a break‐down of the far‐field approximation (near‐field phase shift), which our calculations also show. Our method offers an effective means of improving the accuracy of the widely used time‐domain, phase‐velocity measurements via the evaluation of and corrections for the finite‐frequency phase shift. Plain Language Summary: Surface waves sample the "surface layer" of the Earth with the thickness of the layer depending on the wave's wavelength. Combining surface waves of different wavelengths, or different frequencies, can provide a detailed image of the Earth's structure over a large depth range. Measuring the velocity at which surface waves travel is a crucial step in this process. In this study, we identify a source of errors in the measurements that has not received much notice so far. We first derive a formula for the possible bias and then develop a numerical method to evaluate and correct it. Applications of the numerical method reveal the effects of the bias in two common scenarios, in the surface‐wave studies of the shallow (kilometers deep) and deep (hundreds of kilometers deep) structure of the Earth. Our results provide a means to improve the accuracy of the surface wave measurements and, thus, the accuracy of the surface‐wave imaging of the Earth. Key Points: We identify a source of errors that can cause 0.2%–0.8% error in surface‐wave phase‐velocity measurements The error applies to all the time‐domain methods that use bandpass‐filtered waveforms We derive an explicit formula to evaluate the error and provide a numerical method to compute and remove it