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- Title
A Hybrid Normal Mode‐Collocation Method for Finding the Response of Laterally Homogeneous Compressible Maxwell Viscoelastic Earth Models.
- Authors
Brierley‐Green, Connor; James, Thomas S.
- Abstract
Normal mode analysis is a Laplace‐transform method for calculating the surface‐loading response of laterally homogeneous spherical Earth models with linear viscoelasticity which delivers modal decay times and amplitudes. It can locally fail owing to numerical singularities arising from the viscoelastic parameters, leading to an incomplete accounting of the surface‐loading response. Collocation methods were developed to circumvent this issue. The mixed collocation method includes least‐squares fitting to the Laplace‐transformed Earth response to determine amplitudes assuming the normal mode decay times are known, while the pure collocation method assumes a series of logarithmically regularly spaced inverse decay times for which amplitudes are determined numerically. Both collocation methods may determine amplitudes that are physically unrealistic and all three methods produce crustal motion predictions that differ significantly. The hybrid normal mode‐collocation method presented here applies the normal mode analysis, and then applies the pure collocation to the resulting residuals. This retains the modal structure, while providing an improved fit. Our implementation avoids numerical singularities that may arise from Rayleigh‐Taylor instabilities occurring at large times and can be automated. Vertical crustal motions predicted by the hybrid method for North America with the ICE‐6G_C loading model and the VM5a viscosity structure have a root mean square (RMS) of 4.49 mm/yr and RMS differences with the normal mode, pure, and mixed collocation method of 0.06, 0.23, and 0.25 mm/yr, respectively. Maximum differences reach 0.20, 0.87, and 0.63 mm/yr. The differences increase for a viscosity profile with a greater viscosity increase with depth that exhibits stronger singularity issues. Plain Language Summary: The Earth's response to past and present‐day ice mass change is known as glacial isostatic adjustment (GIA). GIA induces crustal motion and gravitational change and is an important element for understanding regional sea‐level change. The goal of this study was to develop a computer modeling method that can be used to accurately calculate the Earth's GIA response, subject to some simplifying assumptions about the nature of Earth structure and its flow properties, while also being more robust than previous methods. To do this, we created a new method (Hybrid Normal Mode‐Collocation) from two previously published methods to minimize the documented issues of these prior methods. The hybrid method is shown to be robust, produce a more accurate predicted Earth model response, and avoid most of the problems of the previous methods. Key Points: The hybrid method uses normal mode analysis and pure collocation to calculate the surface‐loading response for Maxwell viscoelastic Earth modelsThe hybrid method retains all the significant modal structure that can be found and fits the residual component wellThere are significant differences in the calculated crustal response (vertical and horizontal) between the hybrid method and previously published methods
- Subjects
GLACIAL isostasy; COLLOCATION methods; ROOT-mean-squares; VERTICAL motion; SURFACE of the earth
- Publication
Journal of Geophysical Research. Solid Earth, 2024, Vol 129, Issue 7, p1
- ISSN
2169-9313
- Publication type
Article
- DOI
10.1029/2023JB027238