Inversion method and system for hydro-thermal of permafrost coupled insar with ert

An inversion system for internal hydro-thermal of permafrost coupled InSAR with ERT, comprising:

• an acquisition unit, configured to acquire InSAR ground deformation data, ERT data, and ground temperature from a same study area;
• a separation unit, configured to separate freeze-thaw deformation data based on the InSAR ground deformation data using an improved InSAR deformation separation model of permafrost;
• a determination unit, configured to determine a depth of dynamic freeze-thaw interface and to invert a first water content based on multi-temporal ERT data;
• a correction unit for frost heave model, configured to correct thickness of an active layer in the frost heave theoretical model based on the depth of dynamic freeze-thaw interface, thereby obtaining a corrected frost heave theoretical model;
• an inversion unit for water content, configured to invert a second water content based on the freeze-thaw deformation data using the corrected frost heave theoretical model;
• an optimization unit for hydro-thermal model, configured to input the second water content and ground temperature as initial conditions, and the depth of dynamic freeze-thaw interface as a boundary condition, into a coupled hydro-thermal numerical model;
• and to optimize the coupled hydro-thermal numerical model using the first water content, thereby obtaining an optimized dynamic coupled hydro-thermal numerical model;
• and
• an inversion unit for internal hydro-thermal of permafrost, configured to input InSAR ground deformation data and ground temperature into the optimized dynamic coupled hydro-thermal numerical model, which outputs temperature and a third water content at different periods and depths within the permafrost of the study area;
• wherein a process of optimizing the coupled hydro-thermal numerical model comprises:
• generating N parameter {p1, p2, . . . pN} sets based on prior parameters;
• pi=[λe, ρcp, Kw, θres, α]T is a parameter vector to be optimized, i is a positive integer, λe is an effective thermal conductivity of soil, ρcp is a volumetric heat capacity of soil, Kw is a water permeability, θres is a residual unfrozen water content, α is an expansion coefficient, [ ]T is the transpose of a vector;
• for each parameter set pi, computing a predicted water content value θmodel(z, t;
• pi) at depth z and time t using the coupled hydro-thermal numerical model;
• generating an observation vector yERT=[θERT(z1, t), θERT(z2, t), . . . , θERT(zm, t)]T from the first water content inverted at time t, wherein θERT(zm, t) is the first water content at depth zm and time t obtained from ERT inversion;
• constructing an objective function
• Γ
• ⁡
• (
• p
• i
• )
• =
• ∑
• t
• =
• 1
• N
• t
• ∑
• z
• =
• 1
• N
• z
• [
• θ
• model
• (
• z
• ,
• t
• ;
• p
• i
• )
• -
• θ
• ERT
• (
• z
• ,
• t
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• ]
• 2
• based on the predicted water content values and the observation vector to compute a global residual sum of squares, wherein Nt is a time of observation, Nz is a maximum freezing or thawing thickness, and θERT(z,t) is the first water content at depth z and time t obtained from ERT inversion;
• and
• based on the global residual sum of squares, a minimum residual is obtained through gradient calculation to update hydro-thermal characteristic parameters, resulting in the optimized dynamic coupled hydro-thermal numerical model.