Method for determining properties of underground karst cave

A method for determining properties of an underground karst cave, comprising:

• obtaining horizontal electric field and vertical magnetic field signals of the karst cave, inputting the horizontal electric field and vertical magnetic field signals into a forward model, and obtaining resistivity and polarizability results, wherein the forward model is obtained by training an initial forward model using a training set, and the training set comprises time-domain features;
• wherein training the initial forward model using the training set comprises:
• inputting the time-domain features into the forward model to obtain predicted data, setting priori constraint conditions, converting the constraint conditions into a multi-dataset inversion objective function, performing Taylor expansion on the multi-dataset inversion objective function while neglecting higher-order terms, obtaining first-order and second-order partial derivatives of a Taylor-expanded multi-dataset inversion objective function to derive a data update model, and iteratively correcting the initial forward model using the time-domain features and the predicted data based on the data update model;
• wherein setting the priori constraint conditions comprises:
• Pa(m)=φ(m)+as(m),
• wherein Pa(m) is a total objective function, a is a regularization factor, φ(m) is a sum of squared differences between observed data and the predicted data, and s (m) is a stabilizer;
• an expression of the multi-dataset inversion objective function is:
• P
• α
• (
• m
• )
• =
• 
• W
• 1
• [
• d
• obs
• ⁢
• 1
• -
• F
• 1
• (
• m
• )
• ]
• 
• 2
• +
• 
• W
• 2
• [
• d
• obs
• ⁢
• 2
• -
• F
• 2
• (
• m
• )
• ]
• 
• 2
• +
• …
• +
• 
• W
• n
• [
• d
• obsn
• -
• F
• n
• (
• m
• )
• ]
• 
• 2
• +
• α
• ⁢
• 
• m
• -
• m
• ref
• 
• 2
• ,
• wherein dobsn is measured data from different field quantities or observation areas, Fn(m) is a response function, mref is a prior model, W1 and W2 are weight coefficient matrices for the measured data at 1st and 2nd iterations respectively, and m is a model corresponding to the measured data;
• and
• obtaining the data update model comprises:
• m
• k
• +
• 1
• =
• m
• k
• +
• Δ
• ⁢
• m
• =
• m
• k
• +
• {
• J
• 1
• T
• ⁢
• W
• 1
• T
• ⁢
• W
• 1
• [
• d
• obs
• ⁢
• 1
• -
• F
• 1
• (
• m
• )
• ]
• +
• J
• 2
• T
• ⁢
• W
• 2
• T
• ⁢
• W
• 2
• [
• d
• obs
• ⁢
• 2
• -
• F
• 2
• ⁢
• (
• m
• )
• ]
• +
• …
• +
• J
• e
• T
• ⁢
• W
• n
• T
• ⁢
• W
• n
• [
• d
• obsn
• -
• F
• n
• (
• m
• )
• ]
• +
• α
• ⁡
• (
• m
• ref
• -
• m
• )
• }
• ⁢
• (
• J
• 1
• T
• ⁢
• W
• 1
• T
• ⁢
• W
• 1
• ⁢
• J
• 1
• +
• J
• 2
• T
• ⁢
• W
• 2
• T
• ⁢
• W
• 2
• ⁢
• J
• 2
• +
• …
• +
• J
• n
• T
• ⁢
• W
• n
• T
• ⁢
• W
• n
• ⁢
• J
• n
• +
• α
• )
• -
• 1
• ,
• wherein J is a sensitivity matrix, mk is an iterative model, n is number of the iterations, Wn is a weight coefficient matrix for the measured data at an n-th iteration, and T is a transpose operation.