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The principle of ultrasonic CT is shown in Fig. 4. Abundant data of wave time are collected by fanshaped testing. S₁–S_n are the emitting points, R₁₁, R₁₂…R_ni, R_nj are the corresponding receiving points.

Hypothesize that there are N testing line in the section plane, and the section plane may be separated to M grids on request of calculating accuracy.

Equation 1: Crack depth equation of mode A T₁ – ultrasound wave time DCF; T₂ – ultrasound wave time ACB L₁ – distance DE; L₂ – distance AE H – height of the triangle, depth of the crack

Equation 2: Crack depth equation of mode B T₁ – ultrasound wave time ACE; T₂ – ultrasound wave time ACB L₁ – distance AD; L₂ – distance BD H – height of the triangle, depth of the crack

The result will be got by solving the matrix equation below:

Equation 3: USCT matrix equation l_ij – length of path i in unit j; S_j=1/ V_j – slowness of unit j; t_i – wave time of path i.

The velocity V_j of ultrasonic wave in each unit of the section is given by the reciprocal of each S_j.