US 12,345,150 B2
Reverse time migration imaging method for cased-hole structure based on ultrasonic pitch-catch measurement
Hua Wang, Chengdu (CN); and Meng Li, Chengdu (CN)
Assigned to University of Electronic Science and Technology of China, Chengdu (CN)
Filed by University of Electronic Science and Technology of China, Chengdu (CN)
Filed on Oct. 9, 2022, as Appl. No. 17/962,511.
Claims priority of application No. 202111175499.6 (CN), filed on Oct. 9, 2021.
Prior Publication US 2023/0033271 A1, Feb. 2, 2023
Int. Cl. E21B 47/005 (2012.01); E21B 47/14 (2006.01); G01V 1/50 (2006.01)
CPC E21B 47/005 (2020.05) [G01V 1/50 (2013.01); E21B 47/14 (2013.01); G01V 2210/6242 (2013.01)] 7 Claims
OG exemplary drawing
 
1. A reverse time migration imaging method for a cased-hole structure based on ultrasonic pitch-catch measurement, comprising:
inputting original ultrasonic Lamb waveform data and related parameter files; calculating a theoretical dispersion curve of A0-mode waveforms according to borehole fluid properties, casing thickness, casing elastic parameters and central frequency recorded in the related parameter files; and obtaining a waveform propagating forward or backward from one of two receivers to a certain distance based on A0's phase velocity by using a phase shift method through the following equation:

OG Complex Work Unit Math
wherein g(t) is a waveform travelling at a certain distance x0; F(w) is a frequency spectrum of an original A0-mode waveform at near or far receiver; w is angular frequency; −j is imaginary number; e is natural logarithm; H(w) is a propagation matrix, and k represents wavenumber; and due to dispersion, k is a function of phase velocity v of the A0-mode waveforms;
establishing, according to background information, a two-dimensional migration velocity model including initial density, P-wave velocity and S-wave velocity of a target area;
generating and storing a forward propagating ultrasonic Lamb wavefield based on two-dimensional high-order staggered grid finite difference and non-split perfectly matched layer;
reversing a time axis of the forward propagating ultrasonic Lamb wavefield to generate a reversely propagating ultrasonic Lamb wavefield; and storing the reversely propagating ultrasonic Lamb wavefield;
calculating, based on Hilbert transform, an envelope of the forward propagating ultrasonic Lamb wavefield and an envelope of the reversely propagating ultrasonic Lamb wavefield;
applying a zero-lag cross-correlation imaging condition to the forward propagating ultrasonic Lamb wavefield and the reversely propagating ultrasonic Lamb wavefield to obtain reverse time migration imaging results for ultrasonic pitch-catch measurement; and
applying Laplace filtering to suppress low-frequency imaging noises in the reverse time migration imaging results.