• A novel LIER model integrates laser-thermal effects, residual polarization fields, and thermionic emission to characterize shale anisotropy.
• For out-of-plane anisotropy, the product of LIER parameters follows cubic/impulse functions under continuous laser and exponential under pulsed laser, with a threshold angle.
• Tangential LIER measurements on cylindrical cores effectively separate bias voltage and laser power effects, enhancing model applicability.
• LIER demonstrates potential as a real-time monitoring tool for shale anisotropy during laser drilling operations.
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