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A forward model for optical fiber strain was established based on a planar 3D multi-fracture model. Then the forward method calculating distributed fiber strain induced by multi-fracture growth was proposed. Based on this method, fiber strain evolution during fracturing of the horizontal well was numerically simulated. Fiber strain evolution induced by fracture growth can be divided into three stages: strain increasing, shrinkage convergence, and straight-line convergence, whereas the evolution of fiber strain rate has four stages: strain rate increasing, shrinkage convergence, straight-line convergence, and strain rate reversal after pumping stops. Fiber strain does not flip after pumping stop, while the strain rate flips after pumping stop so that strain rate can reflect injection dynamics. The time when the fracture extends to the fiber and inter-well pressure channeling can be identified by the straight-line convergence band of distributed fiber strain or strain rate, and the non-uniform growth of multiple fractures can be evaluated by using the instants of fractures reaching the fiber monitoring well. When the horizontal section of the fiber monitoring well is within the height range of a hydraulic fracture, the instant of the fracture reaching the fiber can be identified; otherwise, the converging band is not apparent. In multi-stage fracturing, under the influence of stress shadow from previous fracturing stages, the tensile region of fiber strain may not appear, but the fiber strain rate can effectively show the fracture growth behavior in each stage. The evolution law of fiber strain rate in single-stage fracturing can be applied to multi-stage fracturing.

Ground Penetrating Radar (GPR) is a widely used non-destructive testing tool. Constructing an appropriate forward model is crucial for GPR to perform a full-waveform inversion of layered media. In this paper, a forward model for the quasi-monostatic Stepped-Frequency GPR (SFGPR) is proposed. In the model, the GPR and its interaction with the layered medium are represented as a linear equation in which the effects of the antennas are represented by a set of frequency-dependent transfer functions. To verify the accuracy of the proposed model, the authors constructed a quasi-monostatic SFGPR in a laboratory condition and performed a full-waveform inversion of the measurement signals of plasterboard and woodblock with known thickness. In the inversion results, the thickness estimation errors of the plasterboard and woodblock are not more than 0.3 mm, indicating that the proposed forward model has a very high accuracy. The inversion performances of the quasi-monostatic and monostatic SFGPR are further compared for the layered medium constructed with plasterboard and woodblock, which has a small permittivity difference. The results show that the quasi-monostatic SFGPR can obtain more accurate inversion parameters. By estimating the Signal to Noise Ratio (SNR) of the reflected signal from the interface, it is found that the SNR obtained by the quasimonostatic configuration is 10 dB higher than that of the monostatic; therefore, the quasi-monostatic GPR has the better inversion performance.

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Fluorescence Diffuse Optical Tomography (FDOT) is significant for biomedical applications, such as medical diagnostics, drug research. The fluorescence probe distribution in biological tissues can be quantitatively and non-invasively obtained via FDOT, achieving targets positioning and detection. In order to reduce the cost of FDOT, this study designs a FDOT system based on Lattice Boltzmann forward model. The system is used to realize two functions of light propagation simulation and FDOT reconstruction, and is composed of a parameter module, an algorithm module, a result display module and a data interaction module. In order to verify the effectiveness of the platform, this study carries out the light propagation simulation experiment and the FDOT reconstruction experiment, respectively comparing the Monte Carlo (MC) light propagation simulation results and the real position of the light source to be reconstructed. Experiments show that the proposed FDOT system has good reliability and has a high promotion value.

Fluorescent Diffuse Optical Tomography (FDOT), as a new imaging technology, can achieve three-dimensional quantitative functional imaging of probe in biological tissues, and has wide application value in biomedicine. Forward model which describes the photon propagation within a biological tissue is a prerequisite for implementing FDOT and determines the performance of FDOT. To further improve the efficiency of FDOT, this paper proposes a new forward model based on the Lattice Boltzmann (LB) method derived from the discretization of radiation transfer equation and applies it to FDOT. The experimental results of numerical simulation and physical phantom show that the LB-based forward model proposed in this paper can increase the imaging speed of FDOT by about 5 times compared with the traditional diffusion equation method, without reducing its imaging quality.