GNGTS 2017 - 36° Convegno Nazionale

GNGTS 2017 S essione 3.2 679 In this work, we implement two different inversion strategies for the full waveform inversion of IP data: the first is a local inversion based on the Levenberg-Marquardt (LM) algorithm, whereas the second is a global inversion that makes use of the Particle Swarm Optimisation (PSO). The comparisons of results provided by the two algorithms and the singular value decomposition of the inversion kernel are used to analyse the complexity of the objective function and the ill-posedness of this inverse problem. The two inversion strategies are applied to synthetic data to maintain the inversion at a simple level, which allowed us to draw essential conclusions. Synthetic data generation. We define a double dispersion subsurface model to generate the synthetic data. We simulate a pole-dipole acquisition geometry with tension electrode equally spaced of 25 m, and a distance of 200 m from the first electrode to the current electrode. We simulate a dipole-dipole acquisition geometry with the tension electrode spaced 25 m, and an AB distance of 200 m. We generate the V(t) waveforms multiplying the Fourier transform of the I(t) waveform by a double-dispersion Cole-Cole transfer function and then back transforming to time domain. We simulate an 8 s current waveform (2 s On+, 2 s OFF, 2 s ON-, 2 s OFF), sampled at 8 kHz. We add realistic noise to the voltage waveforms to better simulate a field data acquisition. The synthetic current and voltage waves are represented in Fig. 1b, whereas Fig. 1c shows the amplitude spectrum of V ( t ) together with the noise spectrum. Note the typical 50 Hz peak in the noise spectrum. To attenuate the long wavelength noise and the white noise components affecting the synthetic data, a multi-step filtering procedure was applied, which included least-squares de-trending of the full-length waveform and stacking over an 8 s period. This procedure resulted in a final time-series of 64k samples still contaminated by the 50 Hz noise component. The FT spectrum having a bandwidth ranging from 125 mHz to 4 kHz, was then used to compute the complex resistivity transfer function: (2) Fig. 1 - a) CCP used to generate the synthetic data. b) Synthetic square current wave (blue) and synthetic tension wave with recorded noise (red). c) Amplitude spectrum of tension wave and noise. d)Phase spectrum of synthetic data after decimation and windowing. e) Amplitude spectrum of synthetic data after decimation and windowing.