Resolving spectral information from time domain induced polarization data through 2-D inversion

Field-based time domain (TD) induced polarization (IP) surveys are usually modelled by taking into account only the integral chargeability, thus disregarding spectral content. Furthermore, the effect of the transmitted waveform is commonly neglected, biasing inversion results. Given these limitations of conventional approaches, a new 2-D inversion algorithm has been developed using the full voltage decay of the IP response, together with an accurate description of the transmitter waveform and receiver transfer function. This allows reconstruction of the spectral information contained in the TD decay series. The inversion algorithm is based around a 2-D complex conductivity kernel that is computed over a range of frequencies and converted to the TD through a fast Hankel transform. Two key points in the implementation ensure that computation times are minimized. First, the speed of the Jacobian computation, time transformed from frequency domain through the same transformation adopted for the forward response is optimized. Secondly, the reduction of the number of frequencies where the forward response and Jacobian are calculated: cubic splines are used to interpolate the responses to the frequency sampling necessary in the fast Hankel transform. These features, together with parallel computation, ensure inversion times comparable with those of direct current algorithms. The algorithm has been developed in a laterally constrained inversion scheme, and handles both smooth and layered inversions; the latter being helpful in sedimentary environments, where quasi-layered models often represent the actual geology more accurately than smooth minimum-structure models. In the layered inversion approach, a general method to derive the thickness derivative from the complex conductivity Jacobian is also proposed. One synthetic example of layered inversion and one field example of smooth inversion show the capability of the algorithm and illustrates a complete uncertainty analysis of the model parameters. With this new algorithm, in situ TD IP measurements give access to the spectral content of the polarization processes, opening up new applications in environmental and hydrogeophysical investigations.