A novel method to calculate the solid-liquid contact angle is introduced in this study. Using the 3D configuration of a liquid droplet on a solid surface, this method calculates the contact angle along the contact line and provides an angular distribution. Although this method uses the 3D configuration of liquid droplets, it does not require the calculation of the 3D density profile to identify the boundaries of the droplet. This decreases the computational cost of the contact angle calculation greatly. Moreover, no presumption about the shape of the liquid droplet is needed when using the method introduced in this study. Using this method, the relationship between the size and the contact angle of water nano-droplets on a graphite substrate was studied. It is shown that the contact angle generally decreases by increasing the size of the nano-droplet. The microscopic contact angle of 83.0° was obtained for water on graphite which is in a good agreement with previous experimental and numerical studies. Neglecting other nanoscale effects which may influence the contact angle, the line tension of SPC/E (extended simple point charge model) water was calculated to be 3.6×10 N, which is also in good agreement with the previously calculated values.

We developed a sparse multichannel blind deconvolution (SMBD) method. The method is a modification of the multichannel blind deconvolution technique often called Euclid deconvolution, in which the multichannel impulse response of the earth is estimated by solving an homogeneous system of equations. Classical Euclid deconvolution is unstable in the presence of noise and requires the correct estimation of the length of the seismic wavelet. The proposed method, on the other hand, can tolerate moderate levels of noise and does not require a priori knowledge of the length of the wavelet. SMBD solves the homogeneous system of equations arising in Euclid deconvolution by imposing sparsity on the unknown multichannel impulse response. Trivial solutions to the aforementioned homogeneous system of equations are avoided by seeking sparse solutions on the unit sphere. We tested SMBD with synthetic and real data examples. Synthetic examples were used to judge the viability of the method in terms of noise. We found that SMBD gives reasonable estimates of the wavelet and reflectivity series for [Formula: see text]. The results clearly deteriorated when we tried to work on data that were severely contaminated by noise. A real marine data set was also used to test SMBD. In this case, the estimated wavelet was compared with a wavelet estimated by averaging first breaks. The estimated wavelet showed a noticeable resemblance to the average first break with normalized correlation coefficient of 0.92.

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We have developed a sensing and computational framework to estimate seismic velocities of rocks interacting with the drill-bit during the drilling process. The performance of drilling depends on our knowledge of the subsurface. The interaction between the drill-bit and rock can introduce severe vibrations in the drill-string and result in safety and performance issues. However, we can use seismic waves radiated from drill-bit-rock interactions to determine seismic velocities of the rocks interacting with the drill-bit. Our approach consists of a distributed (wave equation) representation of the dynamics of the drill-string for which we show (using Riemann's invariants and a backstepping approach) that it is possible to express the force-on-bit as a function of the top-drive force and the topdrive velocity, without requiring explicit information about the subsurface properties. We also show that seismic waves generated by drill-bit-rock interaction can be modelled as functions of the force-on-bit and of rock velocities. The rock velocity independent formulation of the force-on-bit, along with modelling of the seismic waves generated by drill-bit-rock interaction as a function of force-on-bit and rock velocities allow us to estimate seismic velocities of rocks interacting with the drill-bit. We use the alternating minimization algorithm to estimate the velocities. Numerical examples on simulated data are indicators of the validity of the approach. The proposed methodology is the first step towards a subsurface-aware drilling system.