  Seismic inversion plays a very useful role in detailed stratigraphic
interpretation of seismic data. Seismic inversion enables estimation of rock
properties over the complete seismic section. Traditional and machine
learning-based seismic inversion workflows are limited to inverting each
seismic trace independently of other traces to estimate impedance profiles,
leading to lateral discontinuities in the presence of noise and large
geological variations in the seismic data. In addition, machine learning-based
approaches suffer the problem of overfitting if there is a small number of
wells on which the model is trained. We propose a two-pronged strategy to
overcome these problems. We present a Temporal Convolutional Network that
models seismic traces temporally. We further inject spatial context for each
trace into its estimations of the impedance profile. To counter the problem of
limited labeled data, we also present a joint learning scheme whereby multiple
datasets are simultaneously used for training, sharing beneficial information
among each other. This results in the improvement in generalization performance
on all datasets. We present a case study of acoustic impedance inversion using
the open source SEAM and Marmousi 2 datasets. Our evaluations show that our
proposed approach is able to perform robust and laterally consistent
estimations of impedance in the presence of noisy seismic data and limited
labels. We compare and contrast our approach to other learning-based seismic
inversion methodologies in the literature. On SEAM, we are able to obtain an
average MSE of 0.0966, the lowest among all other methodologies.
