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Deep neural networks (DNNs) can learn accurately from large quantities of labeled input data, but often fail to do so when labelled data are scarce. DNNs sometimes fail to generalize ontest data sampled from different input distributions. Unsupervised Deep Domain Adaptation (DDA)techniques have been proven useful when no labels are available, and when distribution shifts are observed in the target domain (TD). In the present study, experiments are performed on seismic images of the F3 block 3D dataset from offshore Netherlands (source domain; SD) and Penobscot 3D survey data from Canada (target domain; TD). Three geological classes from SD and TD that have similar reflection patterns are considered. A deep neural network architecture named EarthAdaptNet (EAN) is proposed to semantically segment the seismic images when few classes have data scarcity, and we use a transposed residual unit to replace the traditional dilated convolution in the decoder block. The EAN achieved a pixel-level accuracy >84% and an accuracy of ~70% for the minority classes, showing improved performance compared to existing architectures. In addition, we introduce the CORAL (Correlation Alignment) method to the EAN to create an unsupervised deep domain adaptation network (EAN-DDA) for the classification of seismic reflections from F3 and Penobscot, to demonstrate possible approaches when labelled data are unavailable. Maximum class accuracy achieved was ~99% for class 2 of Penobscot, with an overall accuracy>50%. Taken together, the EAN-DDA has the potential to classify target domain seismic facies classes with high accuracy.