Adapting speaker recognition systems to new environments is a widely-used technique to improve a well-performing model learned from large-scale data towards a task-specific small-scale data scenarios. However, previous studies focus on single domain adaptation, which neglects a more practical scenario where training data are collected from multiple acoustic domains needed in forensic scenarios. Audio analysis for forensic speaker recognition offers unique challenges in model training with multi-domain training data due to location/scenario uncertainty and diversity mismatch between reference and naturalistic field recordings. It is also difficult to directly employ small-scale domain-specific data to train complex neural network architectures due to domain mismatch and performance loss. Fine-tuning is a commonly-used method for adaptation in order to retrain the model with weights initialized from a well-trained model. Alternatively, in this study, three novel adaptation methods based on domain adversarial training, discrepancy minimization, and moment-matching approaches are proposed to further promote adaptation performance across multiple acoustic domains. A comprehensive set of experiments are conducted to demonstrate that: 1) diverse acoustic environments do impact speaker recognition performance, which could advance research in audio forensics, 2) domain adversarial training learns the discriminative features which are also invariant to shifts between domains, 3) discrepancy-minimizing adaptation achieves effective performance simultaneously across multiple acoustic domains, and 4) moment-matching adaptation along with dynamic distribution alignment also significantly promotes speaker recognition performance on each domain, especially for the LENA-field domain with noise compared to all other systems.