**1. Introduction**

Seismicity can occur naturally in seismogenic areas or be induced by industrial operations, ranging from laboratory acoustic emission events to large-scale global earthquakes. Under controlled conditions, laboratory and small-scale experiments can reveal the mechanism of fracture initiation and propagation, quantify the changes of reservoir permeability, and evaluate the sti ffness of natural fractures or faults [1,2]. At the exploration scale, passive seismic monitoring has been used to delineate fracture propagation, monitor reservoir deformation and fluid migration, and assess seismic risks associated with many subsurface operations, such as underground coal mining, hydraulic stimulation of unconventional oil and gas reservoirs, geothermal exploitation, and carbon dioxide injection and geological storage [3–9]. A complete and accurate earthquake catalogue is an important basis for subsequent data processing and even directly determines the reliability of seismic monitoring and earthquake prediction at the regional or global scale [10]. Seismic source locations are key information of earthquakes and play an important role in characterizing the geometries of multiscale fractures/faults, evaluating seismic activities, and inverting the source mechanism and in situ stress state. For instance, the spatial and temporal distribution of seismic events can help reveal the mechanism and propagation of rock fractures at the laboratory/small scale, as well as provide important information for the assessment of tectonic and volcanic seismicity at local and regional scales. Seismic location as a typical inverse problem, covering geophysical, seismological, acoustic, and engineering applications at multiple scales, has experienced significant methodological and application progress during the past century [11–15].

With the development of modern seismic instrumentation for dense acquisition and induced (micro) seismicity monitoring technology, new challenges and opportunities have emerged for noise-resistant, automatic, and real-time seismic location methods. Specifically, a new category of waveform-based location methods (e.g., waveform stacking methods and time reverse imaging) has emerged as a counterpart of conventional travel time-based inversion [13,16–18]. Waveform-based methods locate the seismic source by combing the travel time, amplitude, and phase information of seismic waveforms or wavefields to reconstruct and focus the source energy into an image profile [13]. There are three important advantages for waveform-based seismic location methods. First, they are noise-resistant, since multichannel waveforms are involved, and the coherence is enhanced to detect and locate more events. Second, the methods are basically automatic and data-driven, which enables a more e fficient location process and avoids potential subjective interference, such as phase picking. Third, the source locations are resolved as images instead of simple dots, o ffering more insights into source processes and surrounding structures. Stacking-based methods are the most mature and successful methods considering their wide applications across scales. The basic principle of stacking-based location methods is reconstructing and focusing the radiated seismic energy from the source with a certain stacking operator, for example, the di ffraction stacking (DS) operator [19–21] or the cross-correlation stacking (CCS) operator [22–24]. The origin of stacking-based seismic location methods can be traced back to the 1990s. Kiselevitch et al. (1991) proposed to utilize the maxima of the semblance over space, time, and channels to detect and locate microseismic events, and named the method "seismic emission tomography" [25]. Later on, passive seismic emission tomography was developed to locate microseismic events using recorded waveforms from surface arrays [26]. These methods share the same principle with DS in reflection seismology, that is, stacking the waveforms of individual receivers with the corresponding one-way travel time moveout to enhance the di ffracted/scattered seismic energy. CCS is another well-established stacking-based method for source location. CCS exploits correlation waveforms corresponding to di fferential travel times at pairwise receivers from common events.

Stacking-based methods have been applied to field data at multiple scales, including experimental microseismic/acoustic emission events, mining-induced seismicity, hydraulic-fracturing-induced seismicity, volcanic–tectonic seismicity, and regular earthquakes [27–32]. However, more systematic benchmarking studies of these approaches across scales are still needed. Specifically, the imaging resolution characteristics and location reliability resulting from di fferent frequency contents at di fferent scales need to be studied further. Di fferent from the comprehensive literature review of the methodological and application progress of waveform-based methods in Li et al. (2020) [13], the presented work is a case study and is the first attempt at investigating the performance of two specific stacking-based methods with common field datasets across scales. We aim to investigate the feasibility and reliability of the methods through mutually comparing the imaging results and validating the location results with reference locations, which can provide guidance for further evaluations and improvements of the methods.
