## 1 Introduction  
Hypocenter parameters, such as latitude, longitude, depth, and origin time, are a crucial parameter in seismology, and the research work on the field of seismology is particular pertinent to hypocenter parameters [1, 2, 3, 4, 5]. Using the time interval between the arrival of the primary and secondary waves (S-P time interval) that is measured at each station, earthquake location, i.e., latitude and longitude, can be used to determine accurately and easily by analyzing the S-P time interval. However, accurate measurement of the focal depth of an earthquake is a typically more challenging and rewarding work, as the source depth is usually inadequately constrained [6, 7]. Therefore, precise determination of source depth is normally more difficult than determination of location, unless denser seismometers are deployed in the vicinity of the earthquake epicenter. Furthermore, it is well known that precise depth determination for shallow teleseismic events is a very complicated subject [8], and the S-P arrival time interval becomes less and less sensitive to hypocenter parameters as the epicenter distance increases [7, 9]. Seismologists have long recognized that high precision of focal depth remains highly problematic in seismology [10]. [PERSON] [11] gave a general overview of the existing methods to estimate focal depth, which mainly contain waveform-based methods and traveltime-based methods. [PERSON] et al. [12] estimated focal depth by measuring both teleseismic depth phases pP and sP and surface wave amplitude spectra. [PERSON] and [PERSON] [10] proposed an array processing technique to calculate focal depth using pP-P times and double-difference algorithm, which needs two close events. [PERSON] [11] presented a method for accurate depth determination for moderate magnitude earthquakes using teleseismic depth phases pP, sP, and sS data sets. [PERSON] et al. [7] developed Depth-Scanning Algorithm to obtain focal depth at local and regional distances, which was based on the traveltime residuals between the direct and depth phases (Pg, pPg, sPg, sg, sSz, PmP, pPmP, sPmP,SmS, sSmS, etc.). Among all the methods mentioned above, the data used for determining focal depth are from the phases penetrating above the mantle-core boundary, and the methods can not be well constrained. However, the teleseismic depth phases, which almost travel across the whole earth, are well known to assess focal depth and can be a clear improvement on the depth determination accuracy [5; 10; 13; 14]. Since the teleseismic depth phases are sensitive to hypocenter depth, they can be used to obtain more precise focal depth. Firstly, we pre-process the raw seismograms from a seismic array deployed at Guangxi, China, and identify the arrival times of PKIKP and pPKIKP phases based on the peaks of waveforms and cross-correlation. Secondly, we invert the data set of pPKIKP-PKIKP time interval for the focal depth, using the simulated annealing (SA) method. Finally, we verify the accuracy and feasibility of the procedure using the teleseismic data from two events. These public domain data sets are from China Earthquake Administration (CEA), German Research Center for Geosciences (GFZ), International Seismological Center Engdahl-van der Hilst-Buland (ISC-EHB) Bulletin [15], and United States Geological Survey (USGS) catalogue. Thus far, the time difference between the inner core phases pPKIKP-PKIKP has not used to determine earthquake depth, This may be because the arrivals of inner core phases are not clear-cut. On the other hand, due to a long travel through inner core with a nearly vertical incidence to the surface and losing most high frequency compositions, the inner core phases pPKIKP and PKIKP may be difficult to acquire from a teleseismic earthquake. However, if we choose an appropriate band filter for the teleseismic phases, pPKIKP and PKIKP should be identified on the seismograms more simply.