Preliminary Results: Determination of Microseismic Event Locations on Anisotropic Medium Using Time Reverse Modeling

Determining the microseismic event location is crucial in various fields of science such as hazard mitigation, exploration of new fossil energy sources, and others. However, in determining the source location, several problems arise, namely the determination of the source location that is not appropriate due to limited data. To determine the exact location of the event requires a lot of microseismic recording data. We developed a time reverse modeling method for elastic waves. The data used is synthetic data that is generated from forward modeling which seems to originate a source that is located in subsurface at 1,300 m depth. The seismic velocity model used is a layered seismic velocity model with the assumption that every layers is unabsorbed layers. Data from the wavefield recording on the surface is propagated back to the source. From the study, this was found that the microseismic event was at a depth of 1,300 m.


Introduction
Microseismic is a seismic wave with a frequency greather than 1 Hz.These waves are generated by several sources including volcanic tremor (Yukutake, et al., 2017), fault activity (Damanik et al., 2021), subduction zones (Pesicek, et al., 2010), hydraulic fracturing (Lin and Zhang, 2016) and other sources.Therefore, determination of microseismic events location is important in earthquake mitigation and increasing production in oil and gas field.Most studies use the double difference method (Waldhauser and Ellsworth, 2000) in determining the location of microseismic events.This method determines microseismic events (hypocenter) location based on earthquake raypath and does not take into account the characteristics of each medium because if there are some earthquakes having a hypocenter distance smaller than the distance from the hypocenter to the recording station, raypath from these earthquakes is considered to propagate through the same medium.This double difference method has been used to determine the hypocenter location for earthquakes that occurred in Palu (Supendi et al., 2018), Lombok (Sasmi et al., 2020), Ambon (Utama et al., 2018), and Mamuju -Majene (Supendi el al., 2021).Nugraha et al., 2018 used double difference method to relocate the hypocenter of the earthquake swarm around the Jailolo Volcano.
We propose time reverse modeling method using elactic wave to determine microseismic event location.This method involves anisotropy characteristics of the medium propagated by microseismic waves The accuracy of the event location using time reverse modeling (TRM) is influenced by the number of recording station (Gomberg et al., 1990) and the velocity model used.The TRM method is not affected by the station geometry and picking the arrival time of P and S waves.In this paper, we only focus on discussing event locations for applications in the field of disaster mitigation using elastic waves.

Method
Application of time reverse modeling to determine the hypocenter location of the Sumatra-Andaman earthquake has been carried out by Larmat et al., 2006 using the element spectral method.However, this method is constrained by the long computation time because this method is based on the finite element method.Haris et al., 2017 used time reverse modeling to determine passive seismic source location in the South Sumatra basin using an acoustic wave approach To simulate the wave propagation in anisotropic medium, the stress equation (Liu and Sen 2009) is used which is commonly called the elastic wave equation which consists of several equations namely vx, vy and vz are elastic wave velocity in x, y, and z direction, respectively.xx,zz, and zz are 2D stress tensor components. and  are Lame constant.
The wave equation is solved by using the finite difference method so that the wave equation in differential form must be made in discrete form.The discretization model used in this study is the Rotated Staggered Grid (RSG) method (Saenger et al., 2000).In the RSG method, the discrete forms of the operators and can be written as follows: , where u is elastic wavefield, x and z are horizontal and vertical coordinate, r is the grid size in the diagonal direction whose value depends on the vertical (z) and horizontal (x) grid sizes.The finite difference coefficients a1 and a2 are 1.125000 and 4.166667 x 10 −2 , respectively (Liu and Sen 2009;Yang et al, 2015).

Results
In this study, wave modeling using TRM was carried out.The input of this method (TRM), is the seismogram recorded by the station (receiver) on the surface.The data used in TRM is synthetic data so that to obtain synthetic seismogram recordings, forward modeling is required.The subsurface model used is a heterogeneous velocity model where the earth consists of several layers (Figure 1).Each layer has its own P wave velocity (vp), S wave velocity (vs) and density () parameters.The vs value is obtained through the relationship between vp and vs in equation ( 5) below $ = % 1.75

…(5)
In addition to the vp, vs and  parameters, other modeling parameters used in this study are the spatial grid size (∆x = ∆z = ∆h) namely 14 meters, the temporal grid (t) namely 0.0025s, and the anisotropy parameters  and  whose values is 0.2 and -0.2, respectively.
Figure 2 shows two scenarios of the elastic wave forward modeling with sources originating from subsurface.Scenario 1, the source seem to come from a depth of 1300 meters and scenario 2, the source seem to come from a depth of 4375 meters.Figure 3 and Figure 4 are forward modeling seismogram for every scenarios.The recording of scenario 1 is shown in Figure 3 while scenario 2 is shown in Figure 4.
If the spatial grid is enlarged, a dispersion effect will appear in both the forward modeling sample, and the horizontal and vertical component seismograms.Conversely, if the spatial grid is reduced, the dispersion effect will decrease but the computation time will be longer.In anisotropic medium, the dispersion effect also produces a change in the anisotropic constant .The higher the  value, the stronger the dispersion effect.
Figure 5 shows the elastic wave propagation in the reverse time scheme.The wave is emitted from the receiver on the surface to a certain point in subsurface until t = 0.At time t = 0 all the wave fields from the receiver will intersect at a certain point and produce a maximum amplitude.The intersection location of all wave fields originating from the receiver is identified as the event location.

Conclusion
Based on the study, the microseismic event location can be determined using the time reverse modeling (TRM) method.By using TRM the waves coming from the receiver can return to their original location where the waves were generated.Waves raised from a depth of 1300 m when TRM is carried out, the waves will return to their original position, namely at 1300 meter depth and 4375 m depth.

Figure 1 .
Figure 1.The Subsurface Model Assumed to be a Heterogeneous Velocity Model

Figure 5
Figure 5 (left) illustrates the microseismic event location at a depth of 1300 meters while Figure 5 (right) illustrates the microseismic event location at a depth of 4375 meters.

Figure 2 .
Figure 2. Forward Modeling of Elastic Waves on Anisotropic Medium, Source Frequency 6 Hz, h = 14 meters.Microseismic Event Depth is 1300 m (Left) and Microseismic Event Depth is 4375 m (Right)

Figure 4 .
Figure 4. Seismogram Recording of Elastic Wave Propagation on Anisotropic Medium with the event location at 4375 m depth, source frequency 6 Hz, h = 14 meters.Horizontal Component (Left), Vertical Component (Right).

Figure 5 .
Figure 5. Back Propagation of Elastic Waves on Anisotropic Medium, Source Frequency 6 Hz, ∆h = 14 meters.Microseismic Event Depth is 1300 m (Left) and Microseismic Event Depth is 4375 m (Right)