Xuefeng Shang

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ∼27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is >30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(MPML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d0. The optimal parameter space for the maximum value of the linear frequency-shifted factor (α0) and the scaling factor (β0) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.

Crazyseismic: A MATLAB GUI‐Based Software Package for Passive Seismic Data Preprocessing

We introduce an open‐source MATLAB software package, named Crazyseismic, for passive seismic data preprocessing. Built‐in core functions such as seismic phase travel‐time calculation and multichannel cross correlation significantly improve the efficiency of data processing. Compared with conventional command‐line‐style toolboxes, all functions in Crazyseismic are embedded in one single graphic user interface (GUI). The human–machine interactive nature of GUI facilitates data quality control. The simplicity of the software allows users to process Seismic Analysis Code format seismic data with great ease and also provides a means by which users can tailor the software for their specific needs. We demonstrate the power of our software through two field examples: one for P‐wave arrival‐time picking and the other for receiver function calculation. The software can essentially be used for analyzing all major body‐wave phases in seismology.

Multiple seismic reflectors in Earth’s lowermost mantle

Significance Deep in the Earth’s interior, the region just above the core–mantle boundary exerts control on mantle convection and heat loss from the core. It has long been thought that the so-called D″ region is separated from a more uniform mantle above by a single interface, often attributed to a phase transition in Mg perovskite. Systematic deep-mantle exploration with massive seismic waveforms now yields evidence for multiple reflectors up to at least 600 km above the core–mantle boundary. Some of the newly discovered interfaces can be explained by postperovskite transitions in differentiated oceanic slab materials, transported from Earth’s surface through deep subduction and convection. The lowermost mantle appears more complex than hitherto thought, and this complexity is not confined to the canonical D″ region. The modern view of Earth’s lowermost mantle considers a D″ region of enhanced (seismologically inferred) heterogeneity bounded by the core–mantle boundary and an interface some 150–300 km above it, with the latter often attributed to the postperovskite phase transition (in MgSiO3). Seismic exploration of Earth’s deep interior suggests, however, that this view needs modification. So-called ScS and SKKS waves, which probe the lowermost mantle from above and below, respectively, reveal multiple reflectors beneath Central America and East Asia, two areas known for subduction of oceanic plates deep into Earth’s mantle. This observation is inconsistent with expectations from a thermal response of a single isochemical postperovskite transition, but some of the newly observed structures can be explained with postperovskite transitions in differentiated slab materials. Our results imply that the lowermost mantle is more complex than hitherto thought and that interfaces and compositional heterogeneity occur beyond the D″ region sensu stricto.

Understanding acoustic methods for cement bond logginga)

Well cementation is important for oil/gas production, underground gas storage, and CO2 storage, since it isolates the reservoir layers from aquifers to increase well integrity and reduce environmental footprint. This paper analyzes wave modes of different sonic/ultrasonic methods for cement bonding evaluation. A Two dimensional finite difference method is then used to simulate the wavefield for the ultrasonic methods in the cased-hole models. Waveforms of pulse-echo method from different interfaces in a good bonded well are analyzed. Wavefield of the pitch-catch method for free casing, partial or full bonded models with ultra-low density cement are studied. Based on the studies, the modes in different methods are considered as follows: the zero-order symmetric Leaky-Lamb mode (S0) for sonic method, the first-order symmetric Leaky-Lamb mode (S1) for the pulse-echo method, and the zero-order anti-symmetric Leaky-Lamb mode (A0) for the pitch-catch method. For the sonic method, a directional transmitter in both the azimuth and axial directions can generate energy with a large incidence angle and azimuth resolution, which can effectively generate S0 and break out the azimuth limitation of the conventional sonic method. Although combination of pulse-echo and pitch-catch methods can determine the bonding condition of the third interface for the ultra-low density cement case, the pitch-catch cannot tell the fluid annulus thickness behind casing for the partial bonded cased-hole.

On perfectly matched layer schemes in finite difference simulations of acoustic Logging‐While‐Drilling

In the wave propagation simulation by finite difference time domain (FDTD), the perfectly matched layer (PML) is often applied to eliminate the reflection artifacts due to the truncation of the finite computational domain. In the acoustic Logging-While-Drilling (LWD) FDTD simulation, due to high impedance contrast between the drill collar and fluid in the borehole, the stability and efficiency of PML scheme is critical to simulate complicated wave modes accurately. In this paper, we compare four different PML implementations in FDTD in the acoustic LWD simulation, including splitting PML (SPML), Multi-axis PML (MPML), Non-splitting PML (NPML), and complex frequencyshifted PML (CFS-PML). The simulation indicates that NPML and CFS-PML can more efficiently absorb the guide wave reflection from the computational boundaries than SPML and MPML. For large simulation time, SPML, MPML and NPML are numerically instable. However, stability of MPML can be improved further to some extent. Among all, CFS-PML is the best choice for LWD modeling. The effects of CFS-PML parameters on the absorbing efficiency are investigated, including damping profile, frequency-shifted factor, scaling factor and PML thickness. For a typical LWD case, the best value for maximum of quadratic damping profile d0 is about 1. The optimal parameter space for the maximum value of linear frequency-shifted factor α0 and scaling factor β0 depends on the PML damping profile and thickness. If the PML thickness is 10 grids, the reflection residual can be reduced to less than 1%, using optimal CFS-PML parameters, while only about 0.5‰ reflection artifacts are observed for 20 grids PML buffer.