Morphology and possible origins of the Perm anomaly in the lowermost mantle of Earth

We have constrained a small‐scale, dome‐shaped low‐velocity structure near the core‐mantle boundary (CMB) of Earth beneath Perm (the Perm anomaly) using travel‐time analysis and three‐dimensional (3‐D) forward waveform modeling of seismic data sampling of the mantle. The best‐fitting dome‐shaped model centers at 60.0°E, 50.5°N, and has a height of 400 km and a radius that increases from 200 km at the top to 450 km at the CMB. Its velocity reduction varies from 0% at the top to –3.0% at 240km above the CMB to –3.5% at the CMB. A surrounding 240‐km‐thick high‐velocity D'' structure has also been detected. The Perm anomaly may represent a stable small‐scale chemical pile in the lowermost mantle, although the hypothesis of a developing mantle plume cannot be ruled out.


Introduction
Seismic tomography and high-resolution waveform and traveltime analyses have revealed various low-velocity anomalies at the base of Earth's mantle, including two large-scale low-shear-velocity provinces (thousands of kilometers across) beneath the south-central Pacific Ocean and Africa (the Pacific Anomaly and African Anomaly, respectively), several small-scale (hundreds of kilometers across) anomalies beneath Perm, Iceland and Kamchatka (the Perm, Iceland and Kamchatka anomalies, respectively), and patches of ultra-low-velocity zones (with lateral scales of hundreds to tens of kilometers across) (Montelli et al., 2006;Wang Y and Wen LX, 2007;Ritsema et al., 2010;Simmon et al., 2010;Lay and Garnero, 2011;Lekic et al., 2012;Sun DY and Miller, 2013;Thorne et al., 2013;He YM et al., 2014French and Romanowicz, 2015;Zhao CP et al., 2017;Yu SL and Garnero, 2018;Kim et al., 2020). Geodynamic studies have further indicated that the morphologies of the large-and small-scale anomalies place a crucial constraint on their origins and dynamic processes (Mc-Namara, 2019). Seismic studies of the African Anomaly and northeastern Pacific Anomaly have revealed a bell-shaped structure with sloped sides that is expected to be stable and long-lived (Mc-Namara and Zhong SJ, 2004;Wang Y and Wen LX, 2007;Zhao CP et al., 2015). The northwestern Pacific Anomaly has a box-shaped structure with nearly vertical sides, implying that it is a metastable structure (Tan E and Gurnis, 2005;He YM and Wen LX, 2009). Both the Iceland and Kamchatka anomalies have mushroom-shaped or wide-cap-and-narrow-stem features, which fit the typical morphology, in theoretical and experimental modeling, of an unstable mantle plume (Griffiths and Campbell, 1990;He YM et al., 2014. In 2012, Lekic et al. using the forward waveform modeling method, detected a localized low-velocity structure near the coremantle boundary (CMB) beneath Perm (the Perm anomaly) (Lekic et al., 2012). Their simplified model includes a 370-km-thick and 900-km-wide (at the CMB) cylinder with a velocity reduction of -6% beneath Perm. However, the anomalous S diff phases of the event used in that study were recorded in the Taiwan province of China (Fig. 8 of Lekic et al., 2012); in the SKS phases of the same re-cords similar anomalous features have been observed and are therefore probably caused partly by the seismic heterogeneities in the receiver-side crust and upper mantle. The Perm anomaly, including its existence, geometry, and velocity structure, and its relationship with surrounding mantle, must be reassessed. Details regarding the structure of the Perm anomaly will help us understand its origin and dynamic process.
This study presents dense seismic observations that sample the lower mantle beneath Perm and show a systematic shift in arrival time and broadening of the SH and SH diff waveforms with respect to the azimuth. Carefully selected seismic data and forward 3-D waveform modeling with a frequency range of up to 0.125 Hz enable us to reveal fine-scale structural features of the Perm anomaly. Our modeling suggests a dome-shaped low-shear-velocity anomaly with a maximum velocity reduction of -3.5% at the CMB surrounded by a high-velocity D" region near the CMB beneath Perm.

Detection of the Morphology and Velocity Structure of the Perm Anomaly
We first constrain the average shear-wave velocity near the CMB in the region of the Perm anomaly and the geographic extent of the Perm anomaly based on the differential travel-time residuals of ScS-S sampling the region. We then deduce the morphology and detailed velocity structure of the anomaly in the lowermost mantle based on waveform modeling S, S diff waves that cross the anomaly.

Velocity Structure in the Lowermost Mantle Beneath Perm Based on Travel-time Analysis
The geographic extent of the anomaly near the CMB is constrained by using ScSH-SH differential travel-time residuals. Only ScS-S pairs with epicentral distances ranging from 45° and 85° and their ScS bouncing points at the CMB located between 20°N and 75°N and between 10°E and 130°E are examined. By measuring the difference in the peak-to-peak times of the S and ScS phases on the seismograms, the ScS-S differential travel-time residuals are obtained. A Butterworth filter with corner frequencies of 0.008 and 1 Hz has been applied to all seismograms. Finally 25 earthquakes with a total of 398 ScS-S travel-time data points are collected (Table S1 in the Supporting Information). The seismic data show good sampling coverage in the study area ( Figure 1a). Travel-time contributions of the mantle structure at 500 km or more above the CMB are ruled out by using the mantle tomography model GyPSuMS (Simmons et al., 2010), following the same procedures outlined in He YM et al. (2015) ( Table S2 in the  Supporting Information). Thus, lateral velocity variations in the lowermost 500 km of the mantle are attributed mostly to the corrected ScS-S differential travel times, and the average shear-velocity in that depth range is inferred. The inferred shear velocity perturbations exhibit an approximately circular low-velocity area with a radius of approximately 450 km beneath Perm, surrounded by neutral or high-velocity anomalies (Figure 1b). The inferred velocity variations are similar to those obtained in past studies based on tomographic imaging and waveform analysis (Simmons et al., 2010;Ritsema et al., 2011;Lekic et al., 2012).

Morphology and Velocity Structure of the Perm Anomaly Based on Waveform Modeling
We construct a 3D model of the Perm anomaly based on the average velocity structure revealed by the ScS-S differential traveltime residuals and waveform modeling of the S, S diff waves that sample across the anomaly. The S, S diff waveforms have been proven to be highly sensitive to the geometric features of the seismic anomalies (Wen LX, 2002;Wang Y and Wen LX, 2004;To et al., 2005;He YM and Wen LX, 2009;Sun DY et al., 2009;Sun DY and Miller, 2013;Yuan and Romanowicz, 2017). For waveform modeling, we search for broadband tangential displacements of the S, S diff phases ranging from 90° to 110° for all possible events that Figure 1. (a) Study region and ScS reflected points (black crosses) at the CMB, along with earthquakes (red stars), seismic stations (deep blue triangles) and great-circle paths (gray lines) of the seismic phases used in this study. The background is shear-velocity perturbations at the CMB from the global shear-velocity tomographic model GyPSuMS (Simmons et al., 2010). (b) Average shear velocity perturbations in the bottom 500 km of the mantle inferred from the corrected ScS-S traveltime residuals. Blue squares and red circles represent velocity increases and decreases, respectively; their sizes are proportional to the magnitudes of the velocity perturbations. The boundary between low velocities and neutral or high velocities is approximated by the dashed circle. The shear velocity perturbations that are averaged over 1°×1° grids with a Gaussian cap with a radius of 2° are shown as the background.
-3.0% -1.5% 0.0% 1.5% 3.0%   sample the lowermost mantle beneath Perm and the surrounding area. All waveform data are bandpass-filtered from 0.008 to 0.125 Hz. After visual inspection of all available data and exclusion of those with strong anisotropy effects in the upper mantle, we select the S, S diff data of two events for waveform modeling: one event (2010/07/24) occurred in the Philippines and was recorded in Europe, and the other (2010/04/11) occurred in Spain and was recorded in China (Figures 2 and S2 in the Supporting Information). Event 2010/04/11 was also used by Lekic et al. (2012) but mainly with different stations. Both events have simple sourcetime functions as well as high signal-to-noise ratios (Figures 2 and S1 and S2 in the Supporting Information). Seismic data from these two events provide good azimuthal sampling coverage of the Perm anomaly from opposite directions, with event 2010/07/24 at a distance range of 97°-108° and event 2010/04/11 at a distance range of 95°-98° (Figures 2 and S1a and S2a in the Supporting Information).
The travel-time correction for the seismic data from events 2010/07/24 and 2010/04/11 consists of two procedures. We first re-determine the origin time and location of the chosen earthquakes based on SH, sSH phases (Table 1). Then we perform travel-time corrections for the effect of seismic heterogeneities 500 km above the CMB, based on the tomography model GyPSuMS (Simmons et al., 2010), and reference the corrections from seismic data for two events (2013/06/02 and 2011/04/01) that are closer to the seismic stations (Figures 2, S3 and S4 in the Supporting Information and Table 1). The corrected travel-time residuals are attributed to the Perm anomaly.
The waveform complexity and travel time of the S, S diff phases of event 2010/07/24 vary significantly with the sampling azimuth from 314° to 334° (Figures 2c and S1 in the Supporting Information). In general, in the azimuthal range from 314° to 323° the widths of the apparent S diff phases gradually decrease and the travel-time delays increase, whereas in the azimuthal range from 323° to 329° the azimuth-dependent trend reverses, with the widths of the S diff phases increasing and the travel-time delays decreasing. The decrease in the widths of the S diff phases occurs abruptly in the azimuthal range from 332° to 334°. The S diff phase arrives earlier than the theoretical arrivals calculated by the preliminary reference Earth model (PREM) (Dziewonski and Anderson, 1981) in the azimuthal ranges of 314° to 320.5° and 326° to 334°. Most notably, an anomalous phase (labeled S a ) is observed after the S diff phase in the azimuthal range of 314° to 321°, is absent in the middle azimuths up to 326°, re-appears in the azimuthal range of 327° to 329°, and disappears again at large azimuths up to 334°( Figure 2c). The anomalous phase exhibits the same polarity but a smaller amplitude relative to the direct S diff phase, with its separation from the direct S diff phase varying from approximately 9.0 s at 314° to 7.0 s at 321° and from 3.5 s at 327° to 7.0 s at 329°.
Azimuth-dependent waveform variation is also observed in the S, S diff waveforms of event 2010/04/11 in the azimuthal range from 45° to 62° (Figures 2 and S2 in the Supporting Information). Although no clear anomalous phase is observed after the S diff phase, as it is for event 2010/07/24 -likely due in that case to the shorter distance ranges (95°-98°) and narrower azimuthal coverage of the data sampling, the observed waveform and travel-time features are similar to those in the seismic data of event 2010/07/24. In the azimuthal range of 45° to 51° the widths of the apparent S diff phases decrease gradually and the travel-time delays increase slightly, whereas in the azimuthal range from 51° to 62° the widths of the S diff phases increase and the travel-time delays decrease. We constructed 3D testing models based on the seismic structure revealed by the ScS-S differential travel-time residuals ( Figure 1) and searched for the best-fitting models from the waveform modeling of the S, S diff data for events 2010/07/24 and 2010/04/11 ( Figure 2). The travel-time data show a circular area of low velocities with a radius of ~450 km surrounded by normal-or high-velocity anomalies near the CMB beneath Perm (Figure 1b). The waveform variations of events 2010/07/24 and 2010/04/11 suggest that the Perm anomaly is symmetrical north to south. We then set up a series of 3D models composed of a small-scale low-velocity anomaly and a surrounding high-velocity D" layer near the CMB beneath Perm (Figure 3). We tested the models with various lowvelocity anomaly geometries, including mushroom-shaped, cylindrical, dome-shaped and conical, with different heights, sizes, and velocity structures. The lateral extents of the low-velocity an- omaly are limited by the size of the circular area revealed by the travel-time analysis at the CMB and the sampling paths of the S, S diff raypaths of event 2010/07/24. The velocity reduction of the low-velocity anomaly was analyzed from -6% to 0% and the velocity jump of the surrounding high-velocity D" layer was analyzed from 3.5% to 0%, based on the results of previous studies (Wyses-sion et al., 1998;Lekic et al., 2012;He YM et al., 2014. A coupled normal mode/spectral element method was applied to calculate the 3-D synthetic waveforms (Capdeville et al., 2003).
The preferred models have a lowermost portion with a radius of 450 km and velocity reductions from -3% at 240 km above the CMB to -3.5% at the CMB. Models with a larger velocity decrease˚( (for example, from -4% at 240 km to -6% at the CMB) generate large amplitudes in the secondary phase at stations BSL, NAD, WZS, and JFL that do not match the observed waveforms of event 2010/04/11. The preferred models also have an upper portion with a lateral dimension that is smaller than that of the lowermost portion. Models with an upper portion radius of less than 200 km generate azimuthal dependence values and amplitudes that are similar to those of the secondary phase observed in the data (Figure 3, middle and bottom panels, models (a) and (b)). In these versions of the model, the direct S, S diff phase is generated by the seismic structure outside the low-velocity anomaly, whereas the secondary phase is generated by the low-velocity anomaly. Models with an upper portion radius greater than or equal to that of the bottom portion generate a strong secondary phase at every sampled azimuth for event 2010/04/11, a feature that does not match the observed S and S diff (Figure 3, bottom panel, models (c) and (d)). These models also generate much delayed S and S diff phases for event 2010/07/24 that do not match the observations (Figure 3, middle panel, models (c) and (d)). Among the models, we thus choose the dome-shaped model as the preferred model because the synthetics produced by this model fit the observations slightly better that those of the conical model. The synthetic tests indicate that models with a thickness of 350-450 km can produce synthetics that fit the observations. The high-velocity region surrounding the low-velocity anomaly is necessary to explain the faster S diff phases in the azimuthal ranges of 314° to 320.5° and 326° to 334° for event 2010/07/24 and the ScS-S differential travel-time residuals (Figures 1 and 2c). The high-velocity structure also broadens the waveforms of the seismic phases sampling the border of the anomaly and narrows the waveforms of the seismic phases sampling the center of the anomaly.
The best-fitting model is a dome-shaped low-velocity anomaly located at 60.0°E, 50.5°N, with a height of 400 km and a radius that increases from 200 km at the top to 450 km at the CMB (model (a) in Figure 3). Its velocity structure decreases from 0% at the top to -3.0% at 240km and to -3.5% at the CMB. The high-velocity region surrounding the low-velocity anomaly has a velocity jump of 3.0% at 240 km above the CMB following by a negative gradient from 3.0% to 1.0% at the CMB.

Differences From Previous Analysis of the Perm Anomaly
The Perm anomaly was first reported by Lekic et al. (2012). Their study suggested a 370-km-thick and 900-km-wide cylindrical lowvelocity anomaly centered at 54°E, 50°N. Our best-fitting model has a similar thickness and width, but it has a dome-shaped lowvelocity anomaly located at 60.0°E, 50.5°N surrounded by a 240km-thick high-velocity province. The low-velocity structure in our model decreases from 0% at the top to -3.5% at the CMB, which is much smaller than the previous average velocity reduction result of -6% (Lekic et al., 2012). The model by Lekic et al. was derived based on waveform modeling of S, S diff phases from event 2010/04/11, which were mainly recorded in Japan and the Taiwan province of China, whereas our best-fitting model was derived from ScS-S travel-time analysis and waveform modeling of S, S diff phases from events 2010/04/11 and 2010/07/24. In this study, we opt not to use the seismic data of event 2010/04/11 recorded in Taiwan of China because both the S diff and SKS phases of the event show similar anomalously large travel-time delays and amplitudes. Moreover, the records at the same stations for the reference event 2011/04/01 occurring in Greece show similar data features (Figure 2a). It is difficult to rule out the possibility that the observed anomalous features of the seismic data of event 2010/04/11 in Lekic et al. (2012) are contributed to in part by receiver-side crust and upper mantle structures. Instead, we use seismic data recorded in southern China and data reorded in Europe from another event, 2010/07/24, occurring in Mindanao, Philippines. The seismic data recorded in southern China, though with similar sampling azimuths as the data recorded in Taiwan of China, have much smaller travel-time delays, implying a smaller velocity reduction associated with the anomaly. In comparison with previous reports, the dense ScS-S travel-time data used in this study allow the geographic extent of the low-velocity region to be better constrained. The detailed waveform features of the seismic data from events 2010/04/11 and 2010/07/24 -in particular, those of the additional event 2010/07/24 used in this study, allow the morphology and velocity structure of the anomaly to be tightly constrained. Furthermore, our systematic tests of 3-D models based on 3-D forward waveform modeling of the seismic observations with frequency contents of up to 0.125 Hz have enabled us to identify the best-fitting shape of the low-velocity anomaly and the existence of a surrounding high-velocity province.

Possible Interpretation and Dynamic Consequences of the Perm Anomaly Relative to Other Localized Anomalies in the Lowermost Mantle
Seismic studies have now revealed several low-velocity anomalies near the CMB that extend at least several hundred kilometers above the D" layer, with various lateral scales and geometric features Wen LX, 2004, 2007;To et al., 2005;He YM andWen LX, 2009, 2012;Lekic et al., 2012;Sun DY and Miller, 2013;He YM et al., 2015;Zhao CP et al., 2015;French and Romanowicz, 2015). At the regional scale, the African and Pacific Anomalies occupy, respectively, areas of approximately 1.8×10 7 km 2 and 1.9×10 7 km 2 at the CMB. The African Anomaly exhibits a bell-like geometry in the mid-lower mantle extending 1,300 km above the CMB. In the lowermost 300 km of the mantle, the African Anomaly has sharp edges, rapidly varying thicknesses, and a strong shear velocity reduction varying from -2% at the top to approximate of -10% at the bottom. These features imply that the African Anomaly is both compositionally distinct and geologically stable Wen LX, 2004, 2007). The Pacific Anomaly is composed of several piles and each pile has a velocity structure varying from -3% (top) to -5% (CMB). The northwestern pile has sharp sides in the lower mantle that extend at least 740 km above the CMB, whereas the northern pile has sloped sides in the lower mantle that extend approximately 450 km above the CMB. These features imply a metastable thermo-chemical anomaly (northwestern pile) or a geologically stable chemical anomaly (northern pile) (He YM andWen LX, 2009, 2012). At the local scale, three lowvelocity anomalies with lateral dimensions of several hundreds of kilometers at the CMB and surrounded by high-velocity struc-tures are identified beneath Iceland, Kamchatka, and Perm (Lekic et al., 2012;He YM et al., 2014 and this study). The Iceland anomaly has a 600-km-thick mushroom-shaped structure with a velocity structure that decreases from 0% (top) to -6% (CMB). The Kamchatka anomaly has an 800-km-thick narrow-stem-and-widecap structure with a velocity structure varying from 0% at the top to -1.2% at 210 km above the CMB. The Perm anomaly has a 400km-thick dome-shaped structure with a velocity structure that decreases from 0% (top) to 3.5% (CMB) (Figure 4). The mushroomshaped (or narrow-stem-and-wide-cap) structure is a typical morphology of a mantle plume both in theoretical geodynamical modeling (Loper, 1991) and in laboratory experiments (Griffiths and Campbell, 1990), and the Iceland and Kamchatka anomalies may represent two mantle plumes in the lowermost mantle. The dome-shaped feature of the Perm anomaly is apparently different from the mushroom shape of the Iceland anomaly and the widecap-and-narrow-stem shape of the Kamchatka anomaly and may represent a different dynamic process. The geometric feature of the Perm anomaly is similar to the bell-shaped structure of the African Anomaly and may represent a stable chemical pile. However, unlike the regional-scale geometry of the African anomaly, which suggests a stable chemical pile, the local-scale domeshaped structure of the Perm anomaly can also be observed in a particular stage of a developing mantle plume (Farnetani and Samuel, 2005). Thus, the Perm anomaly may represent a stable small-scale chemical pile or a developing mantle plume generated through complex interactions with the surrounding high-velocity mantle.
Our results suggest that revealing the fine-scale morphology of low-velocity anomalies is extremely important for understanding their origins and dynamic processes. It is worthwhile to look further into worldwide high-velocity regions and the ambient mantle for waveform complexities at large distances from 90° to 110°.
Constructing the global framework of regional-and local-scale low-velocity anomalies and surrounding mantle will improve our understanding of the ambiguous dynamic processes in the lowermost mantle.

Conclusion
We have constrained the detailed morphology and velocity structure of the seismic anomaly near the CMB beneath Perm. Traveltime analysis and forward 3D waveform modeling studies suggest that the low-velocity anomaly beneath Perm is a domeshaped feature with a thickness of 400 km and a diameter varying from 400 km (top) to 900 km (CMB) and a surrounding 240-kmthick high-velocity D" structure. The dome-shaped geometry of the Perm anomaly is consistent with that of a stable chemical pile or of a developing mantle plume near the CMB. The best-fitting Iceland model is mushroom-shaped, with a stem with a radius of 350 km in the lowermost 250 km of the mantle and a cap with a radius that increases from 550 km at 250 km above the CMB to 650 km at 600 km above the CMB. The best-fitting Kamchatka model has a wide cap with a diameter of approximately 1600 km and a narrow stem with a diameter of approximately 550 km. The detailed velocity structures of the constructed models are illustrated by different colors in accordance with the legend (e.g., red represents velocity reduction of -3% and white represents velocity reduction of 0%), except the colors of the stem of the Iceland model range from red (a velocity reduction of -3% at 240 km above the CMB) to brown (a velocity reduction of -6% at the CMB). The backgrounds in (a) and (b) are tomographic shear velocity perturbations at the CMB from a tomographic model by Simmons et al. (2010). Azimuth (

Auxiliary Material
This data set contains seismic data for an event (2010/07/24) occurred in Mindanao, Philippines and a reference event (2013/06/02) occurred in Taiwan of China. Both events are recorded in Europe. Seismic data for another event (2010/04/11) occurred in Spain and relative reference event (2011/04/01) occurred in Greece are also presented. Tangential displacements along with epicentral distance or azimuth for events 2010/07/24 and 2010/04/11 are shown in the Figure S1 and Figure S2, respectively. Raypaths, tangential displacements for event 2013/06/02 and radial displacements for event 2010/07/24 are shown in the Figure S3. Figure S4 presents tangential displacements for event 2011/04/01 and radial displacements for event 2010/04/11. Events list for travel time analyses is shown in Tables S1, and correlation coefficients between S and ScS-S, and ScS and ScS-S are shown in Table S2.