Tagh Fault

Feng Cheng
email: cfcf.chengfeng@gmail.com

Carmala Garzione

Marc Jolivet

Weitao Wang

Jibao Dong

Fabiana Richter

Zhaojie Guo

Provenance analysis of the Yumen Basin and northern Qilian Shan: implications for the pre-collisional paleogeography in the NE Tibetan plateau and eastern termination of Altyn

Keywords: Detrital zircon geochronology, Sandstone petrography, Northeastern Tibetan plateau, Altyn Tagh Fault, Cretaceous paleogeography

Understanding the pre-collisional paleogeography in the NE Tibetan plateau provides insights into the growth mechanisms of the northern portion of the plateau in the Cenozoic. We conducted sandstone petrography analysis and determined U-Pb ages for detrital zircons from Cretaceous sandstone from the Yumen Basin and the northern Qilian Shan. Cretaceous strata in the northern Yumen Basin yield a unimodal age population at 290-240 Ma that indicates primary derivation from Bei Shan. Cretaceous strata in the westernmost Yumen Basin contain zircons of 2.6-2.2 Ga, 2.1-1.7 Ga, 1.4-0.7 Ga, 440-380 Ma and 300-230 Ma, suggesting source derivation from both the Qilian Shan and Bei Shan. Within the northern Qilian Shan, Cretaceous strata yield age populations of 2.8-2.3 Ga, 2.1-1.2 Ga, 480-380 Ma and ca. 270 Ma, indicating derivation from the Qilian Shan. Sandstone composition results show that a sample from the northern Qilian Shan contains more lithic fragments and plots in the recycled orogen field of the quartz-feldspar-lithics (QFL) diagram, while samples from Yumen Basin are more quartz-rich and plot close to the continental block field of the QFL diagram. This compositional difference corresponds to source variation, consistent with the detrital zircon record. Combined with existing sedimentology and low-temperature thermochronology datasets, we suggest the presence of Cretaceous topographic relief in the Bei Shan and Qilian Shan prior to India-Asia collision. Considering >300 km post-Cretaceous left-lateral offset along the Altyn Tagh Fault (ATF) and the consistently similar detrital zircon ages spectra of the samples from the Cretaceous to late Oligocene strata in the Yumen Basin, we infer the palaeogeography in the NE Tibetan plateau has been similar from the late Cretaceous to the late Oligocene with ATF termination in the western Yumen Basin instead of having been linked to strike-slip faults in the Alxa or other regions to the east since its initiation.

Introduction

It is widely acknowledged that the India-Asia collision in the early Cenozoic and the ongoing post-collisional convergence have driven the outward growth of the Tibetan plateau [START_REF] Decelles | Implications of shortening in the Himalayan fold-thrust belt for uplift of the Tibetan plateau[END_REF][START_REF] Dewey | The Tectonic Evolution of the Tibetan Plateau[END_REF][START_REF] England | The Cretaceous-Tertiary deformation of the Lhasa block and its implications for crustal thickening in Tibet[END_REF]Kapp et al., 2007b;[START_REF] Molnar | Cenozoic tectonics of Asia: Effects of a continental collision[END_REF][START_REF] Jolivet | Mesozoic and Cenozoic tectonics of the northern edge of the Tibetan plateau: fission-track constraints[END_REF][START_REF] Yin | Geologic evolution of the Himalayan-Tibetan orogen[END_REF]. As the pre-Himalayan orogenesis played a significant role in the topographic evolution of the modern Tibetan plateau, it is crucial to determine the pre-collisional paleogeography in the Tibetan plateau prior to the India-Asia collision.

In recent years, a growing body of evidence has suggested that the southern, southeastern, northern and eastern margins of Tibet (Fig. 1), developed elevated topography prior to the collision (Cheng et al., 2016a;Cheng et al., 2015a;[START_REF] Ding | The Andean-type Gangdese Mountains: Paleoelevation record from the Paleocene-Eocene Linzhou Basin[END_REF][START_REF] England | The Cretaceous-Tertiary deformation of the Lhasa block and its implications for crustal thickening in Tibet[END_REF][START_REF] Enkelmann | Cenozoic exhumation and deformation of northeastern Tibet and the Qinling: Is Tibetan lower crustal flow diverging around the Sichuan Basin[END_REF][START_REF] Jolivet | Mesozoic and Cenozoic tectonics of the northern edge of the Tibetan plateau: fission-track constraints[END_REF]Kapp et al., 2007a;Kapp et al., 2007b;[START_REF] Kapp | Cretaceous-Tertiary shortening, basin development, and volcanism in central Tibet[END_REF][START_REF] Leier | Detrital zircon geochronology of Carboniferous-Cretaceous strata in the Lhasa terrane, Southern Tibet[END_REF][START_REF] Li | Late Cretaceous-Cenozoic basin evolution and topographic growth of the Hoh Xil Basin, central Tibetan Plateau[END_REF][START_REF] Lippert | The Early Cretaceous to present latitude of the central Lhasa-plano (Tibet): A paleomagnetic synthesis with implications for Cenozoic tectonics, paleogeography, and climate of Asia[END_REF][START_REF] Murphy | Did the Indo-Asian collision alone create the Tibetan plateau?[END_REF][START_REF] Pullen | Gangdese retroarc thrust belt and foreland basin deposits in the Damxung area, southern Tibet[END_REF][START_REF] Roger | Mesozoic-Cenozoic tectonothermal evolution of the eastern part of the Tibetan Plateau (Songpan-Garzê, Longmen Shan area): insights from thermochronological data and simple thermal modelling[END_REF]Tian et al., 2016a;Wu et al., 2016;[START_REF] Yang | Sichuan Basin and beyond: Eastward foreland growth of the Tibetan Plateau from an integration of Late Cretaceous-Cenozoic fission track and (U-Th)/He ages of the eastern Tibetan Plateau, Qinling, and Daba Shan[END_REF][START_REF] Zhang | Late Mesozoic-Cenozoic Exhumation of the Northern Hexi Corridor: Constrained by Apatite Fission Track Ages of the Longshoushan[END_REF] (Fig. 1). However, the late Mesozoicearly Cenozoic pre-collisional paleogeography of the northeastern Tibetan plateau is still poorly constrained, which may be attributed in part to the lack of detailed geologic information over the remote and often inaccessible Qilian Shan region (Fig. 1). Given that the present topography might be partly inherited from the Mesozoic geodynamic evolution, it is significant to determine the pre-collisional tectonics or paleogeography in the northeastern Tibetan plateau. Though few groups have conducted field investigations in the Yumen Basin and further inferred that the Qilian Shan to the south and Bei

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Shan to the north might be the two major source areas of the late Mesozoicearly Cenozoic strata in the Yumen Basin (Peng, 2013;Wang et al., 2016c;[START_REF] Yang | Sedimentary Characteristics and Tectonic Setting of the Lower Cretaceous strata in Jiuxi Basin, Gansu[END_REF](Fig. 1), the contribution of each source area as well as its variation through time have not been quantitatively estimated yet. Combined with existing datasets (including sedimentology, low-temperature thermochronology, etc.), a quantitative estimate of contribution of each source area contributes to a better understanding of the late Mesozoicearly Cenozoic paleogeography and growth of the northeastern Tibetan plateau. (Cheng et al., 2016a;Cheng et al., 2015a;[START_REF] England | The Cretaceous-Tertiary deformation of the Lhasa block and its implications for crustal thickening in Tibet[END_REF][START_REF] Enkelmann | Cenozoic exhumation and deformation of northeastern Tibet and the Qinling: Is Tibetan lower crustal flow diverging around the Sichuan Basin[END_REF]George et al., 2001;[START_REF] Jolivet | Mesozoic and Cenozoic tectonics of the northern edge of the Tibetan plateau: fission-track constraints[END_REF]Kapp et al., 2007a;Kapp et al., 2007b;[START_REF] Kapp | Cretaceous-Tertiary shortening, basin development, and volcanism in central Tibet[END_REF][START_REF] Leier | Detrital zircon geochronology of Carboniferous-Cretaceous strata in the Lhasa terrane, Southern Tibet[END_REF][START_REF] Li | Late Cretaceous-Cenozoic basin evolution and topographic growth of the Hoh Xil Basin, central Tibetan Plateau[END_REF][START_REF] Liu | Eocene onset and late Miocene acceleration of Cenozoic intracontinental extension in the North Qinling range-Weihe graben: Insights from apatite fission track thermochronology[END_REF][START_REF] Murphy | Did the Indo-Asian collision alone create the Tibetan plateau?[END_REF][START_REF] Pan | Cretaceous and Cenozoic cooling history of the eastern Qilian Shan, north-eastern margin of the Tibetan Plateau: evidence from apatite fission-track analysis[END_REF][START_REF] Pullen | Gangdese retroarc thrust belt and foreland basin deposits in the Damxung area, southern Tibet[END_REF]Staisch et al., 2014;Tian et al., 2016a;Volkmer et al., 2007;Wang et al., 2017b;[START_REF] Yang | Sichuan Basin and beyond: Eastward foreland growth of the Tibetan Plateau from an integration of Late Cretaceous-Cenozoic fission track and (U-Th)/He ages of the eastern Tibetan Plateau, Qinling, and Daba Shan[END_REF][START_REF] Zhang | Late Mesozoic-Cenozoic Exhumation of the Northern Hexi Corridor: Constrained by Apatite Fission Track Ages of the Longshoushan[END_REF].

The modern left-lateral displacement along the Altyn Tagh Fault (ATF) marks the northern edge of the Tibetan plateau (Figs. 1 and2a) and is considered to have accommodated about 300-500 km of intracontinental deformation in response to India-Asia collision and subsequent postcollisional convergence (Cheng et al., 2015a;Cheng et al., 2015b;Cheng et al., 2016b;Cowgill et al., 2003;[START_REF] Searle | Crustal-lithospheric structure and continental extrusion of Tibet[END_REF][START_REF] Yin | Geologic evolution of the Himalayan-Tibetan orogen[END_REF][START_REF] Yin | Tectonic history of the Altyn Tagh fault system in northern Tibet inferred from Cenozoic sedimentation[END_REF][START_REF] Zhang | Transforming the Miocene Altyn Tagh fault slip into shortening of the north-western Qilian Shan: insights from the drainage basin geometry[END_REF].

However, the question of where the ATF terminated at its eastern tip during the Cenozoic (since its initiation) remains highly debated. Some workers suggest that the ATF terminated in the

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Qilian Shan region since its Eocene or Miocene initiation [START_REF] Burchfiel | Intracrustal detachment within zones of continental deformation[END_REF]Cheng et al., 2015b;Cowgill et al., 2003;Dupont-Nivet et al., 2004;[START_REF] Jolivet | Mesozoic and Cenozoic tectonics of the northern edge of the Tibetan plateau: fission-track constraints[END_REF][START_REF] Métivier | Northeastward growth of the Tibet plateau deduced from balanced reconstruction of two depositional areas: The Qaidam and Hexi Corridor basins, China[END_REF]Wang et al., 2006;Wittlinger et al., 1998;[START_REF] Yin | Geologic evolution of the Himalayan-Tibetan orogen[END_REF][START_REF] Yin | Tectonic history of the Altyn Tagh fault system in northern Tibet inferred from Cenozoic sedimentation[END_REF] (Fig. 1a). On the other hand, based on field investigation in the Yumen Basin, remote sensing image interpretation for the structures in the Hexi Corridor and Alxa block as well as the correlation between tectonic units and sutures in Bei Shan and the Inner Mongolia orogens, some studies argue that the ATF extended beyond the Qilian Shan since its initiation, linking with strike-slip faults in the Alxa block (East Mongolia), or even as far as the subduction system in the Sea of Okhotsk [START_REF] Darby | Did the Altyn Tagh fault extend beyond the Tibetan Plateau?[END_REF][START_REF] Yue | Two-stage evolution model for the Altyn Tagh fault, China[END_REF]. If the Paleogene deformation along the ATF terminated in Qilian Shan, we would expect that the large amounts of sinistral displacement along the ATF since the India-Asia collision were largely transferred into Qilian Shan region and were accommodated by oblique slipping along the faults in the mountain ranges; otherwise such a large amount of deformation would be accommodated through left-lateral strike-slip displacement along the ATF and would be transferred to the region further to the east, out of Tibetan plateau. Given that these two different geometries proposed for the ATF at its eastern termination result in diverse understandings of the timing and mechanisms of crustal deformation in the northern Tibetan plateau, it is of primary importance to distinguish which geometry is accurate.

Detrital zircon geochronology has been developed as a valuable tool for unraveling source to sink relationships within a given area through time [START_REF] Fedo | Detrital zircon analysis of the sedimentary record[END_REF]Thomas, 2011). In addition, great progress has been made in quantitative methods of unmixing detrital geochronology age distributions [START_REF] Licht | Eolian cannibalism: Reworked loess and fluvial sediment as the main sources of the Chinese Loess Plateau[END_REF]Sundell and Saylor, 2017). In this study, we sampled five Cretaceous sandstone samples exposed in the Yumen Basin and northern Qilian (Wang et al., 2016c). The ages presented are from previous geochronology studies [START_REF] Bovet | Evidence of Miocene crustal shortening in the north Qilian Shan from Cenozoic stratigraphy of the western Hexi Corridor, Gansu Province, China[END_REF]Chen et al., 2014b;Chen et al., 2012;[START_REF] Duan | Geochronological and geochemical constraints on the petrogenesis and tectonic significance of Paleozoic dolerite dykes in the southern margin of Alxa Block, North China Craton[END_REF]Gehrels et al., 2003b;Gong et al., 2017;[START_REF] Lu | Geological and geochronological evidence for the Precambrian evolution of the Tarim Craton and surrounding continental fragments[END_REF][START_REF] Song | Tectonics of the North Qilian orogen, NW China. Gondwana Research 23[END_REF]Song et al., 2009;Tseng et al., 2007;Tung et al., 2007;Tung et al., 2016;Wang et al., Wang et al., 2016a;Wei and Song, 2008;Xia and Song, 2010;[START_REF] Xu | The 600-580Ma continental rift basalts in North Qilian Shan, northwest China: Links between the Qilian-Qaidam block and SE Australia, and the reconstruction of East Gondwana[END_REF][START_REF] Yang | Silurian collisional suturing onto the southern margin of the North China Craton: detrital zircon geochronology constraints from the Qilian Orogen[END_REF][START_REF] Yu | Petrogenesis of the early Paleozoic low-Mg and high-Mg adakitic rocks in the North Qilian orogenic belt, NW China: Implications for transition from crustal thickening to extension thinning[END_REF][START_REF] A C C E P T E D M A N U S C R I P T Zeng | Geochemistry, zircon U-Pb dating and Hf isotopies composition of Paleozoic granitoids in Jinchuan, NW China: Constraints on their petrogenesis, source characteristics and tectonic implication[END_REF]Zhang et al., 2007a;Zheng et al., 2017b) [START_REF] Bovet | Evidence of Miocene crustal shortening in the north Qilian Shan from Cenozoic stratigraphy of the western Hexi Corridor, Gansu Province, China[END_REF]Gehrels et al., 2003b).

A C C E P T E D M A N U S C R I P T 2017a;

Regional geology

2.1

Qilian Shan, Yumen Basin and Altyn Tagh Fault

The Qilian Shan marks the northeastern margin of the Tibetan plateau, occupying a transition zone between the high elevation plateau and the adjacent low-elevation cratons [START_REF] Lease | Cenozoic mountain building on the northeastern Tibetan Plateau[END_REF][START_REF] Meyer | Crustal thickening in Gansu-Qinghai, lithospheric mantle subduction, and oblique, strike-slip controlled growth of the Tibet plateau[END_REF]Tapponnier et al., 1990) (Fig. 1). The Qilian Shan contains massive NW-SE striking ranges that grow on folds, thrusts or strike-slip faults accommodating the northward motion of the Tibetan plateau [START_REF] Allen | Partitioning of oblique convergence coupled to the fault locking behavior of fold-and-thrust belts: Evidence from the Qilian Shan, northeastern Tibetan Plateau[END_REF][START_REF] Meyer | Crustal thickening in Gansu-Qinghai, lithospheric mantle subduction, and oblique, strike-slip controlled growth of the Tibet plateau[END_REF][START_REF] Yin | Geologic evolution of the Himalayan-Tibetan orogen[END_REF][START_REF] Zuza | Testing models of Tibetan Plateau formation with Cenozoic shortening estimates across the Qilian Shan-Nan Shan thrust belt[END_REF]. Based on field investigation in the Qaidam Basin and Yumen

Basin, low temperature thermochronology from the basement rocks in the northern Qilian Shan or from the Cenozoic sedimentary rocks in the Yumen Basin, and provenance analysis of the Cenozoic strata in the Yumen Basin and northern Qilian Shan, some studies have argued that

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crustal shortening and surface uplift began in the southern Qilian Shan during the Paleogene (Wang et al., 2017c;[START_REF] Yin | Cenozoic tectonic evolution of Qaidam basin and its surrounding A C C E P T E D M A N U S C R I P T regions (Part 1): The southern Qilian Shan-Nan Shan thrust belt and northern Qaidam basin[END_REF][START_REF] Zhuang | Cenozoic multiple-phase tectonic evolution of the northern Tibetan Plateau: Constraints from sedimentary records from Qaidam basin, Hexi Corridor, and Subei basin, northwest China[END_REF] and later propagated northward into the central and northern Qilian Shan [START_REF] Bovet | Evidence of Miocene crustal shortening in the north Qilian Shan from Cenozoic stratigraphy of the western Hexi Corridor, Gansu Province, China[END_REF][START_REF] Lease | Cenozoic mountain building on the northeastern Tibetan Plateau[END_REF][START_REF] Métivier | Northeastward growth of the Tibet plateau deduced from balanced reconstruction of two depositional areas: The Qaidam and Hexi Corridor basins, China[END_REF][START_REF] Meyer | Crustal thickening in Gansu-Qinghai, lithospheric mantle subduction, and oblique, strike-slip controlled growth of the Tibet plateau[END_REF]Wang et al., 2016b;[START_REF] Zheng | Erosion, fault initiation and topographic growth of the North Qilian Shan (northern Tibetan Plateau)[END_REF][START_REF] Zhuang | Cenozoic multiple-phase tectonic evolution of the northern Tibetan Plateau: Constraints from sedimentary records from Qaidam basin, Hexi Corridor, and Subei basin, northwest China[END_REF]. However, the overall data coverage of dataset is still sparse, which is partly attributed to the lack of detailed geologic information over the remote and often inaccessible mountain ranges in the Qilian Shan.

In this study, we follow the previous definition of the northern Qilian Shan [START_REF] Bovet | Evidence of Miocene crustal shortening in the north Qilian Shan from Cenozoic stratigraphy of the western Hexi Corridor, Gansu Province, China[END_REF]Gehrels et al., 2003b). The extent of the northern Qilian Shan is labelled in Figure 3. The Qilian Shan is bordered by the Hexi Corridor to the north and truncated by the lithosphere-scale, sinistral strike-slip ATF to the west (Figs. 1 and2). Left-lateral displacement along the ATF has accommodated hundreds of kilometers of the post-collisional convergence between the India and Asia, but the estimates of its total offset generally vary between ca. 300 km to ca. 500 km [START_REF] Chen | New paleomagnetic constraints on central Asian kinematics: Displacement along the Altyn Tagh fault and rotation of the Qaidam Basin[END_REF]Cheng et al., 2015a;Cheng et al., 2015b;Cheng et al., 2016b;Cowgill et al., 2003;[START_REF] Ritts | Magnitude of post-Middle Jurassic (Bajocian) displacement on the central Altyn Tagh fault system, northwest China[END_REF][START_REF] Searle | Crustal-lithospheric structure and continental extrusion of Tibet[END_REF][START_REF] Yin | Tectonic history of the Altyn Tagh fault system in northern Tibet inferred from Cenozoic sedimentation[END_REF].

A series of transpressional faults developed in the Hexi Corridor in response to the northward propagation of the Qilian Shan, separating several sub-basins (Wang et al., 2016b).

The Yumen Basin, in the transition zone between the northern Qilian Shan and the Bei Shan, is the westernmost sub-basin of the Hexi Corridor (Fig. 2a). The middle Eocene to Quaternary strata (including the Huoshaogou, Baiyanghe, Sulehe, Yumen, and Jiuquan formations, from the oldest to the youngest) of the Yumen Basin are well-exposed (Peng, 2013;Wang et al., 2016b), composed of alluvial to marginal lacustrine deposits (Dai et al., 2005;Wang et al., 2016c;Wang et al., 2016d;Yang et al., 2011) (Figs. 2-4). Those Cenozoic strata unconformably overlie Lower Cretaceous strata (Figs. 4 and5) that are widespread along the northern Qilian Shan and

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in the Yumen Basin (Figs. 2a and3). In the northern Qilian Shan, the Lower Cretaceous strata mainly consist of thick beds of massive red conglomerate and coarse sandstone associated with high energy proximal fluvial and alluvial fan depositional settings (Peng, 2013) (Fig. 4). In the Yumen Basin, especially in its central and northern parts, the Lower Cretaceous strata are mainly composed of thin beds of greenish grey claystone and siltstone intercalated with thin to thick beds of brownish grey massive sandstone and conglomerate, corresponding to lacustrine facies deposits (Peng, 2013). (2016b), respectively. These five sections are measured from both this study and previous work (Dai et al., 2005;Peng, 2013;Wang et al., 2016b). The paleocurrent measurements are from previous work (Dai et al., 2005;Peng, 2013;Wang et al., 2016c). FZ1-FZ5, and FZ7 are Cenozoic detrital zircon samples from our previous work (Wang et al., 2016c). This early Cretaceous tectonic reactivation might either correspond to the Lhasa/Eurasia collision and subsequent slab break-off, or link with the collision along Mongol-Okhosk

Orogeny and subsequent collapse (Gillespie et al., 2017;Jolivet et al., 2013b;Jolivet et al., 2010).

Due to the lack of the geological information in the remote Qilian Shan region, the early Cretaceous tectonic setting in the Qilian Shan is not well constrained. Based on apatite fission track analysis, previous work has demonstrated Cretaceous cooling and exhumation of the northern Qilian Shan (George et al., 2001;[START_REF] Jolivet | Mesozoic and Cenozoic tectonics of the northern edge of the Tibetan plateau: fission-track constraints[END_REF][START_REF] Pan | Cretaceous and Cenozoic cooling history of the eastern Qilian Shan, north-eastern margin of the Tibetan Plateau: evidence from apatite fission-track analysis[END_REF]. Our field investigation observed a NNE-SSW trending normal fault in the northern Qilian Shan (Fig. 5a), likely indicative of an extensional setting in the northern Qilian Shan during the early Cretaceous.

Further effort should be made to unravel the tectonic setting in the Bei Shan and Qilian Shan regions.

Stratigraphy and sediment characteristics of the studied sections

Three of our studied sections are located in the Yumen Basin, namely the Caogou, Huoshaogou and Hongliuxia sections (Figs. 234). The Jingtieshan and northern Qilian Shan sections are located in the northern Qilian Shan (Figs. 234). In the Caogou and Huoshaogou 3 Approach and Methods

Sandstone petrography

Five Cretaceous sandstone samples, namely CG-K, HSG-K, HLX-K, NQL-K and JST-K, were collected from the Yumen Basin and northern Qilian Shan for petrographic analysis. We prepared standard thin sections and stained the thin sections to identify potassium feldspar. We used cross-polarization microscope to observe the petrographic features, including mineral composition, grain size, sorting and roundness. Cross-polarized light photomicrographs of these five samples are shown in Fig. 6a-6e. Modal compositions were then determined by utilizing the modified Gazzi-Dickinson point-counting method [START_REF] Ingersoll | The effect of grain size on detrital modes: a test of the Gazzi-Dickinson point-counting method[END_REF]. According to the method of [START_REF] Dickinson | Plate tectonics and sandstone compositions[END_REF], sample JTS-K containing more than 25% of matrix or cement has been excluded from consideration (Fig. 6e). A minimum of 400 points were counted per sample. Raw point-counting data are summarized in the supplementary

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Samples were classified and plotted on the ternary diagrams (Fig. 6f-6g) using the scheme outlined in [START_REF] Dickinson | Provenance of North American Phanerozoic sandstones in relation to tectonic setting[END_REF]. We follow the mineral abbreviation of [START_REF] Dickinson | Plate tectonics and sandstone compositions[END_REF] to better describe our results: Qt for total quartz, Qm for monocrystalline quartz, F for feldspar, L for lithic rock fragments, and Lt for total lithic grains including polycrystalline quartz.

Detrital zircon geochronology

Combined with sedimentology and low-temperature thermochronology datasets, detrital zircon U-Pb geochronology has been widely used to understand the paleogeography of a region by reconstructing the source of sediment in ancient sedimentary systems [START_REF] Gehrels | Detrital Zircon U-Pb Geochronology Applied to Tectonics[END_REF][START_REF] Gehrels | Detrital zircon U-Pb geochronology and Hf isotope geochemistry of Paleozoic and Triassic passive margin strata of western North America[END_REF]. In this study, we collected five sandstone samples (about 5kg each) from

Cretaceous outcrops and extracted zircon grains following the standard procedures outlined in [START_REF] Li | Mesozoic-Cenozoic tectonic relationships between the Kuqa subbasin and Tian Shan, northwest China: constraints from depositional records[END_REF]. This work was carried out at the Chengxin Geology Service Co. Ltd., Langfang, China. In order to avoid sampling bias, zircon crystals (generally >200 grains) were mounted in epoxy resin without handpicking, together with fragments or loose grains of Sri Lanka, FC-1, and R33 zircon crystals for use as standards. Zircon crystals were then polished to obtain a smooth internal surface.

Zircon U-Pb dating was conducted using laser ablation inductively coupled plasma mass spectrometry (LA-ICPMS) at the Arizona LaserChron Center [START_REF] Gehrels | Detrital zircon U-Pb geochronology and Hf isotope geochemistry of Paleozoic and Triassic passive margin strata of western North America[END_REF][START_REF] Gehrels | Detrital zircon geochronology by laser-ablation multicollector ICPMS at the Arizona LaserChron Center[END_REF][START_REF] Gehrels | Enhanced precision, accuracy, efficiency, and spatial resolution of U-Pb ages by laser ablation-multicollector-inductively coupled plasmamass spectrometry[END_REF]. All five samples were ablated using a 30 μm laser beam diameter. Detailed methods for analysis on the laser-coupled Thermo Element 2 single-collector ICP-MS were previously described by [START_REF] Pullen | What happens when n= 1000? Creating large-n geochronological datasets with LA-ICP-MS for geologic investigations[END_REF].

Results

Sandstone petrographic results

Samples CG-K and HSG-K were collected in the Caogou and Huoshaogou sections, respectively (Figs. 2 and3), from fine-to medium-grained sandstones. Both samples are well to moderately sorted and characterized by subangular to subrounded grains (Fig. 6a-6b). The modal

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compositions of sample HSG-K are Qt: F: L= 68:22:10, plotting near the boundary between "transitional continental" field and "recycled orogen" field (Fig. 6f) in the QtFL diagram and Qm: F: Lt=59:22:19, plotting near the boundary between "transitional continental" field and "quartzose recycled" field in the QmFLt diagram (Fig. 6g). Modal compositions for sample HSG-K are Qt: F: L= 58:35:7, plotting near the boundary between "transitional continental" field and "recycled orogen" field in the QtFL diagram (Fig. 6f) and Qm: F: Lt=47:35:18, plotting near the boundary between the "transitional continental" field and "mixed" field in the QmFLt diagram (Fig. 6g).

Sample HLX-K was collected in the Hongliuxia section (Figs. 2 and3), from fine-to medium-grained sandstone. Sample HLX-K is characterized by moderately sorted and subangular to subrounded grains (Fig. 6c). Modal compositions for sample HLX-K are Qt: F: L= 62:14:24 and Qm: F: Lt=39:14:48, plotting in the "recycled orogen" field in the QtFL diagram (Fig. 5f) and "quartzose recycled" field in the QmFLt diagram, respectively (Fig. 6g).

Samples NQL-K and JTS-K were collected in the northern Qilian Shan (Figs. Previous studies have suggested that the zircon grains of magmatic origin normally have high

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Th/U radios (>0.1), while the zircon grains of metamorphic origin have low Th/U radios (<0.1) [START_REF] Belousova | Igneous zircon: trace element composition as an indicator of source rock type[END_REF][START_REF] Hoskin | Metamorphic zircon formation by solid-state recrystallization of protolith igneous zircon[END_REF]. Analyzed zircon age vs. Th/U ratios are shown in Figure 7f, indicating the predominant magmatic origin of all the analyzed zircons.

Zircon U-Pb age cumulative probability distribution for each sample are shown in Figure 8.

Following our previous criteria (Cheng et al., 2016a), age peaks are considered major when including at least 20% of the total number of data spread over less than 250 Ma, whereas a minor peak refers to populations representing less than 20% of the total number of data distributed over more than 300 Ma. The Th/U ratios vary from 0.10 to 1.67, with four exceptions of 0.02 (412 Ma), 0.03 (424 Ma), 0.08 (258 Ma) and 0.09 (431 Ma), confirming the predominant magmatic origin of the zircons [START_REF] Belousova | Igneous zircon: trace element composition as an indicator of source rock type[END_REF][START_REF] Hoskin | Metamorphic zircon formation by solid-state recrystallization of protolith igneous zircon[END_REF]. Among the 110 analyzed zircons, 106 U-Pb ages with discordance degree <10% were obtained. The U-Pb ages range from 1957 Ma to 221

Ma with a single peak at 278-240 Ma (Fig. 8i). The zircon crystals in sample HSG-K show euhedral to abraded shapes, with an average size ranging between 25 μm and 150 μm. The Th/U ratios vary from 0.15 to 1.71, with only one exception of 0.05 (247 Ma), confirming a magmatic source. Among the 110 analyzed crystals, 109 effective ages were obtained. The U-Pb ages vary from 1924 Ma to 229 Ma, with a unimodal age peak at 288-242 Ma (Fig. 8j).

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A N U S C R I P T (http://www.laserchron.org). BS2 and BS3 are modern river samples from Bei Shan, from our previous work (Wang et al., 2016c). QL1 and QL2 are modern river samples from Qilian Shan, from our previous work (Wang et al., 2016c). Zircon U-Pb age cumulative probability distributions of these modern river samples are used to characterize the age of granitoid plutons in the Qilian Shan and Bei Shan (Wang et al., 2016c). FZ1, FZ2 and FZ4-FZ7 are Cenozoic samples obtained from the Caogou section, from our previous work (Wang et al., 2016c). CG-K, HSG-K, HLX-K, NQL-K and JTS-K are new samples collected from the Cretaceous strata in the Caogou, Huoshangou, Hongliuxia, Northern Qilian Shan, and Jingtieshan sections, respectively.

Locations of these samples are shown in Figs. detrital zircon data are from Wang et al. (2016c). Note that zircon age distributions from samples FZ1, FZ2, HSG-K and CG-K are statistically similar with those of modern river samples from the Bei Shan region (samples BS2 and BS3), whereas zircon age distributions from samples FZ4, FZ5, FZ6, FZ7, NQL-K, JTS-K and HLX-K are statistically similar with those of modern river samples sourced from the Qilian Shan region (samples QL1 and QL2).

In sample HLX-K, the zircon grains show euhedral to abraded shapes and an average size of 50 μm to 250 μm. The Th/U ratios vary from 0.11 to 2.91, with two exceptions of 0.03 (360 Ma) and 0.04 (1034 Ma), indicative of a largely magmatic origin [START_REF] Belousova | Igneous zircon: trace element composition as an indicator of source rock type[END_REF][START_REF] Hoskin | Metamorphic zircon formation by solid-state recrystallization of protolith igneous zircon[END_REF]. Among the 110 analyzed zircons, 101 ages were obtained with discordance degree <10%. Five major age populations dominate with peaks at ca. 2580-2200 Ma, 2058-1710 Ma, 1380-780 Ma, 440-380 Ma, 280-230 Ma (Fig. 8o).

The zircon grains from sample NQL-K show euhedral to abraded shapes, with an average size ranging between 25 μm to 250 μm. The Th/U ratios range from 0.10 to 1.59, with one exception of 0.03 (388 Ma), confirming a magmatic source [START_REF] Belousova | Igneous zircon: trace element composition as an indicator of source rock type[END_REF][START_REF] Hoskin | Metamorphic zircon formation by solid-state recrystallization of protolith igneous zircon[END_REF]. One-hundred and ten crystals were analyzed, and 100 ages have discordance degree <10%. The U-Pb ages range from 2899 Ma to 231 Ma, and can be divided into three populations with one major peak at ca. 440 Ma and two minor peaks at 1920-1600 Ma and ca.

275 Ma, respectively (Fig. 8p).

In sample JTS-K, the zircon crystals are smaller (20-100 μm) compared with the grains in the previous samples and again show euhedral to abraded shapes. The Th/U ratios range from 0.10 to 5.84, with six exceptions of 1.9*10 -5 (1331 Ma), 0.02 (2705 Ma), 0.03 (233 Ma), 0.06 (392 Ma), 0.09 (991 Ma) and 0.09 (1921 Ma), suggesting the predominant magmatic origin of

A C C E P T E D M

A N U S C R I P T the zircons [START_REF] Belousova | Igneous zircon: trace element composition as an indicator of source rock type[END_REF][START_REF] Hoskin | Metamorphic zircon formation by solid-state recrystallization of protolith igneous zircon[END_REF]. In total, 110 crystals were analyzed, and 97 ages have discordance degree <10%. The U-Pb ages range from 2912 Ma to 155 Ma with four distinct peaks at ca. 2740-2280 Ma, 2050-1180 Ma, 435 Ma and 278 Ma (Fig. 8q).

Discussion

Provenance analysis

By systemically comparing the detrital zircon dataset obtained from the Cretaceous samples in the Yumen Basin and northern Qilian Shan with known ages of the potential source terranes, we can determine the source to sink relationship between the Yumen Basin and the surrounding mountain belts. Based on the detrital zircon analysis of modern fluvial sand samples together with the U-Pb geochronology of basement rocks, previous studies have revealed the distinct U-Pb age signature of the northern Qilian Shan and Bei Shan regions [START_REF] Bovet | Evidence of Miocene crustal shortening in the north Qilian Shan from Cenozoic stratigraphy of the western Hexi Corridor, Gansu Province, China[END_REF]Chen et al., 2014b;Chen et al., 2012;Cheng et al., 2017;[START_REF] Duan | Geochronological and geochemical constraints on the petrogenesis and tectonic significance of Paleozoic dolerite dykes in the southern margin of Alxa Block, North China Craton[END_REF]Gehrels et al., 2003b;Gong et al., 2017;[START_REF] Lu | Geological and geochronological evidence for the Precambrian evolution of the Tarim Craton and surrounding continental fragments[END_REF][START_REF] Song | Tectonics of the North Qilian orogen, NW China. Gondwana Research 23[END_REF]Song et al., 2009;Tseng et al., 2007;Tung et al., 2007;Tung et al., 2016;Wang et al., 2017a;Wang et al., 2016a;Wei and Song, 2008;Xia and Song, 2010;[START_REF] Xu | The 600-580Ma continental rift basalts in North Qilian Shan, northwest China: Links between the Qilian-Qaidam block and SE Australia, and the reconstruction of East Gondwana[END_REF][START_REF] Yang | Silurian collisional suturing onto the southern margin of the North China Craton: detrital zircon geochronology constraints from the Qilian Orogen[END_REF][START_REF] Yu | Petrogenesis of the early Paleozoic low-Mg and high-Mg adakitic rocks in the North Qilian orogenic belt, NW China: Implications for transition from crustal thickening to extension thinning[END_REF][START_REF] A C C E P T E D M A N U S C R I P T Zeng | Geochemistry, zircon U-Pb dating and Hf isotopies composition of Paleozoic granitoids in Jinchuan, NW China: Constraints on their petrogenesis, source characteristics and tectonic implication[END_REF]Zhang et al., 2007a;Zheng et al., 2017b) This interpretation is consistent with the SSE-directed paleoflow reported from the Caogou and Huoshaogou section (Dai et al., 2005;Wang et al., 2016c). The detrital zircon ages distribution of sample HLX-K is complex, dispersed between ca. 3201 Ma and ca. 231 Ma, with a major age

A C C E P T E D M

A N U S C R I P T peak of ca. 420 Ma (Fig. 8o). The early Paleozoic and Precambrian zircons account for ca. 90%

of the total analyzed grains, indicative of a predominant Qilian Shan source during the early Cretaceous. However, in the Hongliuxia section, clast-supported conglomerate shows pebbleimbrication mainly trending towards the south and northwest (Peng, 2013). These multiple paleocurrent directions suggest that both the northern Qilian Shan and the Bei Shan shed materials into the Yumen Basin during that period. The zircon ages spectrum of sample NQL-K is characterized by a single peak at ca. 439 Ma and two potential sub-peaks at 1921-1600 Ma and ca. 270 Ma, respectively. This sample was collected from a thin sandstone lens within a thickly bedded massive conglomerate. The angular cobbles and boulders in the conglomerate are poorly sorted suggesting deposition from a proximal source (Fig. 5h-5i). Finally, the detrital zircon ages distribution in sample JTS-K is characterized by a Permian age peak, a Silurian age peak, and two age populations of 2.8-2.1 Ga and 2.1-1.0 Ga, similar to the age distribution of the modern samples collected from two parallel rivers draining the Qilian Shan (samples QL1 and QL2, Figs.

2, 3 and 8). Moreover, this Cretaceous sandstone sample was collected from a thin sandstone lens that developed in a massive conglomerate bed in the northern Qilian Shan (Figs. 2 and3).

The sandstone is poorly sorted with angular grains, suggesting that the particles have not been transported very far (Figs. 5i and6e). This implies that the northern Qilian Shan served as a source for the sediments in the northern flank of northern Qilian Shan during the early Cretaceous.

Our detrital zircon geochronology study, together with previous paleocurrent analysis in this region, suggest that both the Bei Shan and the northern Qilian Shan served as two significant sources, shedding sediments into the Yumen Basin during the early Cretaceous. This is consistent with the thermochronometry data that suggest rapid initial basement cooling in both

A C C E P T E D M A N U S C R I P T
regions during Cretaceous time (George et al., 2001;Gillespie et al., 2017;[START_REF] Jolivet | Mesozoic and Cenozoic tectonics of the northern edge of the Tibetan plateau: fission-track constraints[END_REF][START_REF] Li | Apatite fission track constraints on the pattern of faulting in the north Qilian Mountain[END_REF][START_REF] Pan | Cretaceous and Cenozoic cooling history of the eastern Qilian Shan, north-eastern margin of the Tibetan Plateau: evidence from apatite fission-track analysis[END_REF][START_REF] Sobel | Jurassic to Cenozoic exhumation history of the Altyn Tagh range, northwest China, constrained by 40Ar/39Ar and apatite fission track thermochronology[END_REF]. However, detrital zircons with early Paleozoic and Precambrian ages, which are distinctive indicators of the northern Qilian Shan source, were only found in Lower Cretaceous samples collected in the northern Qilian Shan (sample JTS-K)

and the northern flank of the Qilian Shan (samples NQL-K and HLX-K). On the other hand, the U-Pb zircon age spectra of Lower Cretaceous samples (samples CG-K and HSG-K) from the Yumen Basin (Caogou and Huoshaogou sections) show a unimodal late Paleozoic age population, suggesting a unique source situated in the Bei Shan region. The south-directed drainage systems derived from the Bei Shan shed detritus in the Yumen Basin, whereas the materials eroded from the northern Qilian Shan appear to have been transported across the northern Qilian Shan, but deposited no further than the southern margin of the Yumen Basin.

The abovementioned provenance interpretation is consistent with our sandstone petrolography analysis (Fig. 6f and6g). Our sandstone petrographic results show that the Lower Cretaceous strata in the northern Qilian Shan (sample NQL-K) were sourced from a recycled orogen provenance setting. In contrast, the Lower Cretaceous strata in the Yumen Basin (samples CG-K, HSG-K and HLX-K) contain more feldspathic and quartzose compositions,

showing a shift towards a continental block source (Fig. 6f and6g). It is likely that the Qilian Shan (recycled orogen provenance) served as the predominant source for the sediments the northern Qilian Shan and southern Yumen Basin while the clastic materials in the northern Yumen Basin are mainly derived from Bei Shan (continental block provenance). According to the QFL ternary diagrams, the feldspar-and quartz-rich sandstones from the Yumen Basin may indicate a deep basement exposure of their source region (i.e. Bei Shan) during the early Cretaceous [START_REF] Dickinson | Provenance of North American Phanerozoic sandstones in relation to tectonic setting[END_REF], rather than a shallow basement exposure that relates to a

A C C E P T E D M A N U S C R I P T
thin-skinned fold-thrust system. Geologic survey also shows that the Paleozoic metasedimentary rocks, which are well-exposed within the Qilian Shan and on the north side of Bei Shan, are not exposed on the south side of Bei Shan, suggestive of a deeper basement exposure in the southern Bei Shan (Fig. 2; See Fig. 2 in He et al. ( 2018)) (He et al., 2018;[START_REF] Manuscript A C C E P T E D M A N U S C R I P T Li | Geochronology, petrogenesis and tectonic implications of Triassic granitoids from Beishan, NW China[END_REF]Xiao et al., 2010). The evidence from deep basement exposure of southern Bei Shan as well as the evidence of the extensional features within the Yumen Basin during the early Cretaceous (Chen et al., 2014a;Peng, 2013;[START_REF] Yang | The shoshonitic volcanic rocks at Hongliuxia: Pulses of the Altyn Tagh fault in Cretaceous?[END_REF][START_REF] Yang | Sedimentary Characteristics and Tectonic Setting of the Lower Cretaceous strata in Jiuxi Basin, Gansu[END_REF] are consistent with recent observations of extensional tectonics. However, further effort should be made to unravel the early Cretaceous tectonic setting in the Bei Shan and Qilian Shan regions.

Although some studies have identified the facies and depositional environments of the Lower Cretaceous strata in the Yumen Basin (Peng, 2013;[START_REF] Yang | Sedimentary Characteristics and Tectonic Setting of the Lower Cretaceous strata in Jiuxi Basin, Gansu[END_REF], few studies have investigated the Lower Cretaceous strata within the Qilian Shan yet. In this study, the Lower Cretaceous proximal deposits in the northern Qilian Shan (Figs. 5h-5i, 6e) and the significant Qilian Shan source detrital zircon signature for the Lower Cretaceous strata samples (see samples NQL-K and JTS-K in Fig. 7t) from the northern Qilian Shan call for pre-existing topographic relief in the northeast margin of the Tibetan plateau prior to the India-Asia collision.

5.2

Quantitatively determined mixing proportions between the Qilian Shan and Bei Shan sources: implication for multiple stages of growth of the NE Tibetan plateau

The detrital zircon ages distribution of the two Cretaceous samples (samples CG-K and HSG-K), characterized by a unimodal late Paleozoic to Mesozoic age peak, are very similar to that of the late Oligoceneearly Miocene samples (samples FZ1 and FZ2, see (Wang et al., 2016c)) collected in the Caogou section (Wang et al., 2016c) (Fig. 4). Previous provenance analysis determined that those late Oligocene -early Miocene strata were mainly derived from In addition, various lines of investigation, including evidence from (1) thermochronology studies on the Cenozoic strata in the Yumen Basin (He et al., 2017;Wang et al., 2016b;Zheng et al., 2017a) and on the basement rocks in the northern Qilian Shan [START_REF] Pan | Cretaceous and Cenozoic cooling history of the eastern Qilian Shan, north-eastern margin of the Tibetan Plateau: evidence from apatite fission-track analysis[END_REF][START_REF] Zheng | Erosion, fault initiation and topographic growth of the North Qilian Shan (northern Tibetan Plateau)[END_REF], (2) magnetostratigraphic studies of sediment accumulation rates in the Yumen Basin (Wang et al., 2016b), (3) stratigraphy and provenance analysis [START_REF] Bovet | Evidence of Miocene crustal shortening in the north Qilian Shan from Cenozoic stratigraphy of the western Hexi Corridor, Gansu Province, China[END_REF][START_REF] Lease | Pulsed Miocene range growth in northeastern Tibet: Insights from Xunhua Basin magnetostratigraphy and provenance[END_REF]Wang et al., 2016c), and (4) sediment color and grain-size studies from sediments preserved in the Yumen Basin (Wang et al., 2016d), have suggested a middle Miocene rapid growth of northern Qilian Shan. We thus infer that the palaeogeography in this region largely stable from the late Cretaceous to late Oligocene time and was then modified since the early Miocene in response to the reactivation of the Qilian Shan region [START_REF] Bovet | Evidence of Miocene crustal shortening in the north Qilian Shan from Cenozoic stratigraphy of the western Hexi Corridor, Gansu Province, China[END_REF]Wang et al., 2016b;Wang et al., 2016c;Wang et al., 2016d;Yue et al., 2004a;[START_REF] Zheng | Erosion, fault initiation and topographic growth of the North Qilian Shan (northern Tibetan Plateau)[END_REF] (Fig. 10).

Given the growing evidence for Oligocene-early Miocene reactivation of deformation in Xianshuihe fault system, Kunlun Shan, Tian Shan, and even the Sayan ranges and Baikal rift system in Siberia to the north [START_REF] Zheng | Erosion, fault initiation and topographic growth of the North Qilian Shan (northern Tibetan Plateau)[END_REF]Hendrix, 2000;Jolivet et al., 2013a;[START_REF] Jolivet | How old is the Baikal Rift Zone? Insight from apatite fission track thermochronology[END_REF]Xu and Kamp, 2000), it is likely that stress has been transferred to the margins of the Tibetan plateau, and even beyond the plateau to the north since India -Asian collision.

Considering the pre-existing Cretaceous positive topography of the Qilian Shan with the Miocene rapid growth of the central-northern Qilian Shan and late Miocene growth of the northern Qilian Shan, we suggest multiple stages of range growth in the Qilian Shan during the Mesozoic and Cenozoic (Fig. 10), similar to that already documented in other parts of northern Tibet (Cheng et al., 2016a;He et al., 2017;[START_REF] Lease | Pulsed Miocene range growth in northeastern Tibet: Insights from Xunhua Basin magnetostratigraphy and provenance[END_REF][START_REF] Wang | Tertiary basin evolution along the northeastern margin of the Tibetan Plateau: Evidence for basin formation during Oligocene transtension[END_REF]Wang et al., 2017d;[START_REF] Yuan | The growth of northeastern Tibet and its relevance to large-scale continental geodynamics: A review of recent studies[END_REF].

Implication for the eastern termination of the Altyn Tagh Fault

Provenance results also imply that the Cenozoic ATF likely died out within the Yumen Basin and have not extended further eastward since its Eocene or Miocene initiation. For instance, previous studies have revealed an >300 km post-Cretaceous offset along the ATF (Cheng et al., 2015a;Cheng et al., 2016b;[START_REF] Ritts | Magnitude of post-Middle Jurassic (Bajocian) displacement on the central Altyn Tagh fault system, northwest China[END_REF][START_REF] Yin | Geologic evolution of the Himalayan-Tibetan orogen[END_REF][START_REF] Yin | Tectonic history of the Altyn Tagh fault system in northern Tibet inferred from Cenozoic sedimentation[END_REF]. If the ATF extended beyond the Yumen Basin and linked with the strike-slip faults of

A C C E P T E D M A N U S C R I P T
the Alxa or regions further to the east [START_REF] Darby | Did the Altyn Tagh fault extend beyond the Tibetan Plateau?[END_REF][START_REF] Yue | Two-stage evolution model for the Altyn Tagh fault, China[END_REF], hundreds of kilometers of sinistral strike-slip motion along the ATF during the Cenozoic would not have been transferred to the oblique thrusting in the Qilian Shan. In other words, the Yumen Basin would have been approximately located near the present-day position of the Suganhu Basin during the Cretaceous after restoring the >300 km sinistral post-Cretaceous offset along the ATF (Fig. 2a). In this case, the Yumen Basin would have received materials eroded from the Dunhuang terrane to the northwest (Fig. 2a). Apatite and zircon fission track data suggest that the Dunhuang terrane has been exhumed no later than the late Triassic-early Jurassic (Jolivet et al., 2001). Given that the basement of the Dunhuang terrane is characterized by a predominant proportion of Archean and Proterozoic rocks (He et al., 2018;[START_REF] Long | New geochemical and combined zircon U-Pb and Lu-Hf isotopic data of orthogneisses in the northern Altyn Tagh, northern margin of the Tibetan plateau: Implication for Archean evolution of the Dunhuang Block and crust formation in NW China[END_REF][START_REF] Zhao | The Archean-Paleoproterozoic crustal evolution in the Dunhuang region, NW China: Constraints from zircon U-Pb geochronology and in situ Hf isotopes[END_REF], the detrital zircon ages spectra of the Cretaceous samples from the Yumen Basin should eastward decrease in the left-lateral slip rate along the eastern end of the ATF [START_REF] Burchfiel | Intracrustal detachment within zones of continental deformation[END_REF][START_REF] Mériaux | The Aksay segment of the northern Altyn Tagh fault: Tectonic geomorphology, landscape evolution, and Holocene slip rate[END_REF][START_REF] Meyer | Crustal thickening in Gansu-Qinghai, lithospheric mantle subduction, and oblique, strike-slip controlled growth of the Tibet plateau[END_REF][START_REF] Xu | Late Quaternary sinistral slip rate along the Altyn Tagh fault and its structural transformation model[END_REF][START_REF] Zhang | Late Quaternary and present-day rates of slip along the Altyn Tagh Fault, northern margin of the Tibetan Plateau[END_REF]Zheng et al., 2013b) (Fig. 10a). Qilian Shan, modified from (Zheng et al., 2013a). The slip rate on each fault is from previous work [START_REF] Chen | Principal tectonic deformation features and their generation mechanism in the Hexi Corridor and its adjacent regions since the late Quaternary[END_REF]Hetzel et al., 2002;[START_REF] Min | Research on the active faults and paleoearthquakes in the western Jiuquan basin[END_REF][START_REF] Xu | Late Quaternary sinistral slip rate along the Altyn Tagh fault and its structural transformation model[END_REF][START_REF] A C C E P T E D M A N U S C R I P T Zheng | Geometric pattern and active tectonics of the Hexi Corridor and its adjacent regions[END_REF]Zheng et al., 2013a;Zheng et al., 2013b). Note that the horizontal slip rate on faults generally decrease eastwards. H: Horizontal slip rate; V: Vertical slip rate; S: Shortening rate across fault. (b)

Schematic models illustrating the topographic variation of the Yumen Basin and northern Qilian Shan, during the Miocene and Cretaceous.

Conclusion

Our provenance analysis reveals that both the northern Qilian Shan and the Bei Shan

Figure 1 .

 1 Figure 1. (a) Digital topographic map of the Tibetan plateau. The timing of the pre-collisional

  . 2a and 3; Shan means "mountain" in Chinese), and determined the U-Pb ages of detrital zircons in these sandstones using laser-ablation inductively-coupled plasma mass spectrometry (LA-ICP-MS). To quantitatively determine mixing proportions of potential source contributions, a newly published software program DZmix(Sundell and Saylor, 2017) is used in this study. These results are interpreted in the context of sandstone petrologic results, previously published detrital zircon geochronology, published paleocurrent data in the Yumen Basin, as well as existing low-temperature thermochronology data in the NE Tibetan plateau for a better understanding of the Cretaceous-Cenozoic paleogeography of the NE Tibetan plateau. Moreover, detrital zircon geochronology is also a powerful means of resolving the displacement history of potentially displaced terranes(Cheng et al., 2016b;[START_REF] Gehrels | Detrital Zircon U-Pb Geochronology Applied to Tectonics[END_REF]. Outcropped near the highly debated eastern end of the ATF, the Cretaceous to Cenozoic strata in the Yumen Basin provide a good proxy for examining the source variation through time due to the potential sinistral slip motion of the ATF since its Eocene or Miocene initiation. In the context of the abovementioned published datasets, we compare age distributions of detrital zircon from the Cretaceous to Cenozoic strata in the Yumen Basin to estimate the potential source variation and further define the geometry of the eastern termination of the ATF.

Figure 2 .

 2 Figure 2. (a) Geological map of the northeastern Tibetan plateau and locations of the detrital

  . (b) and (c) are two cross-sections through the Yumen Basin, showing the distribution of the Cretaceous and Cenozoic strata in this region, modified from Dai et al. (2005). NQF, North Qilian Fault; NKF, northern marginal fault of the Kuantan Shan-Longshou Shan; SKF, southern marginal fault of the Kuantan Shan.

Figure 3 .

 3 Figure 3. Geological map of the Yumen Basin and northern Qilian Shan. The black dash line

Figure 4 .

 4 Figure 4. Lithostratigraphy of the five studied sections. (a) Caogou section (Wang et al., 2016b),

Figure 5 .

 5 Figure 5. Photographs of the Lower Cretaceous strata in the Yumen Basin and Qilian Shan. (a)

  Lower Cretaceous strata underlie unconformably the late Eocene to Oligocene Huoshaogou Fm. (Fig.5b, 5d). The Lower Cretaceous strata mainly consist of thinly bedded of greenish grey laminated claystone and siltstone interbedded with thin to medium tabular beds of grey massive sandstone, corresponding to distal lacustrine facies deposits (Peng, 2013) (Fig.5c, 5e). Paleocurrent measurements indicate south-directed unidirectional paleoflows(Dai et al., 2005). In the Hongliuxia section, the Lower Cretaceous strata were unconformably overlain by the Oligocene Baiyanghe Fm. strata (Fig.5f). The Lower Cretaceous deposits are mainly composed of thin beds of greenish grey claystone and sandy claystone interbedded with greenish grey sandstone, sandy claystone and thick beds of sandstone, corresponding to a distal alluvial plain to proximal lacustrine environments (Peng, 2013)(Fig.5f-5g). Clast imbrications in this section suggest multiple paleocurrent directions (e.g. NNW-directed and south-directed)(Peng, 2013). In the Northern Qilian Shan and Jingtieshan sections, the Lower Cretaceous strata unconformably underlie the Oligocene Baiyanghe Fm., and unconformably overlie the basement rocks of the northern Qilian Shan. The Cretaceous strata are mainly composed of thick beds of purple to red conglomerate intercalated with thin to medium bedded tabular sandstone (Fig.5h-j).The poorly-rounded and poorly-sorted conglomerates indicate that material has not been transported very far, pertaining to proximal deposits (Fig.5h-5j). Detailed sedimentological descriptions of the sampled Cretaceous sections can also be found in Peng (2013).

Figure 6 .

 6 Figure 6. (a)-(e) Cross-polarized light photomicrograph of five Cretaceous samples. (f)-(g) are

  2 and 3), from coarse-to medium-grained sandstones. Both samples are characterized by very poorly to poorly sorted and characterized by very angular to angular grains (Fig.6d-6e). Modal compositions for sample NQL-K are Qt: F: L= 47:17:36 and Qm: F: Lt=30:17:53, plotting in the "recycled orogen" field in the QtFL diagram (Fig.6f) and near the boundary between "quartzose recycled" field and "mixed" field in the QmFLt diagram (Fig.6g), respectively.4.2Detrital zircon geochronology results U-Pb concordia diagrams for zircon grains of each sample are shown in Figure7a-7e.

Figure 7 .

 7 Figure 7. (a)-(e) U-Pb concordia diagrams for zircon grains of each sample. The diagrams were

Figure 8 .

 8 Figure 8. (a)-(s) Zircon U-Pb age cumulative probability distribution for each sample

  2 and 3. Note the consistent age-distribution from Cretaceous to early Miocene samples (g-j). The color change from green to orange in the vertical shaded areas represents source variation. (t) Multidimensional scaling map (Vermeesch, 2013),showing the distinct signature of Bei Shan and Qilian Shan source regions. The multidimensional scaling (MDS) map uses the Kolmogorov-Smirnov (KS) statistic for detrital zircon U-Pb datasets(Stevens et al., 2013; Vermeesch, 2013). Axes are in dimensionless "K-S units" (0 < KS < 1), showing distance between samples. Solid lines and dashed lines connect samples with their "closest" and "second closest" neighbors, respectively. Blue solid circles represent detrital zircon data from the Cretaceous samples in this study. Pink solid circles represent detrital zircon data from the Cenozoic samples fromWang et al. (2016c). Green solid circles represent detrital zircon data from modern river samples in Bei Shan, while yellow solid circles represent detrital zircon data from modern river samples in the Qilian Shan. These four modern rivers

  . The northern Qilian Shan basement mainly consists of Archean-middle Proterozoic orthogeisses/granitoid plutons with zircon U-Pb ages spanning from 2.6 Ga to 1.0 Ga, late Proterozoic intrusions with zircon U-Pb ages between 1.0 Ga and 700 Ma, early Paleozoic granitoid plutons with zircon U-Pb ages ranging from 550 Ma to 420 Ma and a few Permian to Triassic igneous rocks with zircon U-Pb ages ranging between 280. Some work suggests that the PrecambrianA C C E P T E D M A N U S C R I P Tzircons in the northern Qilian Shan might have been recycled from the underthrust basement of the Alxa block(Gehrels et al., 2003a, b). With regards to the basement rocks of the Bei Shan, late Paleozoic and early Mesozoic granite plutons widely crop out, with zircon U-Pb ages ranging from 310 Ma to 230 Ma (Fig.8k-8n).To understand the similarities/dissimilarities between individual samples and basement of Bei Shan and Qilian Shan regions, we adapt the multidimensional scaling (MDS) map that was developed to create a spatial visualization to determine the misfit between age distributions using the Kolmogorov-Smirnov (KS) test as the dissimilarity measure (Vermeesch, 2013). As shown in Figure8t, zircon age distributions of Lower Cretaceous samples from the northern Yumen Basin (HSG-K and CG-K) are statistically different from those of Lower Cretaceous samples from the Qilian Shan (NQL-K and JTS-K) and southern Yumen Basin (HLX-K). Two groups of similarly sourced samples were then identified using the abovementioned metrics: (1) Samples HSG-K and CG-K, which are dominated by a single late Paleozoic-early Mesozoic population,(2) Samples NQL-K, JTS-K and HLX-K, which contain a cosmopolitan assemblage of all major detrital zircon populations.Zircons from samples CG-K and HSG-K are dominated by age peaks at 290-230 Ma, which accounts for approximately 80% of the total dated grains (Fig.8i-8j). The predominant late Paleozoic and early Mesozoic population and the absence of early Paleozoic and Precambrian ages suggest that the Bei Shan served as the source region for the clastic material deposited in the northern Yumen Basin (represented by the Caogou and Huoshaogou sections).

  Bei Shan region(Wang et al., 2016b). In the northeastern edge of the Tibetan plateau, the base of the middle Eocene to Oligocene strata unconformably overlies the Cretaceous strata(Dai et al., 2005; Wang et al., 2016b) (Figs. 4, 5b, 5d and 5f), and the absence of Paleocene and early Eocene strata in this region make it difficult to constrain the paleotopography during the early Paleogene. Nonetheless, the similar detrital zircon ages distribution between the Lower Cretaceous and Oligocene samples as well as the consistent paleocurrent patterns over that period of time indicate that the source of the material deposited in the Yumen Basin (Caogou and Huoshaogou sections) was stable.[START_REF] Bovet | Evidence of Miocene crustal shortening in the north Qilian Shan from Cenozoic stratigraphy of the western Hexi Corridor, Gansu Province, China[END_REF] argued that the paucity of Paleocene and Eocene deposits in the northern Qilian Shan and in the Yumen Basin may reflect that structures in both northern Qilian Shan and Yumen Basin became inactive, and non-sedimentation (or weak erosion) dominated in these areas, possibly a result of sustained high topography. Alternatively, compressive deformation within the both northern Qilian Shan and Yumen Basin would potentially lead to continuous erosion that formed the unconformity between Cretaceous and Eocene strata. This uncertainty highlights the need for further effort on determining the growth history of the NE Tibetan plateau from the late Cretaceous to early Eocene. While simply comparing the detrital zircon age spectra of each sample could reveal general source variation, quantitative analysis helps to elucidate the exact contribution of Qilian Shan and Bei Shan sources through time. This information, combined with the existing sedimentology and low-temperature thermochronology datasets, contributes to a better understating of the distribution of relief in the Qilian Shan and the NE Tibetan plateau. To quantitatively determine mixing proportions between the Qilian Shan and Bei Shan sources, we use the newly developed MATLAB-based DZmix Inverse Monte Carlo method (Sundell and Saylor, 2017). This program yields a single best-fit (highest cross-correlation coefficient R 2 ) inverse Monte Carlo model result A C C E P T E D M A N U S C R I P T for each tested sample (see the pink solid lines in Figure 9) and estimates the respective contributions of the known Qilian Shan and Bei Shan sources for each sample. The Qilian Shan source input is represented by two modern river sand samples QL1 and QL2, and the Bei Shan source input is represented by two modern river sand samples BS2 and BS3. Inverse Monte Carlo model results for each tested sample are presented in Figure 9. Results shows that in the northern Yumen Basin, 100% of the material was derived from basement rocks of the Bei Shan during the Cretaceous (sample HSG-K and CG-K; Fig. 9b, 9d). During the late Oligocene (23.8 Ma, sample FZ1, Fig. 9f), 98% of materials in the northern Yumen Basin are derived from basement rocks of the Bei Shan with only 2% of Qilian Shan sourced debris. However, the contribution of the Qilian Shan source to the northern Yumen Basin increased to 30-48% during the early Miocene (20.6-16.3 Ma, samples FZ2 and FZ3, Fig. 9h and 9j) and dramatically increased to 87-91% during the middle Miocene (15.8-13.1 Ma, samples FZ4 and FZ5, Fig. 9l and 9n). During the late Miocene (7.8 Ma, sample FZ7, Fig. 9p), 82% of the clastic material is derived from basement rocks of the Qilian Shan with 18% from the Bei Shan source. The best-fit inverse Monte Carlo model results further reinforce the conclusion that the Bei Shan was the predominant source of the clastic material deposited in the northern Yumen Basin from the early Cretaceous to the late Oligocene. The contribution of the Qilian Shan basement rocks to the sediments in the Yumen Basin significantly increased during the Miocene, especially during the middle Miocene, which we interpret as the growth of the Qilian Shan. (Fig. 9). Moreover, by simply comparing the detrital zircon spectra of each Cenozoic sample, Wang et al. (2016c) have revealed that a change in source area occurred at ~16.7 Ma in the Yumen Basin. Our quantitative analysis shows the contribution of the Qilian Shan source to the northern Yumen Basin significantly increased from 2% to 30% at ~20.8 Ma. We interpret this early Miocene initial A C C E P T E D M A N U S C R I P T source change as the onset of growth of the Qilian Shan.

Figure 9 .

 9 Figure 9. Unmixing detrital geochronology age distribution. (a), (c), (e), (g), (I), (k), (m) and (o)

  contain a significant amount of Archean and Proterozoic zircon ages. In addition, the proportions of those Precambrian ages populations would vary from Cretaceous to late Oligocene time due to the left-lateral displacement along the ATF(Cheng et al., 2016b; Yue et al., 2004b). The absence of Precambrian zircons in the Cretaceous samples (samples CG-K and HLX-K, Figs.8 and 9), as well as the consistently similar detrital zircon ages spectra of the samples from the lower Cretaceous to the early Miocene strata in the Yumen Basin require that the ATF terminated in the western Yumen Basin and has not been linked to strike-slip faults in the Alxa or regions further to the east since its Eocene or Miocene initiation. This conclusion is in agreement with independent, albeit indirect evidence suggesting that the ATF died out within the Yumen Basin since its initiation, including: (1) the limited (<50 km) offset of the Jurassic and Cretaceous strata in the western Yumen Basin (Fig.2);(2) the high resistivity crust of the Huahai-Jinta Basin(Xiao et al., 2015) which prevents the ATF from passing through (Fig.10a); and (3) the dramatic

Figure 10 .

 10 Figure 10. (a) Geological map showing slip rates on faults in the Yumen Basin and northern

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10

 12345678910 Figure1

  standards were used to correct for isotope fractionation, and the R33 zircon standard was treated as an unknown and used to monitor the fractionation correction. Reported uncertainties include measurement errors at the 1σ level. Analyses with >10% uncertainty (1σ) in206 Pb/ 238 U age are not included. Analyses with >10% uncertainty (1σ) in 206 Pb/ 207 Pb age are not included, unless 206 Pb/ 238 U age is <400 Ma. Best age was determined from 206 Pb/ 238 U age for analyses with 206 Pb/ 238 U age younger than 900 Ma and from 206 Pb/ 207 Pb age for analyses with 206 Pb/ 238 U age older than 900 Ma. U concentration and U/Th ratio were calibrated relative to Sri Lanka zircon standard and are accurate to ~20%. Using the routines in Isoplot 3.7 relative age-probability diagrams (Ludwig, 2008). Isotopic ages with errors and related raw data are presented in the supplementary material.

Common Pb corrections were performed based on the measured

206

Pb/ 204 Pb and the assumed composition of common Pb from

Stacey and Kramers (1975)

. Sri Lanka and FC-1 zircon A C C E P T E D M A N U S C R I P T In order to extract mixing proportions of source rocks contributions, a newly published MATLAB-based inverse Monte Carlo method was used (Sundell and Saylor, 2017). By randomly constructing known source age distribution for comparison to individual mixed samples, this new technique can be used to constrain forward optimization routines to find a best model fit. We then determine mixing proportions of source rock contributions for each tested mixed sample. The details about this inverse Monte Carlo method are available in Sundell and Saylor (2017).

Acknowledgments

The research was funded by grants from the National Science Foundation (EAR-1348005 and OISE-1545859) to Garzione, Open project fund from State Key Laboratory of Loess and Quaternary Geology, Institute of Earth Environment, CAS (No. SKLLQG1701) to Cheng, and National Science and Technology Major Project of China (Grant 2017ZX05008-001) to Guo.

We are grateful to Editor-in-Chief Dr. M. Santosh, Associate Editor Dr. Zeming Zhang, Dr. Kendra Murray and an anonymous reviewer for constructive comments that improved the paper.

We gratefully acknowledge Mark Pecha, Nicky Giesler, Heather Alvarez, Mekha Pereira and Arizona Laserchron Center for their help with detrital zircon analysis. SRTM digital topography is from http://www2.jpl.nasa.gov/srtm.

A C C E P T E D M A N U S C R I P T A C C E P T E D M A N U S C R I P T

Chen, Y., Xia, X., Song, S., 2012. Petrogenesis of Aoyougou high-silica adakite in the North Qilian orogen, NW China: Evidence for decompression melting of oceanic slab. Chinese science bulletin, 1-13. Cheng, F., Fu, S., Jolivet, M., Zhang, C., Guo, Z., 2016a. Source to sink relation between the Eastern Kunlun Range and the Qaidam Basin, northern Tibetan Plateau, during the Cenozoic.

Geological Society of America Bulletin 128, 258-283.

Cheng, F., Guo, Z., Jenkins, H.S., Fu, S., Cheng, X., 2015a. Initial rupture and displacement on the Altyn Tagh fault, northern Tibetan Plateau: Constraints based on residual Mesozoic to Cenozoic strata in the western Qaidam Basin. Geosphere 11, 921-942.

Cheng, F., Jolivet, M., Dupont-Nivet, G., Wang, L., Yu, X., Guo, Z., 2015b. Lateral extrusion along the Altyn Tagh Fault, Qilian Shan (NE Tibet): insight from a 3D crustal budget. Terra Nova 27, 416-425. Cheng, F., Jolivet, M., Fu, S., Zhang, C., Zhang, Q., Guo, Z., 2016b. Large-scale displacement along the Altyn Tagh Fault (North Tibet) since its Eocene initiation: Insight from detrital zircon U-Pb geochronology and subsurface data. Tectonophysics 677-678, 261-279. Cheng, F., Jolivet, M., Hallot, E., Zhang, D., Zhang, C., Guo, Z., 2017. Tectono-magmatic rejuvenation of the Qaidam craton, northern Tibet. Gondwana Research 49, 248-263. Clark, M.K., Farley, K.A., Zheng, D., Wang, Z., Duvall, A.R., 2010. Early Cenozoic faulting of the northern Tibetan Plateau margin from apatite (U-Th)/He ages. Earth and Planetary Science Letters 296, 78-88.

Cowgill, E., Yin, A., Harrison, T.M., Xiao-Feng, W., 2003 Wang, W., Zheng, W., Zhang, P., Li, Q., Kirby, E., Yuan, D., Zheng, D., Liu, C., Wang, Z., Zhang, H., Pang, J., 2017c. Expansion of the Tibetan Plateau during the Neogene. 8, 15887. Wang, X., Deng, L., Zattin, M., Ji, M., Li, J., 2017d Xiao, Q., Shao, G., Liu-Zeng, J., Oskin, M.E., Zhang, J., Zhao, G., Wang, J., 2015. Eastern termination of the Altyn Tagh Fault, western China: Constraints from a magnetotelluric survey.

Journal of Geophysical Research: Solid Earth 120, 2838-2858. Xiao, W., Mao, Q., Windley, B., Han, C., Qu, J., Zhang, J., Ao, S., Guo, Q., Cleven, N., Lin, S., 2010. Paleozoic multiple accretionary and collisional processes of the Beishan orogenic collage. American Journal of Science 310, 1553-1594.


Yann Dauxais

Clément Gautrais
email: clement.gautrais@irisa.fr

Predicting Pass Receiver In Football Using Distance Based Features

Keywords: Pass prediction, Distance based features, Interception prediction

This paper presents our approach to the football pass prediction challenge of the Machine Learning and Data Mining for Sport Analytics workshop at ECML/PKDD 2018. Our solution uses distance based features to predict the receiver of a pass. We show that our model is able to improve prediction results obtained on a similar dataset. One particularity of our approach is the use of failed passes to improve the predictions.

Introduction

Thanks to the availability of football in-game events, recent approaches have studied aspects of the game that provide actionable knowledge for football clubs. For example, passing patterns from La Liga teams have been studied [START_REF] Wang | Discerning tactical patterns for professional soccer teams: an enhanced topic model with applications[END_REF]. Other work focused on estimating football players performance from their actions on the field [START_REF] Decroos | Starss: A spatio-temporal action rating system for soccer[END_REF].

The football pass prediction challenge of the Machine Learning and Data Mining for Sport Analytics workshop at ECML/PKDD 2018 focuses on an aspect of the game that has been seldom studied. Indeed, few work have studied the problem of predicting the receiver of a pass in football. In [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF], Vercruyssen et al. study the performance of predicting the receiver of a pass, based on different types of features: static or dynamic, quantitative or qualitative and relational or non-relational. They recommend using static qualitative features, such as coned based calculus [START_REF] Frank | Qualitative spatial reasoning with cardinal directions[END_REF] and double cross calculus [START_REF] Zimmermann | Qualitative spatial reasoning using orientation, distance, and path knowledge[END_REF]. This study is very relevant to our work, as the dataset they are studying is very similar to ours.

In [START_REF] Steiner | Passing decisions in football: Introducing an empirical approach to estimating the effects of perceptual information and associative knowledge[END_REF], Steiner studies the effects of perceptual information on the probability for a player to receive a pass. He concludes that players with open passing lanes have a higher chance of receiving a pass. Players who are located forward of the passer, close to him or far from an opponent also have a higher chance of receiving a pass. This study is based on quantitative features, and shows pass prediction results similar to [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF]. It should be noted that the data used in [START_REF] Steiner | Passing decisions in football: Introducing an empirical approach to estimating the effects of perceptual information and associative knowledge[END_REF] is not based on real game data, but on scenarios that are evaluated by football players in an offline setting. This might have an influence on the pass decision process of the player.

Work have also been dedicated to the prediction of whether a pass will fail [START_REF] Horton | Automated classification of passing in football[END_REF][START_REF] Travassos | Improving passing actions in team sports by developing interpersonal interactions between players[END_REF], that is whether the opposing team will intercept the ball during the pass. Important factors are ball velocity, defenders distance to the ball carrier [START_REF] Travassos | Improving passing actions in team sports by developing interpersonal interactions between players[END_REF] and distances between players [START_REF] Horton | Automated classification of passing in football[END_REF].

Dataset Presentation

The dataset D contains 12,124 passes performed during 14 different games involving a Belgian football club during the 2014/2015 football season1 . For each pass, we have the x and y positions of all players, as well as the sender and receiver of the pass. We also have the number of seconds elapsed since the beginning of the half when the pass is performed and received. This yields a total of 60 columns (2 * 28 positions, 2 players id and 2 number of seconds). Players 1 to 14 belong to the home team; players 15 to 28 belong to the away team. A thorough description of the dataset can be found on the challenge repository 1 .

Formally, we have D = pass 1 , . . . , pass j , . . . , pass 12124 , with pass j = x 1 , y 1 , . . . , x i , y i , . . . , x 28 , y 28 , i s , i r , t s , t r the j-th pass. x i and y i are the coordinates of player i, p s is the pass sender id, p r the pass receiver id, t s the pass sending time and t r the receiving time.

Dataset Exploration

We here briefly present some of the characteristics of the dataset. First, we have the positions of 28 players, but there are only 11 players on the field for each team. Fortunately, the substitutes are easily identified, as their x and y positions correspond to the Not a Number (NaN) token. Players having at least one coordinate equal to NaN are removed from the the pass vector pass j .

This process yields a total of 22 x and y positions in pass j : one for each player on the field. However, it can happen that a team has less than 11 players on the field, because of an injury or a red card for example. There are 438 pass examples (3.6% of the dataset) were less than 22 players are on the field.

In [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF], the authors consider successful passes only: passes where the receiver and sender are on the same team. In the dataset, there are 2077 examples of failed passes (17.1% of the dataset). Because these passes represent a significant portion of the dataset, we decided to keep them.

We removed passes where the sender and receiver are the same players (6 cases), and passes were either the sender or the receiver have NaN positions (2 cases). The final dataset contains 12116 passes.

Model Description

The problem definition of the pass prediction challenge is quite simple. Challenge problem: For each pass, given the sender and the positions of players, predict the receiver.

General Approach

The idea of our approach is to estimate the probability P i that the sender (player p s ) passes to player i, i = p s . Then, sorting players id in decreasing order of probability P i yields a ranking on the pass receiver prediction. Therefore, the player with rank 1 is the player with index equal to arg max i∈ [START_REF] Decroos | Starss: A spatio-temporal action rating system for soccer[END_REF]22],i =ps P i . We now present the learning of the probabilities P i .

Learning pass probabilities

To learn the pass probabilities P i , we train a classifier, that, given a set of features, outputs the probability that player i receives the pass from player p s . Previous approaches predicting the receiver of a pass use different types of features. While the use of qualitative features (relative positioning of players, with respect to the sender and the receiver of the pass) is recommended [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF], methods based on quantitative features (distances between players and pass lanes) yield similar results in the prediction of the pass receiver [START_REF] Steiner | Passing decisions in football: Introducing an empirical approach to estimating the effects of perceptual information and associative knowledge[END_REF].

To train our classifiers, we use both quantitative and qualitative features. Given the position of the sender and of player i (the potential receiver), we first compute different distance based features. First, we compute the Euclidean distance between both players. Afterwards, we compute the forward distance of the pass, that the difference between player i xcoordinate and the sender x coordinate. Then, we compute the smallest distance between an opponent of the sender and the pass lane. This corresponds to the smallest distance between the line formed by the sender and potential receiver and an opponent of the sender. Next, we compute the smallest and second smallest distance between the sender and players of the opposing team. We also compute the smallest and second smallest distance between the player i and players of the opposing team. Then, we compute a boolean indicating whether the potential receiver and the pass sender are in the same team. Finally, we encode the position of the sender and of player i using a regular grid over the football field. We split the field into 6 rows and 9 columns. Then, the position of a player corresponds to its grid number.

To summarize, we have 10 features to estimate the probability P i that the sender passes to player i: the distance between the sender and player i; the forward distance of the pass; the smallest distance between the pass line and an opponent; the smallest and second smallest distance between the sender and an opponent; the smallest and second smallest distance between player i and an opponent; the sender and receiver grid number and whether the sender and player i are in the same team. With these 10 features, the classifier predicts whether this pass is the one chosen by the sender. If the sender chose to pass to player i, the value to predict is 1, and 0 otherwise.

Results

This section presents the pass receiver prediction results. This corresponds to evaluating the ranking yielded by ordering players id in descending value of P i . 1. MRR and top-1, top-2 and top-3 recall for predicting the receiver id of a pass. The three lines correspond to the whole pass dataset, the successful pass dataset and the failed pass dataset respectively.

In the followings, this ordered list of players id is called V and v j refers to the player id at the jth position in this list V . 2We train different classifiers (random forest, logistic regression and k nearest neighbors) to predict P i . We found that the best performance was achieved when using a random forest with 200 trees. To evaluate the performance of the ranking, we use the same metrics as [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF]: the mean reciprocal rank measure

(V ) = k j=1 rel(v j ) m j=1 rel(v j )
where m is the length of V and rel(v j ) is the relevance of v j and rel(v j ) = 1 if v j is the receiver id and 0 otherwise. It is worth noticing that one and only one player id is relevant for each pass what means that m j=1 rel(v j ) = 1 and R@k(V ) = k j=1 rel(v j ). This recall is then averaged on the pass set like for MRR:

1 n n i=1
R@k(V ). Thereby, the top-1 recalls in the followings are equivalent to accuracy. Reported results correspond to the mean value of the corresponding metric on a 5-folds cross-validation. Table 1 presents the result for these 4 measures.

As one can see, the classifier predicts the good receiver from a list of 21 players in than 84.1% cases. This good classification result is improved to 91.5% when predicting the 3 most probable receivers. We can see by comparing the second and third rows of the table that it is easier to predict the receiver of a successful pass than of an intercepted pass. Furthermore, the prediction improvement between top-1 and top-3 for successful pass is 8.6% when the same improvement for intercepted pass is only 1.7%. It shows that the error on the receiver of an intercepted pass is much higher than for a successful pass.

To compare our results with the ones obtained in [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF], we restrict ourselves to successful passes only, that is passes between two players of the same team. In this case, the rank used for the MRR computation belongs to the interval [START_REF] Decroos | Starss: A spatio-temporal action rating system for soccer[END_REF]10]. [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF] 0.42 0.279 0.416 0.467 Our Best (RF) 0.870(±0.006) 0.803(±0.009) 0.877(±0.005) 0.922(±0.005) DT 555 leaves 0.664(±0.004) 0.507(±0.005) 0.675(±0.005) 0.777(±0.007) Table 2. MRR and top-1, top-2 and top-3 recall for predicting the receiver id of a successful pass. The first line corresponds to the results obtained in [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF] and the 2 other ones to ours: Random Forest (RF) and Decision Tree (DT).

Method MRR top-1 top-2 top-3 Best from
The results are presented in Table 2. It is clear that our approach outperforms the results obtained in [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF] on a similar dataset. Our MRR is 2 times better and our top-1 recall 3 times better. It should be noted that the best model in [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF] uses 555 rules. To perform a more relevant comparison, we show the results for a decision tree having 555 leaves. This classifier still outperforms the results presented in [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF], showing the relevance of our approach.

Learning from Failures

One of the differences between our approach and the one of Vercruyssen et al. [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF] is that we consider opponents as potential receivers. While predicting who will intercept a failed pass is more difficult than predicting who will receive a successful pass, learning from both failed and successful pass can help correct some successful pass decisions. Indeed, when learning from successful passes only, one might over-estimate the probability of a dangerous pass to be successful. Using failed passes can help the classifier to identify these dangerous passes more accurately. This effect can be observed from the analysis of Tables 1 and2. Indeed, the MRR for predicting successful passes when using a classifier trained on both successful and failed passes is 0.909 (second line of Table 1); whereas the MRR for predicting successful passes when using the same classifier trained on successful passes only is 0.870 (second line of Table 2). One interesting thing to note is that the top-1 recall difference between both methods is of 5.8%, while the top-3 recall difference is of 2.5%. This means that while both approaches have a similar top 3 ranking for passes, training on both successful and failed passes leads to a better top 1 ranking. It is also worth noting that, for all passes, the MRR lower bound is equal to 1 21 whereas, for successful passes only, this lower bound is 1 10 . Thereby, it is unfair to compare the MRR of all passes to the one of successful passes only.

Qualitative analysis

We now quickly analyze some predictions of our method by looking at 3 pass examples. These passes are represented in Figure 4.2. The top-left example shows a case where our method correctly identifies the receiver: the label 1 is below the orange sign. The receivers ranked 2 and 3 are also teammates of the sender. The rank 2 player is unlikely to receive the ball, as he is close to 2 opponents. The goalkeeper, ranked 3, is however a safe pass option. We can see that our model suggests good passing options, even though the rank 2 player does not seem appropriate.

The top-right image also shows a case where our method correctly identifies the receiver. One interesting thing to note in that example is that the player ranked 2 is actually an opponent of the sender. An even more interesting fact is that this player is likely to intercept the pass between the sender and the actual receiver. This shows that our method is capable of putting high ranks for interceptions, if they make sense. Finally, the bottom example shows an case where our method is not able to predict the receiver in the top 3. While all options chosen by our method seem reasonable, the sender decided to choose another option. Overall, we can say that our method is able to output meaningful rankings, with some exceptions. These exceptions are mostly due to the fact that our method only takes into account distances. Adding new features can help to further eliminate unlikely passes. Fig. 1. Top 3 ranking for pass receivers in 3 cases. The pass sender is in green, the pass receiver in orange, the sender teammates in blue and the sender opponents in purple. The ranking is indicated as a red number below the symbol.

Conclusion

In this paper, we have illustrated how a simple method, using distance based features, is able to accurately identify the receiver of a football pass. This is done by computing the probability to receive the pass for each player and by predicting the potential receiver with the highest probability. Such approach allows to use a biggest feature set, an thereby, can be generalized. The particularity of this approach is that it also considers failed passes, and predicts the opponent intercepting the pass. For future work, we aim to add new features to strengthen the prediction of the receiver. A good starting point would be to add qualitative features described in [START_REF] Vercruyssen | Qualitative spatial reasoning for soccer pass prediction[END_REF].

( 1 rank

 1 , with n the number of examples, rank the rank of the receiver (rank ∈[START_REF] Decroos | Starss: A spatio-temporal action rating system for soccer[END_REF] 21]), and the recall in the top-1, top-2 and top-3 of the ranking. These recalls are equivalent to recall at k[START_REF] Mcsherry | Computing information retrieval performance measures efficiently in the presence of tied scores[END_REF] for k set up to 1, 2 and 3 respectively: R@k

https://github.com/JanVanHaaren/mlsa18-pass-prediction

Our code is at https://gitlab.inria.fr/cgautrai/prediction_mlsa2018.git