時變基準於臺灣基本測量與地籍測量影響探討

Abstract

「時變基準」(Time-Variant Datum)，乃指該基準之點位坐標，具有隨時間不同而改變之特性。就如地球科學界對地瞭解之應用而言，連續改變之點位坐標是反映現實。但是在基本測量及地籍測量之應用，坐標之時變特性，卻對資料之穩定性及業務之執行，有負面的影響。因此，就時變基準坐標之建置，依其更新頻率，具連續性質者，稱為動態基準(Dynamic Datum)，若累積變化量達到所設定之門檻值時，方才更新坐標，則稱之為半動態基準(Semi-Dynamic Datum)。 除時間面向外，時變之機制，亦有空間面向，各個分區變化量與變化方式不同。由於地球表面塊體間之形變，並非總是單一性之變化，斷層錯動所形成之點位坐標急劇變化，並非單一速度所可描述。因此，採用速度場，模型化連續性之形變，再輔以各點針對單點或區域性大變化之調整，以加常數方式呈現。除此兩者，另一個可能是使用具有預報能力之模型。 本論文以臺灣基本測量與地籍測量為研究標的，探討時變基準之技術與影響程度。在基本測量方面，以大地測量為探討範疇，包含大地基準測量與維護、基本控制測量與控制點檢測等分析；在地籍測量方面，由於數值法地籍測量是純以測繪為目的之所有應用測量中精度需求最高者，且地籍測量成果為我國土地登記、土地政策推動與不動產交易之依據，攸關民眾權益、市場秩序與國家安定等公共議題，故以其做為本論文探討之標的，並分析地籍圖界址點坐標與宗地面積變動量，以評估時變因素對地籍測量之影響。 在大地基準維護議題上，因採行維持TWD97法定參考框架ITRF94的政策，將TWD97[2010]由原始測設採用的ITRF2005成果，經實施兩次框架轉換後，使點位坐標成果產生誤差協變方傳播。本論文以最小自乘法、複合框架轉換法等兩種模式求定框架轉換參數不確定度並據以進行分析，得到的誤差協變方傳播結果相近；分析成果並顯示，由ITRF2000轉換至ITRF94為主要的誤差協變方傳播來源，且實施框架轉換後已產生大地基準站之間相對精度降低的情形。臺灣大地基準站因地殼速度場造成TWD97(1997.0)與TWD97(2010.0)的位移量約為50 cm，而TWD97[2010]成果因執行框架轉換造成的坐標差僅約3.7 cm，相較於速度場位移量甚小，也較框架轉換後坐標中誤差(±7.0 cm)為小。考量未來ITRF實踐與ITRF94的聯結性及框架轉換精度逐漸降低、參考瞬時之遠離等因素，未來臺灣大地基準進行更新維護時，應無繼續維持法定參考框架之必要，而可選擇精度較高之現行ITRF實踐，但新舊基準之間仍能透過框架轉換參數有效聯結。 回顧臺灣歷次大地基準維護作業，均於實際觀測、重新解算之後，以另一組成果，完全取代原先的大地基準。此一作業模式不但耗費大量時間、人力與財力，以原大地基準成果進行測繪之圖資管理維護亦日趨困難。為克服該兩項問題，將大地基準站坐標以框架轉換方式進行未來大地基準維護應為一可行方式。轉換路徑可分三大類：(1)先在法定參考框架上進行時間外插，再進行框架轉換至現行ITRF實踐；(2)直接以靜態基準與現行ITRF實踐（動態基準）之間的框架轉換參數進行轉換；(3)先將法定參考框架坐標成果以聯合模式(ITRF combination model)進行框架轉換至現行ITRF實踐，再以聯合模式求得之現行ITRF實踐的點位速度場進行時間外插。由分析結果發現，如以第一類路徑做為比較標準，後兩類路徑之轉換成果於坐標較差上產生每年約2~4 cm的差異，主要來自速度場之不夠精確；在轉換成果不確定度部分，各種路徑轉換後坐標中誤差均於20年內累積達超過10 cm之等級。如能直接採用與現行ITRF實踐相同之坐標與速度場，僅需進行時間外插，在距離參考瞬時30年後，其坐標中誤差仍維持僅約5 mm，將可大幅提升大地基準之維護精度，並維持基準維護模式與資料之穩定性。為達成此一目標，應逐步規劃增加全臺納入IGS固定站之數量。 在控制測量與數值法地籍測量的影響方面，不論是在各等級基本控制點或加密控制點檢測，或是在地籍圖重測、土地整體開發地籍測量、圖根點補建等地籍測量工作上，皆因時變產生之坐標變動事實造成實務執行與資料管理上之困難。由於控制點的時變事實，加上即時衛星定位之動態測量技術的成熟發展與廣泛應用，配合時變基準的採用，已是未來地籍測量的趨勢。其中，宗地面積之時變情形攸關土地登記與產權保障，為對國家社會影響最為重大之議題。本論文就地籍圖宗地面積之時變情形進行分析發現，小範圍內之地籍測量因時變因素所造成的宗地計算面積變動量非常微小。如以實際界址點坐標進行宗地計算面積時變分析，在30年後該時變量仍在0.1平方公尺以內之宗地筆數約占90%，最大差異量不超過3平方公尺，該變動量甚至遠小於因界址放樣所造成的現地面積差異量。未來在確立大地基準之時變維護模式，有助於資料穩定性之後，將時變基準運用於數值法地籍測量工作應屬可行。

In a time-variant datum, the coordinates of datum stations change with time. Such a continuous coordinate change is inherent in Earth science and its related application fields. However, the time-variant characteristic is disadvantageous for data stability and business execution in basic and cadastral surveying. According to data update frequencies, time-variant datums can be classified into two categories: dynamic and semi-dynamic datums. In a dynamic datum, point coordinates are updated continuously, whereas in a semi-dynamic datum, the coordinates are updated when the accumulating changes reach a threshold. In addition to its temporal aspect, a time-variant datum demonstrates different spatial variations. Plate motions are not globally uniform; therefore, an earthquake- or landslide-induced rapid local deformation cannot be described by a uniform velocity field. Therefore, a velocity field is typically applied to model continuous deformations, and a correction, such as an offset, is introduced to model the displacement engendered by a specific event. Another effective method is to apply a predictable model. In this dissertation, the technique and impact of a time-variant datum on basic and cadastral surveying are investigated. The scope of basic surveying is geodetic surveying including the determination and maintenance of a datum, basic control surveying, and resurvey analysis. Cadastral surveying is examined for the following reasons. First, digital cadastral surveying requires the highest accuracies among all applied surveying tasks that involve pure surveying and mapping. Second, the results of cadastral surveying are used for land registration, public policy implementation, and real estate exchange. Therefore, cadastral surveying is critical for legal rights, market order, and country stability. Changes in the coordinates of boundary points and a parcel area are analyzed to evaluate the impact of a time-variant datum on cadastral surveying. According to the current policy of the Taiwanese government, the legal reference frame, ITRF94, should be applied when maintaining a geodetic datum. Therefore, the resurvey coordinates of TWD97[2010] were transformed back to the original frame but expressed in a recent epoch; this caused covariance propagations. In this dissertation, uncertainties of transformation parameters are determined on the basis of the least squares and compound transformation methods. Both methods yielded similar results, indicating that the transformation from ITRF2000 to ITRF94 was the major error source. Moreover, the relative accuracies seemed to decrease after the frame transformations. The crustal velocities indicated a shift of approximately 50 cm between TWD97(1997.0) and TWD97(2010.0), whereas the average difference between ITRF2005(2010.0) and ITRF94(2010.0) was 3.7 cm, which is considerably lower than the influence of the crustal velocity field and also lower than the standard errors engendered by the frame transformation (±7.0 cm). Because the accuracies of the transformation parameters between later ITRF definitions and ITRF94 may deteriorate when a given epoch is gradually distanced from the initial epoch of ITRF94, it seems unnecessary to continue applying the legal ITRF definition (i.e., ITRF94) when TWD97 datums are maintained in the future. The current ITRF definition demonstrating higher accuracies is recommended for application. Nevertheless, the connection between the updated and the original datums can be executed by the transformation parameters. The historical maintenance of the Taiwan geodetic datum was executed by re-observating and re-solving to replace the original datum with a new one. This process is time consuming and requires considerable human and financial resources. Managing and maintaining mapping results based on the original datum are becoming increasingly difficult. To overcome these problems, maintaining the geodetic datum through frame transformation is a feasible option. The paths of transformations can be classified into three categories: (1) propagating to the indicated epoch within the legal frame (temporal extrapolation) and then transferring to the current ITRF definition at the same epoch (transformation); (2) directly transferring to the current ITRF definition at the indicated epoch by using the transformation parameters between the static datum and the dynamic frame; and (3) transferring to the current ITRF definition at the reference epoch of the geodetic datum with the ITRF combination model and then propagating to the indicated epoch. In this dissertation, the first category is considered the standard path and the results of the other paths are compared. The inaccurate velocity fields in Taiwan engendered a 2 - 4 cm yearly discrepancy with the standard path. In addition, the uncertainties of the coordinates in all paths accumulated to the decimeter level within 20 years. However, when the coordinates and velocities in the current ITRF definition were applied in addition to executing only temporal extrapolation, the uncertainties remained at approximately 5 mm after 30 years. This significantly increased the accuracy of datum maintenance and improved the stability of the maintenance model and geodetic data. Hence, adding permanent stations in Taiwan to the IGS system is recommended. Variant coordinates also cause difficulties in practical execution and database management for many basic surveying and digital cadastral surveying tasks such as the detection surveying of each level of basic control points and encrypted control points, cadastral resurveying, cadastral surveying on integrated land development, and supplementary surveying. Because of the time variance of control points and the advantages and extensive applications of real-time positioning techniques, applying a time-variant datum for cadastral surveying is a likely trend in the future. The variation in a parcel area has crucial social implications, and this is attributable to its direct effect on land registration and the protection of property rights. The parcel area analysis results revealed that the local variation in land area from the long-term deformation trend was quite low. When the actual coordinates were used to compute the areas of the parcels, the area variations of 90% of the parcels were lower than 0.1 m2 after 30 years, and the maximum variation was lower than 3 m2. The degree of variation was even lower than that induced by surveying errors. When a geodetic datum maintenance model that facilitates the stability of geographic data is confirmed, the future application of the time-variant datum in cadastral surveying is feasible.